(%i1) batch("diffeq.max") read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load("stringproc") (%o2) /usr/share/maxima/5.31.3/share/stringproc/stringproc.mac (%i3) alias(convfloat,float) (%o3) [convfloat] (%i4) alias(int_trunc,truncate) (%o4) [truncate] (%i5) alias(elapsed_time_seconds,elapsed_real_time) (%o5) [elapsed_time_seconds] (%i6) alias(ln,log) (%o6) [log] (%i7) alias(arcsin,asin) (%o7) [asin] (%i8) alias(arccos,acos) (%o8) [acos] (%i9) alias(arctan,atan) (%o9) [atan] (%i10) alias(float_abs,abs) (%o10) [mabs] (%i11) keepfloat:true (%o11) true (%i12) mode_declare(display_poles(),fixnum) (%o12) [display_poles()] (%i13) mode_declare(est_size_answer(),convfloat) (%o13) [est_size_answer()] (%i14) mode_declare(test_suggested_h(),convfloat) (%o14) [test_suggested_h()] (%i15) mode_declare(reached_interval(),boolean) (%o15) [reached_interval()] (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%o16) [display_alot([iter], fixnum)] (%i17) mode_declare(adjust_for_pole([h_param],convfloat),convfloat) (%o17) [adjust_for_pole([h_param], convfloat)] (%i18) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%o18) [prog_report([x_start], convfloat, [x_end], convfloat)] (%i19) mode_declare(check_for_pole(),fixnum) (%o19) [check_for_pole()] (%i20) mode_declare(atomall(),fixnum) (%o20) [atomall()] (%i21) mode_declare(log10([x],convfloat),convfloat) (%o21) [log10([x], convfloat)] (%i22) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%o22) [logitem_timestr([fd], fixnum, [secs_in], number)] (%i23) mode_declare(omniout_timestr(secs_in,number),fixnum) (%o23) [omniout_timestr(secs_in, number)] (%i24) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum) (%o24) [zero_ats_ar(ar, array([MAX_TERMS], convfloat))] (%i25) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_ats], fixnum),convfloat) (%o25) [ats([mmm_ats], fixnum, [arr_a], completearray([MAX_TERMS], convfloat), [arr_b], completearray([MAX_TERMS], convfloat), [jjj_ats], fixnum)] (%i26) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_att], fixnum),convfloat) (%o26) [att([mmm_att], fixnum, [arr_a], completearray([MAX_TERMS], convfloat), [arr_b], completearray([MAX_TERMS], convfloat), [jjj_att], fixnum)] (%i27) mode_declare(logitem_ditto([file],fixnum),fixnum) (%o27) [logitem_ditto([file], fixnum)] (%i28) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%o28) [logitem_integer([file], fixnum, [n], fixnum)] (%i29) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%o29) [logitem_good_digits([file], fixnum, [relerror], convfloat)] (%i30) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%o30) [logitem_number([file], fixnum, [x], number)] (%i31) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%o31) [logitem_pole([file], fixnum, [pole], fixnum)] (%i32) mode_declare(logstart([file],fixnum),fixnum) (%o32) [logstart([file], fixnum)] (%i33) mode_declare(logend([file],fixnum),fixnum) (%o33) [logend([file], fixnum)] (%i34) mode_declare(chk_data(),fixnum) (%o34) [chk_data()] (%i35) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%o35) [comp_expect_sec([t_end2], convfloat, [t_start2], convfloat, [t2], convfloat, [clock_sec2], convfloat)] (%i36) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%o36) [comp_percent([t_end2], convfloat, [start2], convfloat, [t2], convfloat)] (%i37) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%o37) [comp_rad_from_ratio([term1], convfloat, [term2], convfloat, [last_no], fixnum)] (%i38) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%o38) [comp_ord_from_ratio([term1], convfloat, [term2], convfloat, [last_no], fixnum)] (%i39) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%o39) [comp_rad_from_three_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [last_no], fixnum)] (%i40) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%o40) [comp_ord_from_three_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [last_no], fixnum)] (%i41) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%o41) [comp_rad_from_six_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [term4], convfloat, [term5], convfloat, [term6], convfloat, [last_no], fixnum)] (%i42) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%o42) [comp_ord_from_six_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [term4], convfloat, [term5], convfloat, [term6], convfloat, [last_no], fixnum)] (%i43) mode_declare(factorial_2([nnn],fixnum),fixnum) (%o43) [factorial_2([nnn], fixnum)] (%i44) mode_declare(factorial_1([nnn],fixnum),fixnum) (%o44) [factorial_1([nnn], fixnum)] (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum) (%o45) [factorial_3([mmm], fixnum, [nnn], fixnum)] (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%o46) [convfloat([mmm], fixnum)] (%i47) mode_declare(elaped_time_seconds(),convfloat) (%o47) [elaped_time_seconds()] (%i48) mode_declare(Si([x],convfloat),convfloat) (%o48) [Si([x], convfloat)] (%i49) mode_declare(Ci([x],convfloat),convfloat) (%o49) [Ci([x], convfloat)] (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%o50) [estimated_needed_step_error([x_start], convfloat, [x_end], convfloat, [estimated_h], convfloat, [estimated_answer], convfloat)] (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%o51) [my_check_sign([x0], convfloat, [xf], convfloat)] (%i52) mode_declare(main_prog(),fixnum) (%o52) [main_prog()] (%i53) define_variable(MAX_TERMS,20,fixnum) (%o53) 20 (%i54) define_variable(glob_iolevel,5,fixnum) (%o54) 5 (%i55) define_variable(glob_yes_pole,4,fixnum) (%o55) 4 (%i56) define_variable(glob_no_pole,3,fixnum) (%o56) 3 (%i57) define_variable(glob_not_given,0,fixnum) (%o57) 0 (%i58) define_variable(glob_no_sing_tests,4,fixnum) (%o58) 4 (%i59) define_variable(glob_ratio_test,1,fixnum) (%o59) 1 (%i60) define_variable(glob_three_term_test,2,fixnum) (%o60) 2 (%i61) define_variable(glob_six_term_test,3,fixnum) (%o61) 3 (%i62) define_variable(glob_log_10,log(10.0),convfloat) (%o62) 2.302585092994046 (%i63) define_variable(ALWAYS,1,fixnum) (%o63) 1 (%i64) define_variable(INFO,2,fixnum) (%o64) 2 (%i65) define_variable(DEBUGL,3,fixnum) (%o65) 3 (%i66) define_variable(DEBUGMASSIVE,4,fixnum) (%o66) 4 (%i67) define_variable(MAX_UNCHANGED,10,fixnum) (%o67) 10 (%i68) define_variable(glob_check_sign,1.0,convfloat) (%o68) 1.0 (%i69) define_variable(glob_desired_digits_correct,8.0,convfloat) (%o69) 8.0 (%i70) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%o70) 0.0 (%i71) define_variable(glob_ratio_of_radius,0.1,convfloat) (%o71) 0.1 (%i72) define_variable(glob_percent_done,0.0,convfloat) (%o72) 0.0 (%i73) define_variable(glob_subiter_method,3,fixnum) (%o73) 3 (%i74) define_variable(glob_total_exp_sec,0.1,convfloat) (%o74) 0.1 (%i75) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%o75) 0.1 (%i76) define_variable(glob_estimated_size_answer,100.0,convfloat) (%o76) 100.0 (%i77) define_variable(glob_html_log,true,boolean) (%o77) true (%i78) define_variable(glob_good_digits,0,fixnum) (%o78) 0 (%i79) define_variable(glob_max_opt_iter,10,fixnum) (%o79) 10 (%i80) define_variable(glob_dump,false,boolean) (%o80) false (%i81) define_variable(glob_djd_debug,true,boolean) (%o81) true (%i82) define_variable(glob_display_flag,true,boolean) (%o82) true (%i83) define_variable(glob_djd_debug2,true,boolean) (%o83) true (%i84) define_variable(glob_sec_in_minute,60,fixnum) (%o84) 60 (%i85) define_variable(glob_min_in_hour,60.0,convfloat) (%o85) 60.0 (%i86) define_variable(glob_hours_in_day,24.0,convfloat) (%o86) 24.0 (%i87) define_variable(glob_days_in_year,365,fixnum) (%o87) 365 (%i88) define_variable(glob_sec_in_hour,3600,fixnum) (%o88) 3600 (%i89) define_variable(glob_sec_in_day,86400,fixnum) (%o89) 86400 (%i90) define_variable(glob_sec_in_year,31536000,fixnum) (%o90) 31536000 (%i91) define_variable(glob_almost_1,0.999,convfloat) (%o91) 0.999 (%i92) define_variable(glob_clock_sec,0.0,convfloat) (%o92) 0.0 (%i93) define_variable(glob_clock_start_sec,0.0,convfloat) (%o93) 0.0 (%i94) define_variable(glob_not_yet_finished,true,boolean) (%o94) true (%i95) define_variable(glob_initial_pass,true,boolean) (%o95) true (%i96) define_variable(glob_not_yet_start_msg,true,boolean) (%o96) true (%i97) define_variable(glob_reached_optimal_h,false,boolean) (%o97) false (%i98) define_variable(glob_optimal_done,false,boolean) (%o98) false (%i99) define_variable(glob_disp_incr,0.1,convfloat) (%o99) 0.1 (%i100) define_variable(glob_h,0.1,convfloat) (%o100) 0.1 (%i101) define_variable(glob_diff_rc_fm,0.1,convfloat) (%o101) 0.1 (%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%o102) 0.1 (%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%o103) 0.1 (%i104) define_variable(glob_diff_ord_fm,0.1,convfloat) (%o104) 0.1 (%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%o105) 0.1 (%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%o106) 0.1 (%i107) define_variable(glob_six_term_ord_save,0.1,convfloat) (%o107) 0.1 (%i108) define_variable(glob_guess_error_rc,0.1,convfloat) (%o108) 0.1 (%i109) define_variable(glob_guess_error_ord,0.1,convfloat) (%o109) 0.1 (%i110) define_variable(glob_max_h,0.1,convfloat) (%o110) 0.1 (%i111) define_variable(glob_min_h,1.0E-6,convfloat) (%o111) 1.0E-6 (%i112) define_variable(glob_type_given_pole,0,fixnum) (%o112) 0 (%i113) define_variable(glob_large_float,1.0E+100,convfloat) (%o113) 1.0E+100 (%i114) define_variable(glob_larger_float,1.1E+100,convfloat) (%o114) 1.1E+100 (%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat) (%o115) 9.9E+100 (%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat) (%o116) 9.9E+100 (%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%o117) 9.9E+100 (%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%o118) 9.9E+100 (%i119) define_variable(glob_last_good_h,0.1,convfloat) (%o119) 0.1 (%i120) define_variable(glob_look_poles,false,boolean) (%o120) false (%i121) define_variable(glob_neg_h,false,boolean) (%o121) false (%i122) define_variable(glob_display_interval,0.0,convfloat) (%o122) 0.0 (%i123) define_variable(glob_next_display,0.0,convfloat) (%o123) 0.0 (%i124) define_variable(glob_dump_analytic,false,boolean) (%o124) false (%i125) define_variable(glob_abserr,1.0E-11,convfloat) (%o125) 1.0E-11 (%i126) define_variable(glob_relerr,1.0E-11,convfloat) (%o126) 1.0E-11 (%i127) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%o127) 1.0E+9 (%i128) define_variable(glob_max_hours,0.0,convfloat) (%o128) 0.0 (%i129) define_variable(glob_max_iter,1000,fixnum) (%o129) 1000 (%i130) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%o130) 1.0E-11 (%i131) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%o131) 1.0E-11 (%i132) define_variable(glob_no_eqs,0,fixnum) (%o132) 0 (%i133) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%o133) 0.0 (%i134) define_variable(glob_optimal_start,0.0,convfloat) (%o134) 0.0 (%i135) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%o135) 1.0001 (%i136) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%o136) 0.9999 (%i137) define_variable(glob_small_float,0.0,convfloat) (%o137) 0.0 (%i138) define_variable(glob_smallish_float,0.0,convfloat) (%o138) 0.0 (%i139) define_variable(glob_unchanged_h_cnt,0,fixnum) (%o139) 0 (%i140) define_variable(glob_warned,false,boolean) (%o140) false (%i141) define_variable(glob_warned2,false,boolean) (%o141) false (%i142) define_variable(glob_max_sec,10000.0,convfloat) (%o142) 10000.0 (%i143) define_variable(glob_orig_start_sec,0.0,convfloat) (%o143) 0.0 (%i144) define_variable(glob_start,0,fixnum) (%o144) 0 (%i145) define_variable(glob_curr_iter_when_opt,0,fixnum) (%o145) 0 (%i146) define_variable(glob_current_iter,0,fixnum) (%o146) 0 (%i147) define_variable(glob_iter,0,fixnum) (%o147) 0 (%i148) define_variable(glob_normmax,0.0,convfloat) (%o148) 0.0 (%i149) define_variable(glob_max_minutes,0.0,convfloat) (%o149) 0.0 (%i150) array(array_y_init,MAX_TERMS) (%o150) array_y_init (%i151) array(array_norms,MAX_TERMS) (%o151) array_norms (%i152) array(array_fact_1,MAX_TERMS) (%o152) array_fact_1 (%i153) array(array_1st_rel_error,2) (%o153) array_1st_rel_error (%i154) array(array_last_rel_error,2) (%o154) array_last_rel_error (%i155) array(array_type_pole,2) (%o155) array_type_pole (%i156) array(array_type_real_pole,2) (%o156) array_type_real_pole (%i157) array(array_type_complex_pole,2) (%o157) array_type_complex_pole (%i158) array(array_y,MAX_TERMS) (%o158) array_y (%i159) array(array_x,MAX_TERMS) (%o159) array_x (%i160) array(array_tmp0,MAX_TERMS) (%o160) array_tmp0 (%i161) array(array_tmp1,MAX_TERMS) (%o161) array_tmp1 (%i162) array(array_tmp2,MAX_TERMS) (%o162) array_tmp2 (%i163) array(array_tmp3,MAX_TERMS) (%o163) array_tmp3 (%i164) array(array_tmp4,MAX_TERMS) (%o164) array_tmp4 (%i165) array(array_tmp5,MAX_TERMS) (%o165) array_tmp5 (%i166) array(array_tmp6,MAX_TERMS) (%o166) array_tmp6 (%i167) array(array_tmp7,MAX_TERMS) (%o167) array_tmp7 (%i168) array(array_tmp8,MAX_TERMS) (%o168) array_tmp8 (%i169) array(array_tmp9,MAX_TERMS) (%o169) array_tmp9 (%i170) array(array_m1,MAX_TERMS) (%o170) array_m1 (%i171) array(array_y_higher,2,MAX_TERMS) (%o171) array_y_higher (%i172) array(array_y_higher_work,2,MAX_TERMS) (%o172) array_y_higher_work (%i173) array(array_y_higher_work2,2,MAX_TERMS) (%o173) array_y_higher_work2 (%i174) array(array_y_set_initial,2,MAX_TERMS) (%o174) array_y_set_initial (%i175) array(array_given_rad_poles,2,3) (%o175) array_given_rad_poles (%i176) array(array_given_ord_poles,2,3) (%o176) array_given_ord_poles (%i177) array(array_rad_test_poles,2,3) (%o177) array_rad_test_poles (%i178) array(array_ord_test_poles,2,3) (%o178) array_ord_test_poles (%i179) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%o179) array_fact_2 (%i180) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%o180) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i181) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%o181) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i182) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%o182) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i183) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%o183) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i184) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%o184) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i185) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%o185) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i186) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%o186) logitem_time(fd, secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs : secs_in, printf(fd, "~%"), secs if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "~d Seconds~%", sec_int)) else printf(fd, " 0.0 Seconds~%"), printf(fd, "~%")), 0) (%i187) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%o187) omniout_timestr(secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs secs : secs_in, if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, "= 0.0 Seconds~%")), 0) (%i188) zero_ats_ar(arr_a):=( block(modedcclare([iii],fixnum),iii:1, while iii <= MAX_TERMS do (arr_a[iii]:0.0,iii:1+iii)),0) (%o188) zero_ats_ar(arr_a) := (block(modedcclare([iii], fixnum), iii : 1, while iii <= MAX_TERMS do (arr_a : 0.0, iii : 1 + iii)), 0) iii (%i189) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:0.0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= MAX_TERMS and iii_ats <= MAX_TERMS then ret_ats :arr_a[iii_ats]*arr_b[lll_ats]+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%o189) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block(mode_declare([[iii_ats, lll_ats, ma_ats], fixnum, [ret_ats], convfloat]), ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, if (lll_ats <= MAX_TERMS) and (iii_ats <= MAX_TERMS) then ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i190) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:0.0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= MAX_TERMS do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS then ret_att :arr_aa[iii_att]*arr_bb[lll_att]*al_att +ret_att,iii_att:1+iii_att), ret_att:ret_att/mmm_att),ret_att) (%o190) att(mmm_att, arr_aa, arr_bb, jjj_att) := block(mode_declare([[al_att, iii_att, lll_att, ma_att], convfloat, [ret_att], fixnum]), ret_att : 0.0, if jjj_att < mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while (iii_att < mmm_att) and (iii_att <= MAX_TERMS) do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if (lll_att <= MAX_TERMS) and (iii_att <= MAX_TERMS) then ret_att : arr_aa arr_bb al_att + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : -------), ret_att) mmm_att (%i191) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%o191) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, ""), 0) (%i192) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%o192) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, ""), 0) (%i193) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%o193) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, ""), 0) (%i194) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), if rel_error # -1.0 then (if rel_error > +1.0E-34 then ( good_digits :3-floor(log10(rel_error)), printf(file,"~d",good_digits)) else (good_digits:16, printf(file,"~d", good_digits))) else printf(file,"Unknown"), printf(file,"")),0) (%o194) logitem_good_digits(file, rel_error) := (block(mode_declare([[good_digits], fixnum]), printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 3 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")), 0) (%i195) log_revs(file,revs):=printf(file,revs) (%o195) log_revs(file, revs) := printf(file, revs) (%i196) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%o196) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, ""), 0) (%i197) logitem_pole(file,pole):=(printf(file,""), if pole = 0 then printf(file,"NA") elseif pole = 1 then printf(file,"Real") elseif pole = 2 then printf(file,"Complex") elseif pole = 4 then printf(file,"Yes") else printf(file,"No"), printf(file,""),0) (%o197) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, ""), 0) (%i198) logstart(file):=(printf(file,""),0) (%o198) logstart(file) := (printf(file, ""), 0) (%i199) logend(file):=(printf(file,"~%"),0) (%o199) logend(file) := (printf(file, "~%"), 0) (%i200) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(ALWAYS,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%o200) chk_data() := (block(mode_declare([[errflag], boolean]), errflag : false, if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()), 0) (%i201) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:clock_sec2, sub1:t_end2-t_start2,sub2:t2-t_start2, if sub1 = 0.0 then sec_left:0.0 else (if sub2 > 0.0 then (rrr:sub1/sub2, sec_left:rrr*ms2-ms2) else sec_left:0.0),sec_left) (%o201) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block(mode_declare([[ms2, rrr, sec_left, sub1, sub2], convfloat]), ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i202) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:100.0*sub2/sub1 else rrr:0.0,rrr) (%o202) comp_percent(t_end2, t_start2, t2) := block(mode_declare([[rrr, sub1, sub2], convfloat]), sub1 : t_end2 - t_start2, 100.0 sub2 sub2 : t2 - t_start2, if sub2 > glob_small_float then rrr : ---------- sub1 else rrr : 0.0, rrr) (%i203) comp_rad_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%o203) comp_rad_from_ratio(term1, term2, last_no) := !term1 glob_h! (if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret) ! term2 ! (%i204) comp_ord_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret :abs(term2)*convfloat(last_no) *log(abs(term1*glob_h/term2)) /log(convfloat(last_no)) +1.0 else ret:glob_larger_float,ret) (%o204) comp_ord_from_ratio(term1, term2, last_no) := !term1 glob_h! mabs(term2) convfloat(last_no) log(!------------!) ! term2 ! (if term2 > 0.0 then ret : -------------------------------------------------- log(convfloat(last_no)) + 1.0 else ret : glob_larger_float, ret) (%i205) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no)), if temp > 0.0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%o205) comp_rad_from_three_terms(term1, term2, term3, last_no) := (temp : mabs(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no)), if temp > 0.0 !term2 glob_h term1! then ret : !------------------! else ret : glob_larger_float, ret) ! temp ! (%i206) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*convfloat(last_no*last_no) +term2*term2*convfloat(last_no*last_no) +4.0*term2*term2 -4.0*term2*term2*convfloat(last_no) -3.0*term1*term3 +4.0*term1*term3*convfloat(last_no)) /(term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no))),ret) (%o206) comp_ord_from_three_terms(term1, term2, term3, last_no) := (ret : mabs((- term1 term3 convfloat(last_no last_no) + term2 term2 convfloat(last_no last_no) + 4.0 term2 term2 - 4.0 term2 term2 convfloat(last_no) - 3.0 term1 term3 + 4.0 term1 term3 convfloat(last_no))/(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no))), ret) (%i207) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # 0.0 and term4 # 0.0 and term3 # 0.0 and term2 # 0.0 and term1 # 0.0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :convfloat(last_no-3)*rm2 -2.0*convfloat(last_no-2)*rm1 +convfloat(last_no-1)*rm0, nr2 :convfloat(last_no-4)*rm3 -2.0*convfloat(last_no-3)*rm2 +convfloat(last_no-2)*rm1, dr1:(-1.0)/rm3+2.0/rm2+(-1.0)/rm1, dr2:(-1.0)/rm4+2.0/rm3+(-1.0)/rm2, ds1:5.0/rm3-8.0/rm2+3.0/rm1, ds2:5.0/rm4-8.0/rm3+3.0/rm2, if abs(nr1*dr2-nr2*dr1) = 0.0 or abs(dr1) = 0.0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) # 0.0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(2.0*dr1) -convfloat(last_no)/2.0, if abs(rcs) # 0.0 then (if rcs > 0.0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%o207) comp_rad_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := (if (term5 # 0.0) and (term4 # 0.0) and (term3 # 0.0) term6 term5 and (term2 # 0.0) and (term1 # 0.0) then (rm0 : -----, rm1 : -----, term5 term4 term4 term3 term2 rm2 : -----, rm3 : -----, rm4 : -----, term3 term2 term1 nr1 : convfloat(last_no - 3) rm2 - 2.0 convfloat(last_no - 2) rm1 + convfloat(last_no - 1) rm0, nr2 : convfloat(last_no - 4) rm3 - 2.0 convfloat(last_no - 3) rm2 + convfloat(last_no - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (mabs(nr1 dr2 - nr2 dr1) = 0.0) or (mabs(dr1) = 0.0) rm4 rm3 rm2 then (rad_c : glob_larger_float, ord_no : glob_larger_float) else (if mabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(last_no) ord_no : ------------- - ------------------, 2.0 dr1 2.0 if mabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) mabs(glob_h) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float))) else (rad_c : glob_larger_float, ord_no : glob_larger_float), glob_six_term_ord_save : ord_no, rad_c) (%i208) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%o208) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := glob_six_term_ord_save (%i209) factorial_2(nnn):=nnn! (%o209) factorial_2(nnn) := nnn! (%i210) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%o210) factorial_1(nnn) := block(mode_declare([[ret], convfloat]), if nnn <= MAX_TERMS then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i211) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS and mmm <= MAX_TERMS then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%o211) factorial_3(mmm, nnn) := block(mode_declare([[ret], convfloat]), if (nnn <= MAX_TERMS) and (mmm <= MAX_TERMS) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i212) log10(x):=log(x)/glob_log_10 log(x) (%o212) log10(x) := ----------- glob_log_10 (%i213) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%o213) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i214) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(10.0,-glob_desired_digits_correct) *abs(estimated_answer), omniout_float(ALWAYS,"estimated_h",32, estimated_h,32,""), omniout_float(ALWAYS,"estimated_answer", 32,estimated_answer,32,""), omniout_float(ALWAYS, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(ALWAYS,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(ALWAYS,"estimated_steps",32, estimated_steps,32,""), step_error :abs( desired_abs_gbl_error/estimated_steps), omniout_float(ALWAYS,"step_error",32, step_error,32,""), step_error) (%o214) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) mabs(estimated_answer), omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""), omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, ""), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h !desired_abs_gbl_error! 32, estimated_steps, 32, ""), step_error : !---------------------!, ! estimated_steps ! omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i215) exact_soln_y(x):=block(1.0/(1.0+x*x)) 1.0 (%o215) exact_soln_y(x) := block(---------) 1.0 + x x (%i216) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 4 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," ")) elseif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > 0.0 and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > 0.0 and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%o216) display_poles() := (block(mode_declare([[rad_given], convfloat]), if glob_type_given_pole = 4 then (rad_given : sqrt(array_given_rad_poles array_given_rad_poles 1, 2 1, 2 + (array_x - array_given_rad_poles ) 1 1, 1 (array_x - array_given_rad_poles )), 1 1, 1 if rad_given < glob_least_given_sing then glob_least_given_sing : rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles < glob_large_float then (omniout_float(ALWAYS, "Ra\ 1, 1 dius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 1 1, 1 glob_least_ratio_sing then glob_least_ratio_sing : array_rad_test_poles , 1, 1 omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 1 "NO POLE (ratio test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < glob_large_float) 1, 2 1, 2 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 2 1, 2 glob_least_3_sing then glob_least_3_sing : array_rad_test_poles , 1, 2 omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO REAL POLE (three term test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < 1, 3 1, 3 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 3 1, 3 glob_least_6_sing then glob_least_6_sing : array_rad_test_poles , 1, 3 omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 3 "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i217) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%o217) my_check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i218) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[1]), omniout_float(ALWAYS,"min_size",32,min_size, 32,"")), if min_size < 1.0 then (min_size:1.0, omniout_float(ALWAYS,"min_size",32,min_size, 32,"")),min_size) (%o218) est_size_answer() := block([min_size], min_size : glob_estimated_size_answer, if !array_y ! < min_size then (min_size : !array_y !, ! 1! ! 1! omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i219) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:0.0,no_terms:MAX_TERMS, hn_div_ho:0.5,hn_div_ho_2:0.25,hn_div_ho_3:0.125, omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(ALWAYS,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%o219) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0, no_terms : MAX_TERMS, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), est_tmp : mabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%i220) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display then ret:true else ret:false,return(ret)) (%o220) reached_interval() := block(mode_declare([[ret], boolean]), if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i221) display_alot(iter):=( block(mode_declare( [[abserr],convfloat,[analytic_val_y],convfloat, [ind_var],convfloat,[numeric_val],convfloat, [relerr],convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(ALWAYS, "x[1] ", 33,ind_var,20, " "), analytic_val_y :exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val-analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33,numeric_val, 20," "), if abs(analytic_val_y) # 0.0 then ( relerr :abserr*100.0 /abs(analytic_val_y), if relerr > 1.0E-34 then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits :16) else (relerr:-1.0, glob_good_digits:-1), if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20, " ")))),0) (%o221) display_alot(iter) := (block(mode_declare([[abserr], convfloat, [analytic_val_y], convfloat, [ind_var], convfloat, [numeric_val], convfloat, [relerr], convfloat, [term_no], fixnum]), if reached_interval() then (if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : mabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if mabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : --------------------, if relerr > 1.0E-34 mabs(analytic_val_y) then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))), 0) (%i222) adjust_for_pole(h_param):=( block(mode_declare( [[hnew],convfloat,[sz2],convfloat,[tmp], convfloat]),hnew:h_param, glob_normmax:glob_small_float, if abs(array_y_higher[1,1]) > glob_small_float then (tmp:abs(array_y_higher[1,1]), if tmp < glob_normmax then glob_normmax:tmp), if glob_look_poles and glob_min_pole_est > glob_small_float and glob_min_pole_est < glob_large_float then (sz2:glob_min_pole_est/10.0, if sz2 < hnew then ( omniout_float(INFO, "glob_h adjusted to ", 20,h_param,12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h:true, glob_curr_iter_when_opt :glob_current_iter, glob_optimal_clock_start_sec :elapsed_time_seconds(), glob_optimal_start:array_x[1]), hnew:sz2),hnew) (%o222) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat, [sz2], convfloat, [tmp], convfloat]), hnew : h_param, glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (glob_min_pole_est > glob_small_float) and (glob_min_pole_est < glob_large_float) glob_min_pole_est then (sz2 : -----------------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), hnew) 1 (%i223) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :total_clock_sec+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ",33, percent_done,4,"%")),0) (%o223) prog_report(x_start, x_end) := (block(mode_declare([[clock_sec], convfloat, [opt_clock_sec], convfloat, [clock_sec1], convfloat, [expect_sec], convfloat, [left_sec], convfloat, [percent_done], convfloat, [total_clock_sec], convfloat]), clock_sec1 : elapsed_time_seconds(), total_clock_sec : clock_sec1 - glob_orig_start_sec, glob_clock_sec : clock_sec1 - glob_clock_start_sec, left_sec : - clock_sec1 + glob_orig_start_sec + glob_max_sec, expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 clock_sec1 - glob_orig_start_sec), opt_clock_sec : clock_sec1 - glob_optimal_clock_start_sec, glob_optimal_expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 opt_clock_sec), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(x_end, x_start, glob_h + array_x ), 1 glob_percent_done : percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")), 0) (%i224) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, term:1,ratio:1.0, while term <= MAX_TERMS do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%o224) check_for_pole() := (block(mode_declare([cnt], fixnum, [dr1, dr2, ds1, ds2, hdrc], convfloat, [m, n], fixnum, [nr1, nr2], convfloat, [ord_no], fixnum, [term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4], convfloat, [found_sing], fixnum, [h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad], convfloat, [last_no], fixnum), glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 1 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 1 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 3) and (found_sing = 1) do (tmp_rad : comp_rad_from_ratio(array_y_higher , array_y_higher , 1, last_no - 1 1, last_no tmp_rad last_no), tmp_ratio : ------------, if (cnt > 0) prev_tmp_rad and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 1 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 1 tmp_ord : comp_ord_from_ratio(array_y_higher , 1, last_no - 1 array_y_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 1 array_ord_test_poles : tmp_ord)), glob_min_pole_est : glob_larger_float, 1, 1 tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 2 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 2 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 4) and (found_sing = 1) do (tmp_rad : comp_rad_from_three_terms(array_y_higher , 1, last_no - 2 array_y_higher , array_y_higher , last_no), 1, last_no - 1 1, last_no tmp_rad tmp_ratio : ------------, if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) prev_tmp_rad and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 2 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 2 tmp_ord : comp_ord_from_three_terms(array_y_higher , 1, last_no - 2 array_y_higher , array_y_higher , last_no), 1, last_no - 1 1, last_no array_rad_test_poles : rad_c, if rad_c < glob_min_pole_est 1, 2 then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), 1, 2 glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 3 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 3 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad : comp_rad_from_six_terms(array_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 tmp_rad array_y_higher , last_no), tmp_ratio : ------------, 1, last_no prev_tmp_rad if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 3 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 3 tmp_ord : comp_ord_from_six_terms(array_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 array_y_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 3 if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), if mabs(glob_min_pole_est) 1, 3 glob_ratio_of_radius < mabs(glob_h) then (h_new : glob_check_sign glob_min_pole_est glob_ratio_of_radius, term : 1, ratio : 1.0, while term <= MAX_TERMS do (array_y : array_y ratio, term term array_y_higher : array_y_higher ratio, 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ------------, term : 1 + term), term term mabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()), 0) (%i225) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_m1[1]*array_const_2D0[1], array_tmp2[1]:array_x[1]*array_tmp1[1], array_tmp3[1]:array_x[1]*array_x[1], array_tmp4[1]:array_const_1D0[1]+array_tmp3[1], array_tmp5[1]:array_tmp2[1]/array_tmp4[1], array_tmp6[1]:array_x[1]*array_x[1], array_tmp7[1]:array_const_1D0[1]+array_tmp6[1], array_tmp8[1]:array_tmp5[1]/array_tmp7[1], array_tmp9[1]:array_tmp8[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp9[1]*expt(glob_h,1) *factorial_3(0,1), if 2 <= MAX_TERMS then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:temporary*1.0/glob_h, array_y_higher[2,1]:temporary,0)),kkk:2, array_tmp1[2]:array_m1[2]*array_const_2D0[1], array_tmp2[2]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp3[2]:array_x[2]*array_x[1] +array_x[1]*array_x[2], array_tmp4[2]:array_tmp3[2], array_tmp5[2]:(array_tmp2[2] -ats(2,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp6[2]:array_x[2]*array_x[1] +array_x[1]*array_x[2], array_tmp7[2]:array_tmp6[2], array_tmp8[2]:(array_tmp5[2] -ats(2,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[2]:array_tmp8[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp9[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:temporary*2.0/glob_h, array_y_higher[2,2]:temporary,0)),kkk:3, array_tmp1[3]:array_m1[3]*array_const_2D0[1], array_tmp2[3]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp3[3]:array_x[2]*array_x[2], array_tmp4[3]:array_tmp3[3], array_tmp5[3]:(array_tmp2[3] -ats(3,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp6[3]:array_x[2]*array_x[2], array_tmp7[3]:array_tmp6[3], array_tmp8[3]:(array_tmp5[3] -ats(3,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[3]:array_tmp8[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp9[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:temporary*3.0/glob_h, array_y_higher[2,3]:temporary,0)),kkk:4, array_tmp1[4]:array_m1[4]*array_const_2D0[1], array_tmp2[4]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp4[4]:array_tmp3[4], array_tmp5[4]:(array_tmp2[4] -ats(4,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp7[4]:array_tmp6[4], array_tmp8[4]:(array_tmp5[4] -ats(4,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[4]:array_tmp8[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp9[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:temporary*4.0/glob_h, array_y_higher[2,4]:temporary,0)),kkk:5, array_tmp1[5]:array_m1[5]*array_const_2D0[1], array_tmp2[5]:array_x[1]*array_tmp1[kkk] +array_x[2]*array_tmp1[kkk-1], array_tmp4[5]:array_tmp3[5], array_tmp5[5]:(array_tmp2[5] -ats(5,array_tmp4,array_tmp5,2)) /array_tmp4[1], array_tmp7[5]:array_tmp6[5], array_tmp8[5]:(array_tmp5[5] -ats(5,array_tmp7,array_tmp8,2)) /array_tmp7[1], array_tmp9[5]:array_tmp8[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp9[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y_higher[2,5]:temporary,0)),kkk:6, while kkk <= MAX_TERMS do (array_tmp1[kkk]:array_m1[kkk]*array_const_2D0[1], array_tmp2[kkk] :array_tmp1[kkk]*array_x[1] +array_tmp1[kkk-1]*array_x[2], array_tmp4[kkk]:array_tmp3[kkk], array_tmp5[kkk] :(array_tmp2[kkk] -ats(kkk,array_tmp4,array_tmp5,2)) /array_tmp4[1],array_tmp7[kkk]:array_tmp6[kkk], array_tmp8[kkk] :(array_tmp5[kkk] -ats(kkk,array_tmp7,array_tmp8,2)) /array_tmp7[1],array_tmp9[kkk]:array_tmp8[kkk], order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp9[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_y[order_d+kkk]:temporary, array_y_higher[1,order_d+kkk]:temporary, term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= MAX_TERMS and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :temporary*adj2/glob_h else temporary:temporary, array_y_higher[adj3,term] :temporary),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%o225) atomall() := (block(mode_declare([[kkk, order_d], fixnum, [adj2, adj3, temporary, term, temp, temp2], convfloat]), array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : array_x array_tmp1 , 1 1 1 1 1 1 array_tmp3 : array_x array_x , array_tmp4 : array_const_1D0 + array_tmp3 , 1 1 1 1 1 1 array_tmp2 1 array_tmp5 : -----------, array_tmp6 : array_x array_x , 1 array_tmp4 1 1 1 1 array_tmp5 1 array_tmp7 : array_const_1D0 + array_tmp6 , array_tmp8 : -----------, 1 1 1 1 array_tmp7 1 array_tmp9 : array_tmp8 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= MAX_TERMS 1, 2 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(0, 1), 1 if 2 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_m1 array_const_2D0 , 2 2 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 2 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp4 : array_tmp3 , array_tmp5 : 2 2 2 array_tmp2 - ats(2, array_tmp4, array_tmp5, 2) 2 -----------------------------------------------, array_tmp4 1 array_tmp6 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp7 : array_tmp6 , array_tmp8 : 2 2 2 array_tmp5 - ats(2, array_tmp7, array_tmp8, 2) 2 -----------------------------------------------, array_tmp9 : array_tmp8 , array_tmp7 2 2 1 if not array_y_set_initial then (if 2 <= MAX_TERMS 1, 3 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2), 2 if 3 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 3 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 , 3 2 2 3 3 array_tmp2 - ats(3, array_tmp4, array_tmp5, 2) 3 array_tmp5 : -----------------------------------------------, 3 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 , 3 2 2 3 3 array_tmp5 - ats(3, array_tmp7, array_tmp8, 2) 3 array_tmp8 : -----------------------------------------------, 3 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= MAX_TERMS then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(2, 3), 3 if 4 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 4 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 4 4 4 array_tmp2 - ats(4, array_tmp4, array_tmp5, 2) 4 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 4 4 1 array_tmp5 - ats(4, array_tmp7, array_tmp8, 2) 4 array_tmp8 : -----------------------------------------------, 4 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= MAX_TERMS then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(3, 4), 4 if 5 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 5 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 5 5 5 array_tmp2 - ats(5, array_tmp4, array_tmp5, 2) 5 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 5 5 1 array_tmp5 - ats(5, array_tmp7, array_tmp8, 2) 5 array_tmp8 : -----------------------------------------------, 5 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= MAX_TERMS then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(4, 5), 5 if 6 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= MAX_TERMS do (array_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , kkk kkk 1 kkk - 1 2 array_tmp4 : array_tmp3 , array_tmp5 : kkk kkk kkk array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2) kkk ---------------------------------------------------, array_tmp4 1 array_tmp7 : array_tmp6 , array_tmp8 : kkk kkk kkk array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2) kkk ---------------------------------------------------, array_tmp7 1 array_tmp9 : array_tmp8 , order_d : 1, kkk kkk if order_d + kkk <= MAX_TERMS then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp9 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while (term >= 1) and (term <= MAX_TERMS) and (adj3 < 1 + order_d) do (if adj3 <= 1 + order_d temporary adj2 then (if adj2 > 0 then temporary : -------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)), 0) (%i226) exact_soln_y(x):=block(1.0/(1.0+x*x)) 1.0 (%o226) exact_soln_y(x) := block(---------) 1.0 + x x (%i227) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,best_h,found_h], convfloat,[repeat_it],fixnum]),Digits:32, max_terms:20,glob_html_log:true,term:1, while term <= MAX_TERMS do (array_y_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_norms[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_fact_1[term]:0.0,term:1+term),term:1, while term <= 2 do (array_1st_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_tmp0[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp3[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp4[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp5[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp6[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp7[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp8[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp9[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term), ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher[ord,term]:0.0,term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher_work[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_higher_work2[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_set_initial[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_rad_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_ord_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= MAX_TERMS do (term:1, while term <= MAX_TERMS do (array_fact_2[ord,term]:0.0,term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_m1),zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),zero_ats_ar(array_tmp6), zero_ats_ar(array_tmp7),zero_ats_ar(array_tmp8), zero_ats_ar(array_tmp9),zero_ats_ar(array_const_1), array_const_1[1]:1,zero_ats_ar(array_const_0D0), array_const_0D0[1]:0.0,zero_ats_ar(array_const_2D0), array_const_2D0[1]:2.0,zero_ats_ar(array_const_1D0), array_const_1D0[1]:1.0,zero_ats_ar(array_m1), array_m1[1]:-1.0,iiif:0, while iiif <= MAX_TERMS do (jjjf:0, while jjjf <= MAX_TERMS do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false,ALWAYS:1,INFO:2,DEBUGL:3, DEBUGMASSIVE:4,MAX_TERMS:20,glob_iolevel:INFO, glob_orig_start_sec:elapsed_time_seconds(), glob_curr_iter_when_opt:0,glob_display_flag:true, glob_no_eqs:1,glob_iter:-1,opt_iter:-1,glob_max_iter:50000, glob_max_hours:0.0,glob_max_minutes:15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; "), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:32,"), omniout_str(ALWAYS,"max_terms:20,"),omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:-2.0,"), omniout_str(ALWAYS,"x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:50,"), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"glob_max_h:0.5,"), omniout_str(ALWAYS,"glob_type_given_pole:4,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_rad_poles[1,1]:0.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_rad_poles[1,2]:1.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_ord_poles[1,1]:1.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"array_given_ord_poles[1,2]:0.0,"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS,"glob_desired_digits_correct:10,"), omniout_str(ALWAYS,"glob_display_interval:0.01,"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:1000000000,"), omniout_str(ALWAYS,"glob_max_minutes:10.0,"), omniout_str(ALWAYS,"glob_subiter_method:3,"), omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS,"exact_soln_y (x) := (block("), omniout_str(ALWAYS," (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS,"));"),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:0.0,glob_smallish_float:0.0, glob_large_float:1.0E+100,glob_larger_float:1.1E+100, glob_almost_1:0.99,x_start:-2.0,x_end:1.0, array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_max_iter:50,glob_max_h:0.5, glob_type_given_pole:4,array_given_rad_poles[1,1]:0.0, array_given_rad_poles[1,2]:1.0, array_given_ord_poles[1,1]:1.0, array_given_ord_poles[1,2]:0.0, glob_desired_digits_correct:10,glob_display_interval:0.01, glob_look_poles:true,glob_max_iter:1000000000, glob_max_minutes:10.0,glob_subiter_method:3, glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, omniout_str(ALWAYS,"START of Optimize"), glob_check_sign:my_check_sign(x_start,x_end),found_h:false, glob_h:glob_min_h*glob_check_sign, if abs(glob_max_h) < abs(glob_h) then glob_h:abs(glob_max_h)*glob_check_sign, if abs(glob_display_interval) < abs(glob_h) then glob_h:abs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h:false, glob_display_interval:abs(glob_display_interval)) else (glob_neg_h:true, glob_display_interval :-abs(glob_display_interval)),chk_data(), best_h:glob_h,min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err:estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(ALWAYS,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:0.0, while opt_iter <= 100 and not found_h do (omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no]*expt(glob_h,term_no-1) /factorial_1(term_no-1),term_no:1+term_no), rows:order_diff,r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),r_order:1+r_order), atomall(),estimated_step_error:test_suggested_h(), omniout_float(ALWAYS,"estimated_step_error",32, estimated_step_error,32,""), if estimated_step_error > est_needed_step_err and opt_iter = 1 or glob_check_sign*glob_h >= glob_check_sign*glob_max_h then (found_h:true, glob_h:glob_check_sign*glob_max_h, best_h:glob_h) elseif estimated_step_error > est_needed_step_err and not found_h then (glob_h:glob_h/2.0,best_h:glob_h, found_h:true) else (glob_h:glob_h*2.0,best_h:glob_h), omniout_float(ALWAYS,"best_h",32,best_h,32,""), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(ALWAYS,"Beginning glob_h too large."), found_h:false), if opt_iter > 100 then (glob_h:glob_check_sign*glob_max_h,found_h:false), if glob_check_sign*glob_display_interval < glob_check_sign*glob_h then glob_h:glob_check_sign*glob_display_interval, if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(ALWAYS,"START of Soultion"), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(), glob_current_iter:0,glob_iter:0, omniout_str(DEBUGL," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(INFO," "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), glob_current_iter:1+glob_current_iter, atomall(),display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1), term_no:MAX_TERMS, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(ALWAYS,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; "), omniout_int(INFO, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-09T00:24:57-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_str(html_log_file,"16"), logitem_good_digits(html_log_file, array_last_rel_error[ 1]), logitem_integer(html_log_file, MAX_TERMS), if glob_least_given_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_given_sing), 0) else ( logitem_str(html_log_file, "NOT GIVEN"),0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o227) main_prog() := block(mode_declare([[d1, d2, d3, d4, est_err_2], convfloat, [niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii], fixnum, [temp_sum], convfloat, [current_iter], fixnum, [x_start, x_end], convfloat, [it, opt_iter], fixnum, [tmp], convfloat, [subiter], fixnum, [est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h], convfloat, [repeat_it], fixnum]), Digits : 32, max_terms : 20, glob_html_log : true, term : 1, while term <= MAX_TERMS do (array_y_init : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_type_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_real_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_complex_pole : 0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_y : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_x : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp5 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp6 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp7 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp8 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp9 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_rad_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_ord_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= MAX_TERMS do (term : 1, while term <= MAX_TERMS do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), zero_ats_ar(array_y), zero_ats_ar(array_x), zero_ats_ar(array_m1), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5), zero_ats_ar(array_tmp6), zero_ats_ar(array_tmp7), zero_ats_ar(array_tmp8), zero_ats_ar(array_tmp9), zero_ats_ar(array_const_1), array_const_1 : 1, zero_ats_ar(array_const_0D0), array_const_0D0 : 0.0, 1 1 zero_ats_ar(array_const_2D0), array_const_2D0 : 2.0, 1 zero_ats_ar(array_const_1D0), array_const_1D0 : 1.0, zero_ats_ar(array_m1), 1 array_m1 : - 1.0, iiif : 0, while iiif <= MAX_TERMS do (jjjf : 0, 1 while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0, iiif iiif, jjjf jjjf : 1 + jjjf), iiif : 1 + iiif), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, ALWAYS : 1, INFO : 2, DEBUGL : 3, 1, 20 DEBUGMASSIVE : 4, MAX_TERMS : 20, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x \ * x + 1.0 ) / ( x * x + 1.0 ) ; "), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:20,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-2.0,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:50,"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "glob_max_h:0.5,"), omniout_str(ALWAYS, "glob_type_given_pole:4,"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "array_given_rad_poles[1,1]:0.0,"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "array_given_rad_poles[1,2]:1.0,"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "array_given_ord_poles[1,1]:1.0,"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "array_given_ord_poles[1,2]:0.0,"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000000,"), omniout_str(ALWAYS, "glob_max_minutes:10.0,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_larger_float : 1.1E+100, glob_almost_1 : 0.99, x_start : - 2.0, x_end : 1.0, array_y_init : exact_soln_y(x_start), glob_look_poles : true, 1 + 0 glob_max_iter : 50, glob_max_h : 0.5, glob_type_given_pole : 4, array_given_rad_poles : 0.0, array_given_rad_poles : 1.0, 1, 1 1, 2 array_given_ord_poles : 1.0, array_given_ord_poles : 0.0, 1, 1 1, 2 glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 1000000000, glob_max_minutes : 10.0, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_sec : 3600.0 glob_max_hours + 60.0 glob_max_minutes, omniout_str(ALWAYS, "START of Optimize"), glob_check_sign : my_check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h glob_check_sign, if mabs(glob_max_h) < mabs(glob_h) then glob_h : mabs(glob_max_h) glob_check_sign, if mabs(glob_display_interval) < mabs(glob_h) then glob_h : mabs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : mabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - mabs(glob_display_interval)), chk_data(), best_h : glob_h, min_value : glob_larger_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y_higher : r_order, term_no array_y_init expt(glob_h, term_no - 1) it ----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_check_sign glob_h >= glob_check_sign glob_max_h) then (found_h : true, glob_h : glob_check_sign glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) and (not found_h) glob_h then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_check_sign glob_max_h, found_h : false), if glob_check_sign glob_display_interval < glob_check_sign glob_h then glob_h : glob_check_sign glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y_higher : r_order, term_no array_y_init expt(glob_h, term_no - 1) it ----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (glob_clock_sec - glob_orig_start_sec < glob_max_sec) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, iii : MAX_TERMS, 2 while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, iii : MAX_TERMS, factorial_1(calc_term - 1) while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, iii : MAX_TERMS, factorial_1(calc_term - 1) while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : MAX_TERMS, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - glob_orig_start_sec >= glob_max_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x \ , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.\ 0 ) ; "), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-09T00:24:57-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y \ , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x \ + 1.0 ) ; "), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 1 logitem_float(html_log_file, glob_h), logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, MAX_TERMS), if glob_least_given_sing < glob_large_float then (logitem_float(html_log_file, glob_least_given_sing), 0) else (logitem_str(html_log_file, "NOT GIVEN"), 0), if glob_least_ratio_sing < glob_large_float then (logitem_float(html_log_file, glob_least_ratio_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_3_sing < glob_large_float then (logitem_float(html_log_file, glob_least_3_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_6_sing < glob_large_float then (logitem_float(html_log_file, glob_least_6_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then (logitem_time(html_log_file, glob_total_exp_sec), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i228) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%o228) main() := (alias(convfloat, convfloat), compile(all), main_prog()) (%i229) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable fixnum in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable good_digits in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable rad_given in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ALWAYS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable analytic_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable array_y_higher in translation. warning: encountered undefined variable tmp in translation. warning: variable glob_normmax (declared type convfloat) assigned type any. warning: encountered undefined variable glob_normmax in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable hnew in translation. warning: encountered undefined variable sz2 in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_current_iter in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_optimal_start (declared type convfloat) assigned type any. warning: encountered undefined variable glob_reached_optimal_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable h_new in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_m1 in translation. warning: encountered undefined variable array_const_2D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_const_1D0 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_tmp6 in translation. warning: encountered undefined variable array_tmp7 in translation. warning: encountered undefined variable array_tmp8 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp9 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_init in translation. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable ord in translation. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable jjjf in translation. warning: encountered undefined variable INFO in translation. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable x_start in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable est_answer in translation. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: encountered undefined variable order_diff in translation. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: encountered undefined variable it in translation. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable best_h in translation. warning: encountered undefined variable glob_html_log in translation. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable DEBUGL in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_current_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable calc_term in translation. warning: encountered undefined variable temp_sum in translation. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. WARNING: in $ADJUST_FOR_POLE : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $ADJUST_FOR_POLE : $GLOB_OPTIMAL_START is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. Warning: modedcclare has a function or macro call which has not been translated properly. The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################" "##############temp/sing4postode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:20," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-2.0," "x_end:1.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:50," "" "" "" "glob_max_h:0.5," "glob_type_given_pole:4," "" "array_given_rad_poles[1,1]:0.0," "" "array_given_rad_poles[1,2]:1.0," "" "array_given_ord_poles[1,1]:1.0," "" "array_given_ord_poles[1,2]:0.0," "" "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:1000000000," "glob_max_minutes:10.0," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0 / (x * x + 1.0)) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 3. "" estimated_steps = 3000000. "" step_error = 3.333333333333333700000000000000000E-17 "" est_needed_step_err = 3.333333333333333700000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.1444173827950842000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-102 "" estimated_step_error = 1.1444173827950842000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-102 "" best_h = 2.000000E-6 "" opt_iter = 2 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.50005523887052800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" estimated_step_error = 7.50005523887052800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.9152381398818196000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-93 "" estimated_step_error = 4.9152381398818196000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-93 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.22125300823260350000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 "" estimated_step_error = 3.22125300823260350000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 "" best_h = 1.600000E-5 "" opt_iter = 5 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.111083701862952500000000000000000000000000000000000000000000000000000000000000000000000000000000000E-83 "" estimated_step_error = 2.111083701862952500000000000000000000000000000000000000000000000000000000000000000000000000000000000E-83 "" best_h = 3.200000E-5 "" opt_iter = 6 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.383524180073925000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" estimated_step_error = 1.383524180073925000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" best_h = 6.400000E-5 "" opt_iter = 7 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 9.06712128275963400000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 9.06712128275963400000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 1.280000E-4 "" opt_iter = 8 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.942303599376941000000000000000000000000000000000000000000000000000000000000000000000E-69 "" estimated_step_error = 5.942303599376941000000000000000000000000000000000000000000000000000000000000000000000E-69 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.8944463877632823000000000000000000000000000000000000000000000000000000000000000E-64 "" estimated_step_error = 3.8944463877632823000000000000000000000000000000000000000000000000000000000000000E-64 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.55239323685381440000000000000000000000000000000000000000000000000000000000E-59 "" estimated_step_error = 2.55239323685381440000000000000000000000000000000000000000000000000000000000E-59 "" best_h = 1.024000E-3 "" opt_iter = 11 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.6729053398146995000000000000000000000000000000000000000000000000000000E-54 "" estimated_step_error = 1.6729053398146995000000000000000000000000000000000000000000000000000000E-54 "" best_h = 2.048000E-3 "" opt_iter = 12 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.09657668453830390000000000000000000000000000000000000000000000000E-49 "" estimated_step_error = 1.09657668453830390000000000000000000000000000000000000000000000000E-49 "" best_h = 4.096000E-3 "" opt_iter = 13 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.189428737484040000000000000000000000000000000000000000000000E-45 "" estimated_step_error = 7.189428737484040000000000000000000000000000000000000000000000E-45 "" best_h = 8.192000E-3 "" opt_iter = 14 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.7154734812236160000000000000000000000000000000000000000E-40 "" estimated_step_error = 4.7154734812236160000000000000000000000000000000000000000E-40 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.09533482528111100000000000000000000000000000000000E-35 "" estimated_step_error = 3.09533482528111100000000000000000000000000000000000E-35 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.035138606917342700000000000000000000000000000E-30 "" estimated_step_error = 2.035138606917342700000000000000000000000000000E-30 "" best_h = 6.553600E-2 "" opt_iter = 17 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.34243499284434600000000000000000000000000E-25 "" estimated_step_error = 1.34243499284434600000000000000000000000000E-25 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 8.913275833425122000000000000000000000E-21 "" estimated_step_error = 8.913275833425122000000000000000000000E-21 "" best_h = 0.262144 "" opt_iter = 19 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.9971339416820060000000000000000E-16 "" estimated_step_error = 5.9971339416820060000000000000000E-16 "" best_h = 0.131072 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -2. " " y[1] (analytic) = 0.2 " " y[1] (numeric) = 0.2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.23606797749979 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.23606797749977 " " Order of pole (six term test) = 0.9999999999999476 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.99 " " y[1] (analytic) = 0.2016088385314812 " " y[1] (numeric) = 0.20160883853148123 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.376704306110809700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2271281956816047 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2271281956815985 " " Order of pole (six term test) = 0.9999999999999778 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.98 " " y[1] (analytic) = 0.20323550930818632 " " y[1] (numeric) = 0.20323550930818635 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.36568534259140500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2181974664127626 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2181974664127346 " " Order of pole (six term test) = 0.9999999999999414 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.97 " " y[1] (analytic) = 0.20488024749533895 " " y[1] (numeric) = 0.204880247495339 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.709443780446463300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2092758994747577 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.20927589947473 " " Order of pole (six term test) = 0.9999999999999449 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.96 " " y[1] (analytic) = 0.20654329147389294 " " y[1] (numeric) = 0.20654329147389297 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.343813949006289500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2003636063160106 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2003636063159893 " " Order of pole (six term test) = 0.9999999999999751 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.95 " " y[1] (analytic) = 0.20822488287350338 " " y[1] (numeric) = 0.20822488287350344 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.66592303788115700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.191460700081113 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1914607000810746 " " Order of pole (six term test) = 0.9999999999999591 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.94 " " y[1] (analytic) = 0.2099252666050886 " " y[1] (numeric) = 0.20992526660508865 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.64432920005219800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.182567295640618 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1825672956405957 " " Order of pole (six term test) = 1.0000000000000062 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.93 " " y[1] (analytic) = 0.21164469089292895 " " y[1] (numeric) = 0.211644690892929 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.62284638452570100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1736835096213984 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1736835096213984 " " Order of pole (six term test) = 1.000000000000007 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.92 " " y[1] (analytic) = 0.21338340730624786 " " y[1] (numeric) = 0.2133834073062479 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.601474591301667000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1648094604375694 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1648094604375743 " " Order of pole (six term test) = 1.000000000000023 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.91 " " y[1] (analytic) = 0.21514167079021537 " " y[1] (numeric) = 0.2151416707902154 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.290106910190047300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1559452683219953 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1559452683219784 " " Order of pole (six term test) = 0.9999999999999911 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9 " " y[1] (analytic) = 0.2169197396963124 " " y[1] (numeric) = 0.2169197396963124 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1470910553583886 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1470910553583824 " " Order of pole (six term test) = 1.0000000000000115 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.89 " " y[1] (analytic) = 0.21871787581199012 " " y[1] (numeric) = 0.21871787581199015 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.269012672722169600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1382469455140116 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1382469455139965 " " Order of pole (six term test) = 1.000000000000008 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.88 " " y[1] (analytic) = 0.2205363443895554 " " y[1] (numeric) = 0.22053634438955544 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.258548820715077500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1294130646729865 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1294130646729768 " " Order of pole (six term test) = 1.0000000000000595 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8699999999999999 " " y[1] (analytic) = 0.2223754141742089 " " y[1] (numeric) = 0.22237541417420895 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.496280959718433200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1205895406702355 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1205895406702298 " " Order of pole (six term test) = 1.0000000000000098 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8599999999999999 " " y[1] (analytic) = 0.22423535743115974 " " y[1] (numeric) = 0.2242353574311598 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.47557530030917400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1117765033260505 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.111776503326046 " " Order of pole (six term test) = 1.0000000000000364 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8499999999999999 " " y[1] (analytic) = 0.22611644997173547 " " y[1] (numeric) = 0.2261164499717355 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.227490331601188600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1029740844813087 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1029740844813047 " " Order of pole (six term test) = 1.0000000000000169 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8399999999999999 " " y[1] (analytic) = 0.22801897117840209 " " y[1] (numeric) = 0.22801897117840209 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.094182418033348 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0941824180333475 " " Order of pole (six term test) = 1.0000000000000595 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8299999999999998 " " y[1] (analytic) = 0.22994320402860496 " " y[1] (numeric) = 0.22994320402860496 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0854016399725017 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.085401639972495 " " Order of pole (six term test) = 0.9999999999999822 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8199999999999998 " " y[1] (analytic) = 0.2318894351173361 " " y[1] (numeric) = 0.2318894351173361 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.076631888419322 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0766318884193176 " " Order of pole (six term test) = 0.9999999999999654 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8099999999999998 " " y[1] (analytic) = 0.2338579546783284 " " y[1] (numeric) = 0.23385795467832843 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.186856168899907800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.067873303662485 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.067873303662488 " " Order of pole (six term test) = 1.000000000000063 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7999999999999998 " " y[1] (analytic) = 0.23584905660377362 " " y[1] (numeric) = 0.23584905660377364 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.176836406102665800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0591260281974 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0591260281973924 " " Order of pole (six term test) = 0.9999999999999583 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7899999999999998 " " y[1] (analytic) = 0.23786303846245335 " " y[1] (numeric) = 0.23786303846245338 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.16687215445665500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0503902067655315 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0503902067655293 " " Order of pole (six term test) = 0.9999999999999885 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7799999999999998 " " y[1] (analytic) = 0.2399002015161693 " " y[1] (numeric) = 0.23990020151616934 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.156963413961875400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0416659863944444 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0416659863944338 " " Order of pole (six term test) = 0.9999999999998996 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7699999999999998 " " y[1] (analytic) = 0.24196085073435122 " " y[1] (numeric) = 0.24196085073435125 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.147110184618327200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.032953516438583 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0329535164385852 " " Order of pole (six term test) = 1.0000000000000293 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7599999999999998 " " y[1] (analytic) = 0.24404529480671613 " " y[1] (numeric) = 0.2440452948067162 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.274624932852020700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0242529486207994 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0242529486208123 " " Order of pole (six term test) = 1.0000000000001235 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7499999999999998 " " y[1] (analytic) = 0.2461538461538462 " " y[1] (numeric) = 0.24615384615384622 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.127570259384924300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0155644370746373 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0155644370746413 " " Order of pole (six term test) = 1.000000000000031 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7399999999999998 " " y[1] (analytic) = 0.24828682093554477 " " y[1] (numeric) = 0.2482868209355448 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.117883563495070100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.006888138387389 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.006888138387417 " " Order of pole (six term test) = 1.0000000000002052 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7299999999999998 " " y[1] (analytic) = 0.2504445390568259 " " y[1] (numeric) = 0.2504445390568259 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9982242116439284 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.998224211643921 " " Order of pole (six term test) = 0.9999999999999343 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7199999999999998 " " y[1] (analytic) = 0.25262732417138245 " " y[1] (numeric) = 0.2526273241713824 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.19735341033810900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.989572818471342 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9895728184713433 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7099999999999997 " " y[1] (analytic) = 0.25483550368237307 " " y[1] (numeric) = 0.25483550368237307 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9809341230843591 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.980934123084365 " " Order of pole (six term test) = 1.0000000000000444 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6999999999999997 " " y[1] (analytic) = 0.25706940874035994 " " y[1] (numeric) = 0.25706940874035994 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9723082923316018 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.972308292331608 " " Order of pole (six term test) = 1.0000000000000497 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6899999999999997 " " y[1] (analytic) = 0.25932937423822 " " y[1] (numeric) = 0.25932937423822 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.963695495742657 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9636954957426698 " " Order of pole (six term test) = 1.0000000000000897 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6799999999999997 " " y[1] (analytic) = 0.26161573880284644 " " y[1] (numeric) = 0.26161573880284644 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9550959055759898 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9550959055760004 " " Order of pole (six term test) = 1.000000000000072 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6699999999999997 " " y[1] (analytic) = 0.26392884478344647 " " y[1] (numeric) = 0.26392884478344647 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9465096968677036 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9465096968677271 " " Order of pole (six term test) = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6599999999999997 " " y[1] (analytic) = 0.266269038236234 " " y[1] (numeric) = 0.266269038236234 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9379370474811608 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9379370474811568 " " Order of pole (six term test) = 0.9999999999999787 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6499999999999997 " " y[1] (analytic) = 0.2686366689053057 " " y[1] (numeric) = 0.2686366689053057 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9293781381574735 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9293781381574828 " " Order of pole (six term test) = 1.0000000000000657 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6399999999999997 " " y[1] (analytic) = 0.27103209019947966 " " y[1] (numeric) = 0.2710320901994797 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.048139435828488800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.920833152566875 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9208331525668811 " " Order of pole (six term test) = 1.0000000000000435 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6299999999999997 " " y[1] (analytic) = 0.27345565916486647 " " y[1] (numeric) = 0.2734556591648665 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.02998728937586720000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9123022773609821 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9123022773609748 " " Order of pole (six term test) = 0.9999999999999547 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6199999999999997 " " y[1] (analytic) = 0.27590773645293026 " " y[1] (numeric) = 0.27590773645293026 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9037857022259619 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.903785702225978 " " Order of pole (six term test) = 1.0000000000001004 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6099999999999997 " " y[1] (analytic) = 0.2783886862837895 " " y[1] (numeric) = 0.27838868628378954 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.99401606337801180000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8952836199366043 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.895283619936625 " " Order of pole (six term test) = 1.0000000000001252 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5999999999999996 " " y[1] (analytic) = 0.28089887640449446 " " y[1] (numeric) = 0.2808988764044945 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.976196983832778400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8867962264113205 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.886796226411329 " " Order of pole (six term test) = 1.0000000000000515 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5899999999999996 " " y[1] (analytic) = 0.2834386780420057 " " y[1] (numeric) = 0.28343867804200573 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.95848892659000700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8783237207680679 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8783237207680807 " " Order of pole (six term test) = 1.0000000000000773 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5799999999999996 " " y[1] (analytic) = 0.2860084658505893 " " y[1] (numeric) = 0.2860084658505893 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.869866305381216 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8698663053812583 " " Order of pole (six term test) = 1.0000000000002593 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5699999999999996 " " y[1] (analytic) = 0.2886086178533292 " " y[1] (numeric) = 0.28860861785332925 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.92340587901185200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8614241859393572 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.861424185939372 " " Order of pole (six term test) = 1.0000000000000897 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5599999999999996 " " y[1] (analytic) = 0.2912395153774465 " " y[1] (numeric) = 0.2912395153774466 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.906030888676468200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8529975715040747 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8529975715040812 " " Order of pole (six term test) = 1.00000000000004 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5499999999999996 " " y[1] (analytic) = 0.2939015429831007 " " y[1] (numeric) = 0.29390154298310084 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.777533841287094600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8445866745696715 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.844586674569689 " " Order of pole (six term test) = 1.0000000000001048 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5399999999999996 " " y[1] (analytic) = 0.29659508838533644 " " y[1] (numeric) = 0.2965950883853365 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.871613974913088300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8361917111238681 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.836191711123869 " " Order of pole (six term test) = 1.0000000000000044 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5299999999999996 " " y[1] (analytic) = 0.2993205423688229 " " y[1] (numeric) = 0.29932054236882294 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.85457205148509200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8278129007094788 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.827812900709475 " " Order of pole (six term test) = 0.9999999999999796 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5199999999999996 " " y[1] (analytic) = 0.3020782986950219 " " y[1] (numeric) = 0.3020782986950219 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.819450466487065 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.819450466487073 " " Order of pole (six term test) = 1.0000000000000506 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5099999999999996 " " y[1] (analytic) = 0.3048687540014025 " " y[1] (numeric) = 0.30486875400140256 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.820821271536487400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.811104635298579 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8111046352985753 " " Order of pole (six term test) = 0.9999999999999787 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4999999999999996 " " y[1] (analytic) = 0.3076923076923078 " " y[1] (numeric) = 0.3076923076923079 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.804112415015878800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8027756377319943 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8027756377319883 " " Order of pole (six term test) = 0.9999999999999654 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4899999999999995 " " y[1] (analytic) = 0.3105493618210616 " " y[1] (numeric) = 0.31054936182106163 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.787514580797732700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.794463708186933 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7944637081869215 " " Order of pole (six term test) = 0.9999999999999316 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4799999999999995 " " y[1] (analytic) = 0.3134403209628888 " " y[1] (numeric) = 0.3134403209628888 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7861690849412881 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7861690849412903 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4699999999999995 " " y[1] (analytic) = 0.31636559207820575 " " y[1] (numeric) = 0.31636559207820575 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.777892010218843 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7778920102188347 " " Order of pole (six term test) = 0.999999999999952 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4599999999999995 " " y[1] (analytic) = 0.31932558436581954 " " y[1] (numeric) = 0.3193255843658196 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.738387211958069300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7696327302578911 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7696327302579127 " " Order of pole (six term test) = 1.0000000000001261 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4499999999999995 " " y[1] (analytic) = 0.32232070910556015 " " y[1] (numeric) = 0.3223207091055602 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.722233466949773500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7613914953808534 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7613914953808532 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4399999999999995 " " y[1] (analytic) = 0.3253513794898492 " " y[1] (numeric) = 0.3253513794898492 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7531685600648896 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.753168560064864 " " Order of pole (six term test) = 0.999999999999849 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4299999999999995 " " y[1] (analytic) = 0.3284180104436929 " " y[1] (numeric) = 0.3284180104436929 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7449641830135076 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7449641830135385 " " Order of pole (six term test) = 1.000000000000183 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4199999999999995 " " y[1] (analytic) = 0.33152101843256876 " " y[1] (numeric) = 0.3315210184325688 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.674438365739660300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.736778627229158 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7367786272291783 " " Order of pole (six term test) = 1.00000000000012 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4099999999999995 " " y[1] (analytic) = 0.33466082125765556 " " y[1] (numeric) = 0.33466082125765556 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7286121600868132 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.728612160086809 " " Order of pole (six term test) = 0.9999999999999751 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3999999999999995 " " y[1] (analytic) = 0.33783783783783805 " " y[1] (numeric) = 0.33783783783783805 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7204650534085248 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.720465053408545 " " Order of pole (six term test) = 1.000000000000119 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3899999999999995 " " y[1] (analytic) = 0.3410524879779 " " y[1] (numeric) = 0.3410524879779 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7123375835389465 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7123375835388703 " " Order of pole (six term test) = 0.9999999999995506 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3799999999999994 " " y[1] (analytic) = 0.3443051921222974 " " y[1] (numeric) = 0.34430519212229743 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.612265876360651500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7042300314218144 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7042300314214336 " " Order of pole (six term test) = 0.9999999999977627 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3699999999999994 " " y[1] (analytic) = 0.34759637109388597 " " y[1] (numeric) = 0.347596371093886 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.597000309772055600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6961426826773738 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6961426826773665 " " Order of pole (six term test) = 0.9999999999999565 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3599999999999994 " " y[1] (analytic) = 0.350926445816957 " " y[1] (numeric) = 0.35092644581695703 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.58184576548592200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.688075827680735 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6880758276807266 " " Order of pole (six term test) = 0.999999999999952 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3499999999999994 " " y[1] (analytic) = 0.35429583702391515 " " y[1] (numeric) = 0.35429583702391526 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.133604487004502700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6800297616411437 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6800297616411177 " " Order of pole (six term test) = 0.999999999999849 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3399999999999994 " " y[1] (analytic) = 0.3577049649449136 " " y[1] (numeric) = 0.3577049649449137 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.10373948764208600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6720047846821486 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.672004784682124 " " Order of pole (six term test) = 0.9999999999998579 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3299999999999994 " " y[1] (analytic) = 0.3611542489797394 " " y[1] (numeric) = 0.3611542489797395 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.074096532884594300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6640012019226424 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6640012019226578 " " Order of pole (six term test) = 1.0000000000000906 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3199999999999994 " " y[1] (analytic) = 0.36464410735122543 " " y[1] (numeric) = 0.3646441073512255 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.522337811366013800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6560193235587555 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6560193235587657 " " Order of pole (six term test) = 1.0000000000000586 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3099999999999994 " " y[1] (analytic) = 0.36817495673944284 " " y[1] (numeric) = 0.3681749567394429 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.50773837859219300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6480594649465772 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6480594649466025 " " Order of pole (six term test) = 1.0000000000001492 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2999999999999994 " " y[1] (analytic) = 0.371747211895911 " " y[1] (numeric) = 0.3717472118959111 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.9864999362416700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.640121946685672 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6401219466856651 " " Order of pole (six term test) = 0.9999999999999618 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2899999999999994 " " y[1] (analytic) = 0.3753612852370409 " " y[1] (numeric) = 0.375361285237041 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.95774515990387800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6322070947033647 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6322070947033518 " " Order of pole (six term test) = 0.9999999999999254 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2799999999999994 " " y[1] (analytic) = 0.37901758641600997 " " y[1] (numeric) = 0.37901758641601 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.464606214085505400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6243152403397556 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6243152403397563 " " Order of pole (six term test) = 1.0000000000000044 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2699999999999994 " " y[1] (analytic) = 0.38271652187224947 " " y[1] (numeric) = 0.3827165218722495 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.45045087052153500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.616446720433432 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6164467204334472 " " Order of pole (six term test) = 1.000000000000088 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2599999999999993 " " y[1] (analytic) = 0.38645849435770624 " " y[1] (numeric) = 0.3864584943577063 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.436406549260026400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.608601877407831 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6086018774078394 " " Order of pole (six term test) = 1.0000000000000515 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2499999999999993 " " y[1] (analytic) = 0.3902439024390247 " " y[1] (numeric) = 0.3902439024390247 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6007810593582117 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.600781059358218 " " Order of pole (six term test) = 1.0000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2399999999999993 " " y[1] (analytic) = 0.39407313997477955 " " y[1] (numeric) = 0.3940731399747796 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.408650973644397800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5929846201391897 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.59298462013919 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2299999999999993 " " y[1] (analytic) = 0.39794659556687517 " " y[1] (numeric) = 0.3979465955668752 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.394939719290277000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5852129194527775 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.585212919452778 " " Order of pole (six term test) = 1.0000000000000027 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2199999999999993 " " y[1] (analytic) = 0.4018646519852116 " " y[1] (numeric) = 0.4018646519852117 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.76267897447723800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5774663229368793 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5774663229368873 " " Order of pole (six term test) = 1.0000000000000462 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2099999999999993 " " y[1] (analytic) = 0.4058276855647095 " " y[1] (numeric) = 0.40582768556470955 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.367850277489423300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5697452022541742 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5697452022541958 " " Order of pole (six term test) = 1.000000000000127 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1999999999999993 " " y[1] (analytic) = 0.4098360655737707 " " y[1] (numeric) = 0.40983606557377084 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.708944180085380300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5620499351813304 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5620499351813835 " " Order of pole (six term test) = 1.0000000000003082 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1899999999999993 " " y[1] (analytic) = 0.41389015355324726 " " y[1] (numeric) = 0.4138901535532473 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.341204924898419500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5543809056984708 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5543809056985851 " " Order of pole (six term test) = 1.0000000000006608 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1799999999999993 " " y[1] (analytic) = 0.4179903026249794 " " y[1] (numeric) = 0.41799030262497944 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.328048782056611400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5467385040788242 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5467385040788677 " " Order of pole (six term test) = 1.0000000000002496 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1699999999999993 " " y[1] (analytic) = 0.42213685676896484 " " y[1] (numeric) = 0.42213685676896484 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5391231269784749 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5391231269784793 " " Order of pole (six term test) = 1.0000000000000258 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1599999999999993 " " y[1] (analytic) = 0.4263301500682131 " " y[1] (numeric) = 0.4263301500682132 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.302069563280382800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5315351775261312 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.531535177526114 " " Order of pole (six term test) = 0.9999999999999005 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1499999999999992 " " y[1] (analytic) = 0.43057050592034485 " " y[1] (numeric) = 0.4305705059203448 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.28924648734596200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5239750654128164 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5239750654128017 " " Order of pole (six term test) = 0.9999999999999156 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1399999999999992 " " y[1] (analytic) = 0.43485823621499425 " " y[1] (numeric) = 0.43485823621499425 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5164432069813885 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5164432069813782 " " Order of pole (six term test) = 0.9999999999999423 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1299999999999992 " " y[1] (analytic) = 0.4391936404760863 " " y[1] (numeric) = 0.4391936404760863 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5089400253157839 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5089400253157856 " " Order of pole (six term test) = 1.0000000000000115 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1199999999999992 " " y[1] (analytic) = 0.4435770049680628 " " y[1] (numeric) = 0.44357700496806285 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.251443393357475600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5014659503298762 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.501465950329863 " " Order of pole (six term test) = 0.9999999999999245 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1099999999999992 " " y[1] (analytic) = 0.4480086017651543 " " y[1] (numeric) = 0.4480086017651543 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4940214188558336 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4940214188558445 " " Order of pole (six term test) = 1.000000000000063 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0999999999999992 " " y[1] (analytic) = 0.4524886877828058 " " y[1] (numeric) = 0.4524886877828058 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.48660687473185 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4866068747318348 " " Order of pole (six term test) = 0.9999999999999112 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0899999999999992 " " y[1] (analytic) = 0.4570175037703948 " " y[1] (numeric) = 0.4570175037703948 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.479222768889121 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4792227688891129 " " Order of pole (six term test) = 0.9999999999999503 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0799999999999992 " " y[1] (analytic) = 0.4615952732644021 " " y[1] (numeric) = 0.46159527326440214 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.202593580273968700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4718695594379274 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.471869559437928 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0699999999999992 " " y[1] (analytic) = 0.46622220150123594 " " y[1] (numeric) = 0.46622220150123583 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.38131736551849600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4645477117526755 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4645477117526757 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0599999999999992 " " y[1] (analytic) = 0.47089847428894377 " " y[1] (numeric) = 0.47089847428894366 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.3576696150939800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4572576985557488 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4572576985557384 " " Order of pole (six term test) = 0.9999999999999378 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0499999999999992 " " y[1] (analytic) = 0.4756242568370991 " " y[1] (numeric) = 0.4756242568370991 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4499999999999993 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4499999999999937 " " Order of pole (six term test) = 0.9999999999999654 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0399999999999991 " " y[1] (analytic) = 0.48039969254419723 " " y[1] (numeric) = 0.4803996925441972 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.155520124029861800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.442775103749714 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4427751037497052 " " Order of pole (six term test) = 0.9999999999999503 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0299999999999991 " " y[1] (analytic) = 0.48522490174195776 " " y[1] (numeric) = 0.4852249017419578 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.144029315724991600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4355835050598758 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.435583505059878 " " Order of pole (six term test) = 1.0000000000000115 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0199999999999991 " " y[1] (analytic) = 0.4900999803960012 " " y[1] (numeric) = 0.4900999803960012 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4284257068535269 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4284257068535184 " " Order of pole (six term test) = 0.999999999999952 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0099999999999991 " " y[1] (analytic) = 0.4950249987624379 " " y[1] (numeric) = 0.49502499876243794 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.121380766022638500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4213022197970417 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4213022197970406 " " Order of pole (six term test) = 0.9999999999999938 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9999999999999991 " " y[1] (analytic) = 0.5000000000000004 " " y[1] (numeric) = 0.5000000000000004 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4142135623730945 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.9899999999999991 " " y[1] (analytic) = 0.505024998737438 " " y[1] (numeric) = 0.505024998737438 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4071602609511107 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4071602609511085 " " Order of pole (six term test) = 0.9999999999999876 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9799999999999991 " " y[1] (analytic) = 0.5100999795960013 " " y[1] (numeric) = 0.5100999795960013 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4001428498549704 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4001428498549708 " " Order of pole (six term test) = 1.0000000000000018 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9699999999999991 " " y[1] (analytic) = 0.5152248956669591 " " y[1] (numeric) = 0.5152248956669591 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.393161871427724 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3931618714277227 " " Order of pole (six term test) = 0.9999999999999947 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9599999999999991 " " y[1] (analytic) = 0.5203996669442137 " " y[1] (numeric) = 0.5203996669442136 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.133404564119698600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.386217876093076 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3862178760930772 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9499999999999991 " " y[1] (analytic) = 0.5256241787122213 " " y[1] (numeric) = 0.5256241787122212 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.112199304349357800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3793114224133716 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3793114224133707 " " Order of pole (six term test) = 0.9999999999999956 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9399999999999991 " " y[1] (analytic) = 0.5308982798895737 " " y[1] (numeric) = 0.5308982798895736 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.091216089183942400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3724430771438203 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3724430771438214 " " Order of pole (six term test) = 1.0000000000000027 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.929999999999999 " " y[1] (analytic) = 0.5362217813287581 " " y[1] (numeric) = 0.5362217813287581 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.36561341528267 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3656134152826713 " " Order of pole (six term test) = 1.000000000000008 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.919999999999999 " " y[1] (analytic) = 0.5415944540727908 " " y[1] (numeric) = 0.5415944540727908 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3588230201170417 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3588230201170413 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = -0.909999999999999 " " y[1] (analytic) = 0.5470160275696083 " " y[1] (numeric) = 0.5470160275696083 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3520724832641178 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3520724832641176 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.899999999999999 " " y[1] (analytic) = 0.5524861878453043 " " y[1] (numeric) = 0.5524861878453045 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.009503674571531700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3453624047073705 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.34536240470737 " " Order of pole (six term test) = 0.9999999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.889999999999999 " " y[1] (analytic) = 0.5580045756375208 " " y[1] (numeric) = 0.5580045756375208 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3386933928274982 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3386933928274989 " " Order of pole (six term test) = 1.0000000000000062 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.879999999999999 " " y[1] (analytic) = 0.5635707844905326 " " y[1] (numeric) = 0.5635707844905327 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.96997973489487580000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3320660644277362 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3320660644277356 " " Order of pole (six term test) = 0.9999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.869999999999999 " " y[1] (analytic) = 0.5691843588138205 " " y[1] (numeric) = 0.5691843588138205 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3254810447531862 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3254810447531893 " " Order of pole (six term test) = 1.0000000000000222 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.859999999999999 " " y[1] (analytic) = 0.5748447919061859 " " y[1] (numeric) = 0.574844791906186 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.931343973637920400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3189389675038032 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3189389675038046 " " Order of pole (six term test) = 1.0000000000000133 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.849999999999999 " " y[1] (analytic) = 0.5805515239477509 " " y[1] (numeric) = 0.580551523947751 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.912359159916830200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3124404748406682 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3124404748406686 " " Order of pole (six term test) = 1.0000000000000053 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.839999999999999 " " y[1] (analytic) = 0.5863039399624772 " " y[1] (numeric) = 0.5863039399624772 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.30598621738516 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3059862173851584 " " Order of pole (six term test) = 0.9999999999999885 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.829999999999999 " " y[1] (analytic) = 0.5921013677541601 " " y[1] (numeric) = 0.5921013677541602 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.875055666289425000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2995768542106305 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.299576854210633 " " Order of pole (six term test) = 1.0000000000000204 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.819999999999999 " " y[1] (analytic) = 0.5979430758191826 " " y[1] (numeric) = 0.5979430758191827 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.8567369863831100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2932130528261763 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2932130528261772 " " Order of pole (six term test) = 1.000000000000008 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8099999999999989 " " y[1] (analytic) = 0.6038282712396601 " " y[1] (numeric) = 0.6038282712396601 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2868954891520905 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.286895489152092 " " Order of pole (six term test) = 1.0000000000000124 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7999999999999989 " " y[1] (analytic) = 0.6097560975609763 " " y[1] (numeric) = 0.6097560975609763 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2806248474865691 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2806248474865667 " " Order of pole (six term test) = 0.9999999999999813 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7899999999999989 " " y[1] (analytic) = 0.6157256326580882 " " y[1] (numeric) = 0.6157256326580882 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2744018204632315 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2744018204632332 " " Order of pole (six term test) = 1.000000000000016 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7799999999999989 " " y[1] (analytic) = 0.6217358865953749 " " y[1] (numeric) = 0.6217358865953749 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2682271089990145 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.268227108999018 " " Order of pole (six term test) = 1.0000000000000275 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7699999999999989 " " y[1] (analytic) = 0.6277857994852163 " " y[1] (numeric) = 0.6277857994852163 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2621014222319846 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2621014222319844 " " Order of pole (six term test) = 0.9999999999999947 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7599999999999989 " " y[1] (analytic) = 0.6338742393509135 " " y[1] (numeric) = 0.6338742393509135 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.256025477448606 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2560254774486115 " " Order of pole (six term test) = 1.0000000000000444 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7499999999999989 " " y[1] (analytic) = 0.6400000000000007 " " y[1] (numeric) = 0.6400000000000007 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2499999999999993 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.250000000000004 " " Order of pole (six term test) = 1.0000000000000364 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7399999999999989 " " y[1] (analytic) = 0.6461617989144489 " " y[1] (numeric) = 0.6461617989144489 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2440257232067182 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2440257232067193 " " Order of pole (six term test) = 1.000000000000007 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7299999999999989 " " y[1] (analytic) = 0.6523582751647211 " " y[1] (numeric) = 0.6523582751647212 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.701860874447900800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2381033882515622 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2381033882515289 " " Order of pole (six term test) = 0.99999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7199999999999989 " " y[1] (analytic) = 0.6585879873551114 " " y[1] (numeric) = 0.6585879873551114 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2322337440599485 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2322337440599684 " " Order of pole (six term test) = 1.0000000000001616 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7099999999999989 " " y[1] (analytic) = 0.6648494116082714 " " y[1] (numeric) = 0.6648494116082715 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.669886451338696300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.226417547167358 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2264175471673635 " " Order of pole (six term test) = 1.0000000000000453 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6999999999999988 " " y[1] (analytic) = 0.6711409395973161 " " y[1] (numeric) = 0.6711409395973162 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.654232306691481300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2206555615733696 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2206555615733719 " " Order of pole (six term test) = 1.0000000000000195 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6899999999999988 " " y[1] (analytic) = 0.677460876634375 " " y[1] (numeric) = 0.6774608766343752 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.63880020664919220000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.214948558581802 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2149485585817952 " " Order of pole (six term test) = 0.9999999999999467 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6799999999999988 " " y[1] (analytic) = 0.6838074398249461 " " y[1] (numeric) = 0.6838074398249461 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2092973166264773 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2092973166264755 " " Order of pole (six term test) = 0.9999999999999876 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6699999999999988 " " y[1] (analytic) = 0.690178756297882 " " y[1] (numeric) = 0.690178756297882 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2037026210821336 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2037026210821313 " " Order of pole (six term test) = 0.9999999999999831 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6599999999999988 " " y[1] (analytic) = 0.6965728615213159 " " y[1] (numeric) = 0.6965728615213159 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.198165264060012 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1981652640600158 " " Order of pole (six term test) = 1.000000000000032 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6499999999999988 " " y[1] (analytic) = 0.7029876977152907 " " y[1] (numeric) = 0.7029876977152908 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.579292252529283500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1926860441876557 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.192686044187663 " " Order of pole (six term test) = 1.0000000000000604 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6399999999999988 " " y[1] (analytic) = 0.709421112372305 " " y[1] (numeric) = 0.709421112372305 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1872657663724657 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.187265766372465 " " Order of pole (six term test) = 0.9999999999999938 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6299999999999988 " " y[1] (analytic) = 0.7158708568974165 " " y[1] (numeric) = 0.7158708568974165 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1819052415485762 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1819052415485765 " " Order of pole (six term test) = 1.0000000000000009 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6199999999999988 " " y[1] (analytic) = 0.7223345853799488 " " y[1] (numeric) = 0.7223345853799488 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1766052864066177 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1766052864066243 " " Order of pole (six term test) = 1.0000000000000524 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6099999999999988 " " y[1] (analytic) = 0.7288098535092202 " " y[1] (numeric) = 0.7288098535092202 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1713667231059617 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.17136672310597 " " Order of pole (six term test) = 1.0000000000000666 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5999999999999988 " " y[1] (analytic) = 0.7352941176470597 " " y[1] (numeric) = 0.7352941176470597 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1661903789690595 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1661903789690538 " " Order of pole (six term test) = 0.9999999999999565 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5899999999999987 " " y[1] (analytic) = 0.7417847340701736 " " y[1] (numeric) = 0.7417847340701736 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1610770861575033 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1610770861575106 " " Order of pole (six term test) = 1.000000000000056 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5799999999999987 " " y[1] (analytic) = 0.7482789583956908 " " y[1] (numeric) = 0.7482789583956907 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.483702050109057500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1560276813294734 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.156027681329461 " " Order of pole (six term test) = 0.9999999999999005 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5699999999999987 " " y[1] (analytic) = 0.7547739452034123 " " y[1] (numeric) = 0.7547739452034123 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1510430052782556 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1510430052782443 " " Order of pole (six term test) = 0.9999999999999103 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5599999999999987 " " y[1] (analytic) = 0.7612667478684539 " " y[1] (numeric) = 0.7612667478684538 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.45838896514760400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1461239025515515 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1461239025515497 " " Order of pole (six term test) = 0.999999999999984 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5499999999999987 " " y[1] (analytic) = 0.767754318618043 " " y[1] (numeric) = 0.767754318618043 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.141271221051332 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1412712210513345 " " Order of pole (six term test) = 1.0000000000000169 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5399999999999987 " " y[1] (analytic) = 0.7742335088262629 " " y[1] (numeric) = 0.7742335088262627 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.433964058605850500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.136485811614029 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1364858116140295 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5299999999999987 " " y[1] (analytic) = 0.7807010695604661 " " y[1] (numeric) = 0.780701069560466 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.422084672242361300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.131768527570898 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1317685275708964 " " Order of pole (six term test) = 0.9999999999999885 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5199999999999987 " " y[1] (analytic) = 0.787153652392948 " " y[1] (numeric) = 0.7871536523929479 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.410427330483797500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.127120224288429 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1271202242884302 " " Order of pole (six term test) = 1.0000000000000107 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5099999999999987 " " y[1] (analytic) = 0.7935878104912317 " " y[1] (numeric) = 0.7935878104912316 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.398992033330158400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1225417586887352 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1225417586887327 " " Order of pole (six term test) = 0.9999999999999698 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.49999999999999867 " " y[1] (analytic) = 0.8000000000000008 " " y[1] (numeric) = 0.8000000000000007 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.387778780781444300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1180339887498942 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1180339887498953 " " Order of pole (six term test) = 1.0000000000000098 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.48999999999999866 " " y[1] (analytic) = 0.806386581727281 " " y[1] (numeric) = 0.8063865817272807 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.753575145675310500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1135977729862783 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.113597772986278 " " Order of pole (six term test) = 0.9999999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.47999999999999865 " " y[1] (analytic) = 0.812743823146945 " " y[1] (numeric) = 0.8127438231469447 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.098055228496373400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.109233969908963 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1092339699089635 " " Order of pole (six term test) = 1.0000000000000053 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.46999999999999864 " " y[1] (analytic) = 0.8190679007289713 " " y[1] (numeric) = 0.8190679007289711 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.710942581529704500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1049434374663705 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1049434374663705 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = -0.45999999999999863 " " y[1] (analytic) = 0.8253549026081224 " " y[1] (numeric) = 0.8253549026081222 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.690292433271676600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1007270324653604 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1007270324653597 " " Order of pole (six term test) = 0.9999999999999938 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4499999999999986 " " y[1] (analytic) = 0.8316008316008324 " " y[1] (numeric) = 0.8316008316008323 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.335043187111749400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0965856099730649 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0965856099730646 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4399999999999986 " " y[1] (analytic) = 0.8378016085790894 " " y[1] (numeric) = 0.8378016085790891 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.650324404385171000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0925200226998124 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0925200226998124 " " Order of pole (six term test) = 1.0000000000000009 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4299999999999986 " " y[1] (analytic) = 0.8439530762089636 " " y[1] (numeric) = 0.8439530762089634 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.63100652375669300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0885311203635837 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0885311203635832 " " Order of pole (six term test) = 0.9999999999999956 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4199999999999986 " " y[1] (analytic) = 0.8500510030601844 " " y[1] (numeric) = 0.8500510030601842 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.612132732338065500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0846197490364993 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0846197490364993 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4099999999999986 " " y[1] (analytic) = 0.8560910880917738 " " y[1] (numeric) = 0.8560910880917736 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.59370303012928800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0807867504739308 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0807867504739301 " " Order of pole (six term test) = 0.9999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3999999999999986 " " y[1] (analytic) = 0.8620689655172422 " " y[1] (numeric) = 0.862068965517242 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.575717417130360400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0770329614269003 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0770329614269012 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.38999999999999857 " " y[1] (analytic) = 0.8679802100512117 " " y[1] (numeric) = 0.8679802100512114 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.83726384001192470000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0733592129385199 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0733592129385197 " " Order of pole (six term test) = 0.9999999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.37999999999999856 " " y[1] (analytic) = 0.873820342537575 " " y[1] (numeric) = 0.8738203425375748 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.54107845876205600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0697663296253062 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0697663296253064 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.36999999999999855 " " y[1] (analytic) = 0.879584835957429 " " y[1] (numeric) = 0.8795848359574286 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.786637670089017500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0662551289442874 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0662551289442879 " " Order of pole (six term test) = 1.0000000000000044 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.35999999999999854 " " y[1] (analytic) = 0.8852691218130319 " " y[1] (numeric) = 0.8852691218130317 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.254107928616575700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0628264204469133 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0628264204469138 " " Order of pole (six term test) = 1.0000000000000044 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.34999999999999853 " " y[1] (analytic) = 0.8908685968819607 " " y[1] (numeric) = 0.8908685968819605 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.492450690283474200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.059481005020854 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.059481005020855 " " Order of pole (six term test) = 1.000000000000008 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3399999999999985 " " y[1] (analytic) = 0.8963786303334537 " " y[1] (numeric) = 0.8963786303334534 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.47712961254364700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0562196741208711 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0562196741208723 " " Order of pole (six term test) = 1.0000000000000115 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3299999999999985 " " y[1] (analytic) = 0.9017945711966822 " " y[1] (numeric) = 0.9017945711966819 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.462252624013670200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0530432089900201 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.053043208990027 " " Order of pole (six term test) = 1.0000000000000657 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3199999999999985 " " y[1] (analytic) = 0.9071117561683608 " " y[1] (numeric) = 0.9071117561683605 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.67172958704031440000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0499523798725345 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0499523798725523 " " Order of pole (six term test) = 1.0000000000001679 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3099999999999985 " " y[1] (analytic) = 0.9123255177447321 " " y[1] (numeric) = 0.9123255177447318 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.65074637187489900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.046947945219818 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0469479452198147 " " Order of pole (six term test) = 0.9999999999999716 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2999999999999985 " " y[1] (analytic) = 0.9174311926605512 " " y[1] (numeric) = 0.917431192660551 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.420286193682839300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0440306508910546 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0440306508910542 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2899999999999985 " " y[1] (analytic) = 0.9224241306152576 " " y[1] (numeric) = 0.9224241306152574 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.407185561992262500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.041201229350023 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0412012293500226 " " Order of pole (six term test) = 0.9999999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2799999999999985 " " y[1] (analytic) = 0.9272997032640957 " " y[1] (numeric) = 0.9272997032640955 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.394529019511535700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0384603988597731 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0384603988597743 " " Order of pole (six term test) = 1.0000000000000107 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.26999999999999846 " " y[1] (analytic) = 0.9320533134495301 " " y[1] (numeric) = 0.9320533134495298 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.57347484936098800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0358088626768933 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0358088626768915 " " Order of pole (six term test) = 0.9999999999999858 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.25999999999999845 " " y[1] (analytic) = 0.9366804046459355 " " y[1] (numeric) = 0.9366804046459353 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.370548202179632600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0332473082471587 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.03324730824716 " " Order of pole (six term test) = 1.0000000000000133 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.24999999999999845 " " y[1] (analytic) = 0.9411764705882361 " " y[1] (numeric) = 0.9411764705882357 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.538835890992683000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0307764064044147 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0307764064044158 " " Order of pole (six term test) = 1.000000000000007 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.23999999999999844 " " y[1] (analytic) = 0.9455370650529508 " " y[1] (numeric) = 0.9455370650529504 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.52251561253069400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0283968105745949 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.028396810574594 " " Order of pole (six term test) = 0.999999999999992 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.22999999999999843 " " y[1] (analytic) = 0.9497578117580023 " " y[1] (numeric) = 0.949757811758002 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.506861467883480000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0261091559868274 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0261091559868267 " " Order of pole (six term test) = 0.9999999999999947 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.21999999999999842 " " y[1] (analytic) = 0.9538344143456702 " " y[1] (numeric) = 0.9538344143456698 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.4918734570510400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.023914058893616 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0239140588936158 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2099999999999984 " " y[1] (analytic) = 0.9577626664112638 " " y[1] (numeric) = 0.9577626664112635 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.477551580033375600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0218121158021172 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0218121158021176 " " Order of pole (six term test) = 1.0000000000000044 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.1999999999999984 " " y[1] (analytic) = 0.9615384615384621 " " y[1] (numeric) = 0.9615384615384618 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.463895836830487000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0198039027185566 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0198039027185557 " " Order of pole (six term test) = 0.9999999999999911 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.1899999999999984 " " y[1] (analytic) = 0.9651578033008403 " " y[1] (numeric) = 0.9651578033008399 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.601208303256495400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0178899744078431 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0178899744078416 " " Order of pole (six term test) = 0.9999999999999876 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.17999999999999838 " " y[1] (analytic) = 0.9686168151879123 " " y[1] (numeric) = 0.9686168151879119 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.58477700249204370000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0160708636704427 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0160708636704354 " " Order of pole (six term test) = 0.9999999999999343 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.16999999999999837 " " y[1] (analytic) = 0.971911750413063 " " y[1] (numeric) = 0.9719117504130627 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.42692541011046900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0143470806385748 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.014347080638576 " " Order of pole (six term test) = 1.0000000000000115 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.15999999999999837 " " y[1] (analytic) = 0.975039001560063 " " y[1] (numeric) = 0.9750390015600625 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.5545789362222400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0127191120937726 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0127191120937717 " " Order of pole (six term test) = 0.9999999999999893 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.14999999999999836 " " y[1] (analytic) = 0.9779951100244504 " " y[1] (numeric) = 0.9779951100244499 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.540812170716888600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.011187420807834 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0111874208078337 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.13999999999999835 " " y[1] (analytic) = 0.9807767752059635 " " y[1] (numeric) = 0.9807767752059632 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.395950187723427700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0097524449091468 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0097524449091462 " " Order of pole (six term test) = 0.9999999999999938 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.12999999999999834 " " y[1] (analytic) = 0.9833808634083986 " " y[1] (numeric) = 0.9833808634083981 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.51594317496528400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0084145972763383 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.008414597276338 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.11999999999999834 " " y[1] (analytic) = 0.9858044164037859 " " y[1] (numeric) = 0.9858044164037856 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.37863070853927500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0071742649611335 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0071742649611333 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = -0.10999999999999835 " " y[1] (analytic) = 0.9880446596186152 " " y[1] (numeric) = 0.9880446596186149 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.370970169669361700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0060318086422515 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0060318086422526 " " Order of pole (six term test) = 1.0000000000000124 " " " " "TOP MAIN SOLVE Loop" x[1] = -9.99999999999983600E-2 " " y[1] (analytic) = 0.9900990099009905 " " y[1] (numeric) = 0.9900990099009902 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.36397576461422300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0049875621120887 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0049875621120876 " " Order of pole (six term test) = 0.9999999999999902 " " " " "TOP MAIN SOLVE Loop" x[1] = -8.99999999999983600E-2 " " y[1] (analytic) = 0.9919650828290847 " " y[1] (numeric) = 0.9919650828290845 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.2384316622492400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0040418317978588 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0040418317978574 " " Order of pole (six term test) = 0.9999999999999876 " " " " "TOP MAIN SOLVE Loop" x[1] = -7.99999999999983600E-2 " " y[1] (analytic) = 0.9936406995230527 " " y[1] (numeric) = 0.9936406995230525 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.234656903965514500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.003194896318756 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0031948963187571 " " Order of pole (six term test) = 1.0000000000000107 " " " " "TOP MAIN SOLVE Loop" x[1] = -6.99999999999983700E-2 " " y[1] (analytic) = 0.9951238929246694 " " y[1] (numeric) = 0.9951238929246691 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.346989352337458300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0024470060806205 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.00244700608062 " " Order of pole (six term test) = 0.9999999999999956 " " " " "TOP MAIN SOLVE Loop" x[1] = -5.99999999999983700E-2 " " y[1] (analytic) = 0.9964129135113593 " " y[1] (numeric) = 0.9964129135113591 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.22843965502761400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0017983829094554 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0017983829094566 " " Order of pole (six term test) = 1.0000000000000107 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.999999999999837000E-2 " " y[1] (analytic) = 0.9975062344139651 " " y[1] (numeric) = 0.997506234413965 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.112998582186719400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0012492197250393 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0012492197250407 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.99999999999983650E-2 " " y[1] (analytic) = 0.9984025559105433 " " y[1] (numeric) = 0.998402555910543 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.223998762929113300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0007996802557442 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0007996802557446 " " Order of pole (six term test) = 1.0000000000000044 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.99999999999983600E-2 " " y[1] (analytic) = 0.9991008092716556 " " y[1] (numeric) = 0.9991008092716555 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.11122222534731900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0004498987955368 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0004498987955368 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.99999999999983580E-2 " " y[1] (analytic) = 0.9996001599360256 " " y[1] (numeric) = 0.9996001599360255 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.110667113835006500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.000199980003999 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0001999800039985 " " Order of pole (six term test) = 0.9999999999999947 " " " " "TOP MAIN SOLVE Loop" x[1] = -9.99999999999835900E-3 " " y[1] (analytic) = 0.9999000099990001 " " y[1] (numeric) = 0.999900009999 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.110334046927619000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0000499987500624 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0000499987500633 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6410484082740595000000000000000E-15 " " y[1] (analytic) = 1. " " y[1] (numeric) = 0.9999999999999999 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.110223024625156500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1. " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6410484082740592000000000000000E-15 " " Order of pole (three term test) = 11.999999999999998 " " Radius of convergence (six term test) for eq 1 = 0.9999999999999998 " " Order of pole (six term test) = 0.9999999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000164100E-2 " " y[1] (analytic) = 0.9999000099990001 " " y[1] (numeric) = 0.999900009999 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.110334046927619000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0000499987500624 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0000499987500637 " " Order of pole (six term test) = 1.0000000000000107 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000016410E-2 " " y[1] (analytic) = 0.9996001599360256 " " y[1] (numeric) = 0.9996001599360255 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.110667113835006500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.000199980003999 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0001999800039998 " " Order of pole (six term test) = 1.000000000000007 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.000000000000164000E-2 " " y[1] (analytic) = 0.9991008092716553 " " y[1] (numeric) = 0.9991008092716553 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.000449898795537 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0004498987955368 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.000000000000164500E-2 " " y[1] (analytic) = 0.998402555910543 " " y[1] (numeric) = 0.9984025559105429 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.111999381464556900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0007996802557444 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0007996802557448 " " Order of pole (six term test) = 1.0000000000000044 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000016400E-2 " " y[1] (analytic) = 0.9975062344139649 " " y[1] (numeric) = 0.9975062344139649 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0012492197250393 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0012492197250409 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.00000000000016500E-2 " " y[1] (analytic) = 0.9964129135113589 " " y[1] (numeric) = 0.9964129135113589 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0017983829094557 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0017983829094557 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000016400E-2 " " y[1] (analytic) = 0.995123892924669 " " y[1] (numeric) = 0.9951238929246689 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.115663117445820000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0024470060806208 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.002447006080621 " " Order of pole (six term test) = 1.0000000000000027 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000016400E-2 " " y[1] (analytic) = 0.9936406995230522 " " y[1] (numeric) = 0.9936406995230521 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.117328451982757700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0031948963187562 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.003194896318755 " " Order of pole (six term test) = 0.9999999999999858 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000016300E-2 " " y[1] (analytic) = 0.9919650828290842 " " y[1] (numeric) = 0.991965082829084 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.23843166224924100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.004041831797859 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0040418317978586 " " Order of pole (six term test) = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000163 " " y[1] (analytic) = 0.9900990099009899 " " y[1] (numeric) = 0.9900990099009896 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.24265050974281680000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0049875621120892 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0049875621120892 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000162 " " y[1] (analytic) = 0.9880446596186143 " " y[1] (numeric) = 0.9880446596186143 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.006031808642252 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0060318086422517 " " Order of pole (six term test) = 1.0000000000000009 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000162 " " y[1] (analytic) = 0.9858044164037851 " " y[1] (numeric) = 0.985804416403785 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.126210236179759200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.007174264961134 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0071742649611344 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000161 " " y[1] (analytic) = 0.9833808634083977 " " y[1] (numeric) = 0.9833808634083976 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.128985793741322100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0084145972763388 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0084145972763388 " " Order of pole (six term test) = 1.0000000000000018 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000162 " " y[1] (analytic) = 0.9807767752059626 " " y[1] (numeric) = 0.9807767752059626 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0097524449091473 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0097524449091462 " " Order of pole (six term test) = 0.999999999999992 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000163 " " y[1] (analytic) = 0.9779951100244495 " " y[1] (numeric) = 0.9779951100244494 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.13520304267922300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0111874208078344 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0111874208078329 " " Order of pole (six term test) = 0.9999999999999867 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000164 " " y[1] (analytic) = 0.975039001560062 " " y[1] (numeric) = 0.9750390015600618 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.13864473405556110000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0127191120937733 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0127191120937729 " " Order of pole (six term test) = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000165 " " y[1] (analytic) = 0.9719117504130619 " " y[1] (numeric) = 0.9719117504130619 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0143470806385755 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0143470806385775 " " Order of pole (six term test) = 1.0000000000000169 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000166 " " y[1] (analytic) = 0.9686168151879111 " " y[1] (numeric) = 0.968616815187911 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.146194250623012300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0160708636704434 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0160708636704443 " " Order of pole (six term test) = 1.000000000000008 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000167 " " y[1] (analytic) = 0.965157803300839 " " y[1] (numeric) = 0.965157803300839 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0178899744078438 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0178899744078413 " " Order of pole (six term test) = 0.9999999999999787 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000168 " " y[1] (analytic) = 0.9615384615384609 " " y[1] (numeric) = 0.9615384615384608 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.154631945610163600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0198039027185573 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0198039027185595 " " Order of pole (six term test) = 1.0000000000000222 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000169 " " y[1] (analytic) = 0.9577626664112626 " " y[1] (numeric) = 0.9577626664112625 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.159183860011126600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0218121158021178 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.021812115802118 " " Order of pole (six term test) = 1.0000000000000018 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000017 " " y[1] (analytic) = 0.953834414345669 " " y[1] (numeric) = 0.9538344143456687 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.327915638034029600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0239140588936166 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0239140588936149 " " Order of pole (six term test) = 0.9999999999999822 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000017 " " y[1] (analytic) = 0.949757811758001 " " y[1] (numeric) = 0.9497578117580008 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.337907645255656300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.026109155986828 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0261091559868258 " " Order of pole (six term test) = 0.9999999999999796 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000017 " " y[1] (analytic) = 0.9455370650529494 " " y[1] (numeric) = 0.9455370650529491 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.52251561253069900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0283968105745958 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.028396810574595 " " Order of pole (six term test) = 0.9999999999999956 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000017 " " y[1] (analytic) = 0.9411764705882345 " " y[1] (numeric) = 0.9411764705882343 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.359223927328459600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0307764064044156 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0307764064044151 " " Order of pole (six term test) = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.26000000000000173 " " y[1] (analytic) = 0.9366804046459339 " " y[1] (numeric) = 0.9366804046459337 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.370548202179636500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0332473082471596 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0332473082471605 " " Order of pole (six term test) = 1.000000000000008 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000174 " " y[1] (analytic) = 0.9320533134495286 " " y[1] (numeric) = 0.9320533134495282 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.57347484936099400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0358088626768942 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0358088626768902 " " Order of pole (six term test) = 0.9999999999999654 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000175 " " y[1] (analytic) = 0.9272997032640942 " " y[1] (numeric) = 0.9272997032640938 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.591793529267309000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.038460398859774 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0384603988597778 " " Order of pole (six term test) = 1.0000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000176 " " y[1] (analytic) = 0.9224241306152561 " " y[1] (numeric) = 0.9224241306152557 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.610778342988400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.041201229350024 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0412012293500224 " " Order of pole (six term test) = 0.9999999999999885 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000177 " " y[1] (analytic) = 0.9174311926605496 " " y[1] (numeric) = 0.9174311926605493 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.63042929052426500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0440306508910555 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0440306508910593 " " Order of pole (six term test) = 1.0000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3100000000000018 " " y[1] (analytic) = 0.9123255177447304 " " y[1] (numeric) = 0.9123255177447301 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.433830914583270700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.046947945219819 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0469479452198236 " " Order of pole (six term test) = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000018 " " y[1] (analytic) = 0.907111756168359 " " y[1] (numeric) = 0.9071117561683587 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.67172958704032160000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0499523798725354 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0499523798725339 " " Order of pole (six term test) = 0.9999999999999858 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000018 " " y[1] (analytic) = 0.9017945711966805 " " y[1] (numeric) = 0.9017945711966802 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.69337893602051200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.053043208990021 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.053043208990025 " " Order of pole (six term test) = 1.00000000000004 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000018 " " y[1] (analytic) = 0.8963786303334519 " " y[1] (numeric) = 0.8963786303334516 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.715694418815478400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.056219674120872 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0562196741208718 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000018 " " y[1] (analytic) = 0.890868596881959 " " y[1] (numeric) = 0.8908685968819586 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.738676035425218500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0594810050208552 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0594810050208563 " " Order of pole (six term test) = 1.0000000000000115 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000018 " " y[1] (analytic) = 0.8852691218130302 " " y[1] (numeric) = 0.8852691218130299 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.76232378584973500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0628264204469144 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0628264204469144 " " Order of pole (six term test) = 1.0000000000000009 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000018 " " y[1] (analytic) = 0.8795848359574271 " " y[1] (numeric) = 0.8795848359574268 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.78663767008902600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0662551289442885 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0662551289442888 " " Order of pole (six term test) = 1.0000000000000027 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.38000000000000184 " " y[1] (analytic) = 0.8738203425375732 " " y[1] (numeric) = 0.8738203425375729 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.811617688143092400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0697663296253073 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0697663296253068 " " Order of pole (six term test) = 0.9999999999999956 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000185 " " y[1] (analytic) = 0.8679802100512097 " " y[1] (numeric) = 0.8679802100512094 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.837263840011933500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.073359212938521 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0733592129385203 " " Order of pole (six term test) = 0.999999999999992 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000185 " " y[1] (analytic) = 0.8620689655172403 " " y[1] (numeric) = 0.8620689655172399 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.151434834260733000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0770329614269014 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0770329614269023 " " Order of pole (six term test) = 1.0000000000000062 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000186 " " y[1] (analytic) = 0.8560910880917719 " " y[1] (numeric) = 0.8560910880917715 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.18740606025858800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0807867504739321 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0807867504739315 " " Order of pole (six term test) = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000187 " " y[1] (analytic) = 0.8500510030601824 " " y[1] (numeric) = 0.8500510030601821 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.918199098507108600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0846197490365006 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0846197490365008 " " Order of pole (six term test) = 1.0000000000000018 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4300000000000019 " " y[1] (analytic) = 0.8439530762089617 " " y[1] (numeric) = 0.8439530762089613 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.94650978563504950000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.088531120363585 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0885311203635843 " " Order of pole (six term test) = 0.9999999999999956 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000019 " " y[1] (analytic) = 0.8378016085790873 " " y[1] (numeric) = 0.837801608579087 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.650324404385177600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0925200226998137 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0925200226998142 " " Order of pole (six term test) = 1.0000000000000027 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000019 " " y[1] (analytic) = 0.8316008316008304 " " y[1] (numeric) = 0.8316008316008302 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.670086374223505400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0965856099730662 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0965856099730664 " " Order of pole (six term test) = 1.0000000000000018 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000019 " " y[1] (analytic) = 0.8253549026081203 " " y[1] (numeric) = 0.8253549026081201 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.690292433271683000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.100727032465362 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1007270324653617 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000019 " " y[1] (analytic) = 0.8190679007289692 " " y[1] (numeric) = 0.819067900728969 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.710942581529711700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1049434374663718 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1049434374663707 " " Order of pole (six term test) = 0.9999999999999902 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000019 " " y[1] (analytic) = 0.8127438231469428 " " y[1] (numeric) = 0.8127438231469426 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.732036818997589700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1092339699089646 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.109233969908964 " " Order of pole (six term test) = 0.9999999999999938 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.49000000000000193 " " y[1] (analytic) = 0.8063865817272787 " " y[1] (numeric) = 0.8063865817272786 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.376787572837658800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1135977729862798 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1135977729862796 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000019 " " y[1] (analytic) = 0.7999999999999988 " " y[1] (numeric) = 0.7999999999999986 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.77555756156289500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1180339887498956 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1180339887498933 " " Order of pole (six term test) = 0.9999999999999796 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000019 " " y[1] (analytic) = 0.7935878104912296 " " y[1] (numeric) = 0.7935878104912295 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.39899203333016200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1225417586887367 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.122541758688737 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000019 " " y[1] (analytic) = 0.7871536523929459 " " y[1] (numeric) = 0.7871536523929458 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.41042733048380100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1271202242884306 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1271202242884306 " " Order of pole (six term test) = 1.0000000000000009 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000019 " " y[1] (analytic) = 0.780701069560464 " " y[1] (numeric) = 0.7807010695604639 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.422084672242365200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1317685275708995 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1317685275708969 " " Order of pole (six term test) = 0.9999999999999787 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000019 " " y[1] (analytic) = 0.7742335088262607 " " y[1] (numeric) = 0.7742335088262606 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.433964058605854400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1364858116140306 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.13648581161403 " " Order of pole (six term test) = 0.9999999999999956 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000019 " " y[1] (analytic) = 0.767754318618041 " " y[1] (numeric) = 0.7677543186180409 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.446065489574268600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1412712210513336 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1412712210513314 " " Order of pole (six term test) = 0.9999999999999831 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000019 " " y[1] (analytic) = 0.7612667478684519 " " y[1] (numeric) = 0.7612667478684517 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.91677793029521600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.146123902551553 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1461239025515566 " " Order of pole (six term test) = 1.0000000000000275 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.570000000000002 " " y[1] (analytic) = 0.7547739452034103 " " y[1] (numeric) = 0.7547739452034102 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.470934485325872000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1510430052782572 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1510430052782608 " " Order of pole (six term test) = 1.0000000000000284 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.580000000000002 " " y[1] (analytic) = 0.7482789583956887 " " y[1] (numeric) = 0.7482789583956886 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.483702050109061700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.156027681329475 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.156027681329473 " " Order of pole (six term test) = 0.999999999999984 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.590000000000002 " " y[1] (analytic) = 0.7417847340701715 " " y[1] (numeric) = 0.7417847340701715 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.161077086157505 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1610770861574962 " " Order of pole (six term test) = 0.9999999999999316 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.600000000000002 " " y[1] (analytic) = 0.7352941176470575 " " y[1] (numeric) = 0.7352941176470575 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.166190378969061 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1661903789690593 " " Order of pole (six term test) = 0.9999999999999849 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.610000000000002 " " y[1] (analytic) = 0.7288098535092182 " " y[1] (numeric) = 0.7288098535092181 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.5233370120881798000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1713667231059632 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1713667231059595 " " Order of pole (six term test) = 0.9999999999999689 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.620000000000002 " " y[1] (analytic) = 0.7223345853799467 " " y[1] (numeric) = 0.7223345853799467 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1766052864066192 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.176605286406619 " " Order of pole (six term test) = 0.9999999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.630000000000002 " " y[1] (analytic) = 0.7158708568974145 " " y[1] (numeric) = 0.7158708568974144 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.55087054309888400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.181905241548578 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.181905241548583 " " Order of pole (six term test) = 1.0000000000000409 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.640000000000002 " " y[1] (analytic) = 0.7094211123723029 " " y[1] (numeric) = 0.7094211123723029 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1872657663724675 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1872657663724548 " " Order of pole (six term test) = 0.999999999999897 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.650000000000002 " " y[1] (analytic) = 0.7029876977152887 " " y[1] (numeric) = 0.7029876977152887 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1926860441876574 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.192686044187659 " " Order of pole (six term test) = 1.0000000000000133 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.660000000000002 " " y[1] (analytic) = 0.6965728615213138 " " y[1] (numeric) = 0.6965728615213138 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1981652640600138 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1981652640600189 " " Order of pole (six term test) = 1.00000000000004 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.670000000000002 " " y[1] (analytic) = 0.6901787562978798 " " y[1] (numeric) = 0.6901787562978798 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2037026210821353 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2037026210821302 " " Order of pole (six term test) = 0.9999999999999609 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.680000000000002 " " y[1] (analytic) = 0.683807439824944 " " y[1] (numeric) = 0.683807439824944 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.209297316626479 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2092973166264864 " " Order of pole (six term test) = 1.0000000000000586 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000021 " " y[1] (analytic) = 0.677460876634373 " " y[1] (numeric) = 0.677460876634373 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2149485585818038 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2149485585818063 " " Order of pole (six term test) = 1.0000000000000204 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000021 " " y[1] (analytic) = 0.6711409395973141 " " y[1] (numeric) = 0.6711409395973141 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2206555615733714 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2206555615733643 " " Order of pole (six term test) = 0.999999999999944 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000021 " " y[1] (analytic) = 0.6648494116082695 " " y[1] (numeric) = 0.6648494116082694 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.66988645133870100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2264175471673597 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.226417547167365 " " Order of pole (six term test) = 1.0000000000000435 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000021 " " y[1] (analytic) = 0.6585879873551094 " " y[1] (numeric) = 0.6585879873551093 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.68576264059084100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2322337440599502 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2322337440599649 " " Order of pole (six term test) = 1.0000000000001181 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000021 " " y[1] (analytic) = 0.6523582751647192 " " y[1] (numeric) = 0.6523582751647191 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.701860874447905500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.238103388251564 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2381033882515278 " " Order of pole (six term test) = 0.9999999999997087 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000021 " " y[1] (analytic) = 0.6461617989144468 " " y[1] (numeric) = 0.6461617989144468 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2440257232067202 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2440257232067127 " " Order of pole (six term test) = 0.9999999999999369 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000021 " " y[1] (analytic) = 0.6399999999999987 " " y[1] (numeric) = 0.6399999999999987 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2500000000000013 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2500000000000027 " " Order of pole (six term test) = 1.0000000000000107 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000021 " " y[1] (analytic) = 0.6338742393509115 " " y[1] (numeric) = 0.6338742393509115 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2560254774486077 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2560254774486088 " " Order of pole (six term test) = 1.0000000000000098 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000021 " " y[1] (analytic) = 0.6277857994852143 " " y[1] (numeric) = 0.6277857994852143 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2621014222319866 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2621014222319844 " " Order of pole (six term test) = 0.9999999999999822 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000021 " " y[1] (analytic) = 0.6217358865953729 " " y[1] (numeric) = 0.6217358865953729 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2682271089990165 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2682271089990176 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000021 " " y[1] (analytic) = 0.6157256326580862 " " y[1] (numeric) = 0.6157256326580862 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2744018204632335 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2744018204632388 " " Order of pole (six term test) = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000022 " " y[1] (analytic) = 0.6097560975609744 " " y[1] (numeric) = 0.6097560975609743 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.820765760385260300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2806248474865711 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.280624847486573 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000022 " " y[1] (analytic) = 0.6038282712396582 " " y[1] (numeric) = 0.6038282712396581 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.838640351081725600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2868954891520925 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2868954891520963 " " Order of pole (six term test) = 1.000000000000031 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000022 " " y[1] (analytic) = 0.5979430758191807 " " y[1] (numeric) = 0.5979430758191807 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2932130528261783 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2932130528261778 " " Order of pole (six term test) = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000022 " " y[1] (analytic) = 0.5921013677541582 " " y[1] (numeric) = 0.5921013677541582 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2995768542106325 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2995768542106367 " " Order of pole (six term test) = 1.0000000000000346 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000022 " " y[1] (analytic) = 0.5863039399624753 " " y[1] (numeric) = 0.5863039399624753 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.305986217385162 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3059862173851604 " " Order of pole (six term test) = 0.9999999999999885 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000022 " " y[1] (analytic) = 0.5805515239477491 " " y[1] (numeric) = 0.5805515239477491 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3124404748406702 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.312440474840671 " " Order of pole (six term test) = 1.000000000000008 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000022 " " y[1] (analytic) = 0.5748447919061841 " " y[1] (numeric) = 0.5748447919061841 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3189389675038052 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3189389675038081 " " Order of pole (six term test) = 1.0000000000000249 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000022 " " y[1] (analytic) = 0.5691843588138186 " " y[1] (numeric) = 0.5691843588138186 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3254810447531884 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3254810447531897 " " Order of pole (six term test) = 1.0000000000000124 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000022 " " y[1] (analytic) = 0.5635707844905308 " " y[1] (numeric) = 0.5635707844905308 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3320660644277384 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3320660644277396 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000022 " " y[1] (analytic) = 0.5580045756375189 " " y[1] (numeric) = 0.558004575637519 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.98963068243074780000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3386933928275002 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3386933928275013 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000022 " " y[1] (analytic) = 0.5524861878453027 " " y[1] (numeric) = 0.5524861878453027 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3453624047073725 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3453624047073722 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000023 " " y[1] (analytic) = 0.5470160275696065 " " y[1] (numeric) = 0.5470160275696067 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.02959871131725300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.35207248326412 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3520724832641198 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000023 " " y[1] (analytic) = 0.541594454072789 " " y[1] (numeric) = 0.5415944540727892 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.049915792667893800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3588230201170437 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3588230201170435 " " Order of pole (six term test) = 0.9999999999999991 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000023 " " y[1] (analytic) = 0.5362217813287563 " " y[1] (numeric) = 0.5362217813287564 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.070454918623459200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3656134152826722 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3656134152826704 " " Order of pole (six term test) = 0.9999999999999893 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000023 " " y[1] (analytic) = 0.530898279889572 " " y[1] (numeric) = 0.5308982798895721 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.091216089183949900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3724430771438225 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3724430771438216 " " Order of pole (six term test) = 0.9999999999999947 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000023 " " y[1] (analytic) = 0.5256241787122196 " " y[1] (numeric) = 0.5256241787122197 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.11219930434936500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3793114224133738 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.379311422413373 " " Order of pole (six term test) = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000023 " " y[1] (analytic) = 0.5203996669442119 " " y[1] (numeric) = 0.520399666944212 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.133404564119705800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3862178760930781 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.386217876093077 " " Order of pole (six term test) = 0.9999999999999938 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000023 " " y[1] (analytic) = 0.5152248956669574 " " y[1] (numeric) = 0.5152248956669575 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.154831868494971600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3931618714277263 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3931618714277216 " " Order of pole (six term test) = 0.9999999999999734 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000023 " " y[1] (analytic) = 0.5100999795959996 " " y[1] (numeric) = 0.5100999795959997 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.176481217475162000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4001428498549726 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4001428498549686 " " Order of pole (six term test) = 0.999999999999976 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000023 " " y[1] (analytic) = 0.5050249987374363 " " y[1] (numeric) = 0.5050249987374364 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.198352611060277700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4071602609511131 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.407160260951113 " " Order of pole (six term test) = 1.0000000000000018 " " "Finished!" "diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; " Iterations = 300 "Total Elapsed Time "= 11 Seconds "Elapsed Time(since restart) "= 11 Seconds "Time to Timeout "= 9 Minutes 48 Seconds Percent Done = 100.3333333333334 "%" (%o229) true (%o229) diffeq.max