(%i1) batch("temp/diffeq.sin_sqrt_lin.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sin_sqrt_lin.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([40],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],convfloat),[jjj_att],fixnum), convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,40,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[40],convfloat) (%i173) completearray(array_norms,[40],convfloat) (%i174) completearray(array_fact_1,[40],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[40],convfloat) (%i184) completearray(array_x,[40],convfloat) (%i185) completearray(array_tmp0,[40],convfloat) (%i186) completearray(array_tmp1,[40],convfloat) (%i187) completearray(array_tmp2,[40],convfloat) (%i188) completearray(array_tmp3,[40],convfloat) (%i189) completearray(array_tmp4_g,[40],convfloat) (%i190) completearray(array_tmp4,[40],convfloat) (%i191) completearray(array_tmp5,[40],convfloat) (%i192) completearray(array_m1,[40],convfloat) (%i193) completearray(array_y_higher,[2,40],convfloat) (%i194) completearray(array_y_higher_work,[2,40],convfloat) (%i195) completearray(array_y_higher_work2,[2,40],convfloat) (%i196) completearray(array_y_set_initial,[2,40],convfloat) (%i197) completearray(array_given_rad_poles,[2,3],convfloat) (%i198) completearray(array_given_ord_poles,[2,3],convfloat) (%i199) completearray(array_rad_test_poles,[2,4],convfloat) (%i200) completearray(array_ord_test_poles,[2,4],convfloat) (%i201) completearray(array_fact_2,[40,40],convfloat) (%i202) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i203) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i204) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i205) 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)) (%i206) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i207) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i208) 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) (%i209) 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) (%i210) zero_ats_ar(arr_a):=( block(mode_declare([iii],fixnum),iii:1, while iii <= ats_max_terms do (arr_a[iii]:glob__0,iii:1+iii)),0) (%i211) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:glob__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 <= ats_max_terms and iii_ats <= ats_max_terms then ret_ats :c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%i212) 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:glob__0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= ats_max_terms do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= ats_max_terms and iii_att <= ats_max_terms then ret_att :c(arr_aa[iii_att])*c(arr_bb[lll_att]) *c(al_att) +ret_att,iii_att:1+iii_att), ret_att:ret_att/c(mmm_att)),ret_att) (%i213) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i214) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i215) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i216) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i217) log_revs(file,revs):=printf(file,revs) (%i218) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i219) logitem_h_reason(file):=(printf(file,""), if glob_h_reason = 1 then printf(file,"Max H") elseif glob_h_reason = 2 then printf(file,"Display_interval") elseif glob_h_reason = 3 then printf(file,"Optimal") elseif glob_h_reason = 4 then printf(file,"Pole Accuracy") elseif glob_h_reason = 5 then printf(file,"Min H (Pole)") elseif glob_h_reason = 6 then printf(file,"Pole") elseif glob_h_reason = 7 then printf(file,"Opt Iter") else printf(file,"Impossible"), printf(file,""),0) (%i220) logstart(file):=(printf(file,""),0) (%i221) logend(file):=(printf(file,"~%"),0) (%i222) 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) (%i223) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:c(clock_sec2), sub1:c(t_end2-t_start2),sub2:c(t2-t_start2), if sub1 = glob__0 then sec_left:glob__0 else (if sub2 > glob__0 then (rrr:sub1/sub2, sec_left:rrr*c(ms2)-c(ms2)) else sec_left:glob__0),sec_left) (%i224) 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:glob__100*sub2/sub1 else rrr:0.0,rrr) (%i225) comp_rad_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%i226) comp_ord_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret :abs(term2)*c(last_no) *log(abs(term1*glob_h/term2)) /log(c(last_no)) +glob__1 else ret:glob_larger_float,ret) (%i227) c(in_val):=(ret:in_val,ret) (%i228) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3-term1*term3*c(last_no) +glob__m2*term2*term2 +term2*term2*c(last_no)), if abs(temp) > glob__0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%i229) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*c(last_no*last_no) +term2*term2*c(last_no*last_no) +glob__4*term2*term2 -glob__4*term2*term2*c(last_no) -glob__3*term1*term3 +glob__4*term1*term3*c(last_no)) /(term1*term3-term1*term3*c(last_no) -glob__2*term2*term2 +term2*term2*c(last_no))), ret) (%i230) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # glob__0 and term4 # glob__0 and term3 # glob__0 and term2 # glob__0 and term1 # glob__0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :c(last_no-3)*rm2 -glob__2*c(last_no-2)*rm1 +c(last_no-1)*rm0, nr2 :c(last_no-4)*rm3 -glob__2*c(last_no-3)*rm2 +c(last_no-2)*rm1, dr1 :(-glob__1)/rm3+glob__2/rm2 +glob__m1/rm1, dr2 :(-glob__1)/rm4+glob__2/rm3 +glob__m1/rm2, ds1 :glob__5/rm3-glob__8/rm2 +glob__3/rm1, ds2 :glob__5/rm4-glob__8/rm3 +glob__3/rm2, if abs(nr1*dr2-nr2*dr1) = glob__0 or abs(dr1) = glob__0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) > glob__0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(glob__2*dr1) -c(last_no)/glob__2, if abs(rcs) # glob__0 then (if rcs > glob__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) (%i231) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i232) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i233) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_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) (%i234) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i235) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i236) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms and mmm <= ats_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) (%i237) log10(x):=log(x)/glob_log_10 (%i238) c(x):=x (%i239) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y) else x^y (%i240) 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(glob__10, c(-glob_desired_digits_correct)) *c(abs(c(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 :c( abs(desired_abs_gbl_error) /sqrt(c(estimated_steps)) /c(ats_max_terms)), omniout_float(always,"step_error",32, step_error,32,""), step_error) (%i241) exact_soln_y(x):=block( sin(sqrt(c(3.0)+c(2.0)*c(x))) -sqrt(c(3.0)+c(2.0)*c(x))*cos(sqrt(c(3.0)+c(2.0)*c(x)))) (%o241) exact_soln_y(x) := block(sin(sqrt(c(3.0) + c(2.0) c(x))) - sqrt(c(3.0) + c(2.0) c(x)) cos(sqrt(c(3.0) + c(2.0) c(x)))) (%i242) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 1 or glob_type_given_pole = 2 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])), 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," "), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given) elseif glob_type_given_pole = 3 then omniout_str(always, "NO POLE (given) for Equation 1") elseif glob_type_given_pole = 5 then omniout_str(always, "SOME 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] > glob__small 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] > glob__small 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) (%i243) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i244) 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 < glob__1 then (min_size:glob__1, omniout_float(always,"min_size",32,min_size, 32,"")),min_size) (%i245) 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:glob__small, no_terms:ats_max_terms,hn_div_ho:glob__0_5, hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__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) (%i246) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:ats_max_terms, hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25, hn_div_ho_3:glob__0_125, est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3) +c(abs(array_y[no_terms-1])) *c(hn_div_ho_2) +c(abs(array_y[no_terms-2])) *c(hn_div_ho) +c(abs(array_y[no_terms-3])), if glob_prec*c(abs(array_y[1])) > c(est_tmp) then est_tmp :c(glob_prec)*c(abs(array_y[1])), if c(est_tmp) >= c(array_max_est_error[1]) then array_max_est_error[1]:c(est_tmp)) (%i247) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display -glob_h/glob__10 then ret:true else ret:false, return(ret)) (%i248) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_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, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(24) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i249) 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 :c(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 c(percent_done) < glob__100 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) (%i250) 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),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+ats_max_terms,cnt:0, while last_no < ats_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), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, 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)), 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+ats_max_terms,cnt:0, while last_no < ats_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), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, 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)), 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+ats_max_terms,cnt:0, while last_no < ats_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), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, 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, omniout_str(always, "SETTING H FOR POLE"), glob_h_reason:6, if glob_check_sign*glob_min_h > glob_check_sign*h_new then ( omniout_str(always, "SETTING H FOR MIN H"), h_new:glob_min_h,glob_h_reason:5), term:1,ratio:c(1.0), while term <= ats_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) (%i251) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_2D0[1]*array_x[1], array_tmp2[1]:array_const_3D0[1]+array_tmp1[1], array_tmp3[1]:sqrt(array_tmp2[1]), array_tmp4_g[1]:cos(array_tmp3[1]), array_tmp4[1]:sin(array_tmp3[1]), array_tmp5[1]:array_tmp4[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp5[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_const_2D0[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_tmp2[2]/array_tmp3[1]/glob__2, array_tmp4_g[2]:neg(att(1,array_tmp4,array_tmp3,1)), array_tmp4[2]:att(1,array_tmp4_g,array_tmp3,1), array_tmp5[2]:array_tmp4[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp5[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary),0)), kkk:3,array_tmp3[3]:0, array_tmp3[3]:neg(ats(3,array_tmp3,array_tmp3,2)) /array_tmp3[1] /glob__2, array_tmp4_g[3]:neg(att(2,array_tmp4,array_tmp3,1)), array_tmp4[3]:att(2,array_tmp4_g,array_tmp3,1), array_tmp5[3]:array_tmp4[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp5[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary),0)), kkk:4,array_tmp3[4]:0, array_tmp3[4]:neg(ats(4,array_tmp3,array_tmp3,2)) /array_tmp3[1] /glob__2, array_tmp4_g[4]:neg(att(3,array_tmp4,array_tmp3,1)), array_tmp4[4]:att(3,array_tmp4_g,array_tmp3,1), array_tmp5[4]:array_tmp4[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp5[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary),0)), kkk:5,array_tmp3[5]:0, array_tmp3[5]:neg(ats(5,array_tmp3,array_tmp3,2)) /array_tmp3[1] /glob__2, array_tmp4_g[5]:neg(att(4,array_tmp4,array_tmp3,1)), array_tmp4[5]:att(4,array_tmp4_g,array_tmp3,1), array_tmp5[5]:array_tmp4[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp5[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp3[kkk]:0, array_tmp3[kkk] :neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] /glob__2, array_tmp4[kkk] :att(kkk-1,array_tmp4_g,array_tmp3,1), array_tmp4_g[kkk] :neg(att(kkk-1,array_tmp4,array_tmp3,1)), array_tmp5[kkk]:array_tmp4[kkk],order_d:1, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp5[kkk])*expt(glob_h,c(order_d)) *c( factorial_3( kkk-1, -1+order_d+kkk)), array_y[order_d+kkk]:c(temporary), array_y_higher[1,order_d+kkk]:c(temporary), term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= ats_max_terms and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :c(temporary)*c(adj2) /c(glob_h) else temporary:c(temporary), array_y_higher[adj3,term] :c(temporary)),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%i252) exact_soln_y(x):=block( sin(sqrt(c(3.0)+c(2.0)*c(x))) -sqrt(c(3.0)+c(2.0)*c(x))*cos(sqrt(c(3.0)+c(2.0)*c(x)))) (%o252) exact_soln_y(x) := block(sin(sqrt(c(3.0) + c(2.0) c(x))) - sqrt(c(3.0) + c(2.0) c(x)) cos(sqrt(c(3.0) + c(2.0) c(x)))) (%i253) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],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,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:40, glob_html_log:true,term:1, while term <= 40 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(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 <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 40 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp4_g[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp5[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_set_initial[ord,term]:c(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]:c(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]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 40 do (term:1, while term <= 40 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), 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_g),zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),zero_ats_ar(array_m1), zero_ats_ar(array_const_1),array_const_1[1]:c(1), zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0), zero_ats_ar(array_const_2D0),array_const_2D0[1]:c(2.0), zero_ats_ar(array_const_3D0),array_const_3D0[1]:c(3.0), zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_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, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false, array_y_set_initial[1,31]:false, array_y_set_initial[1,32]:false, array_y_set_initial[1,33]:false, array_y_set_initial[1,34]:false, array_y_set_initial[1,35]:false, array_y_set_initial[1,36]:false, array_y_set_initial[1,37]:false, array_y_set_initial[1,38]:false, array_y_set_initial[1,39]:false, array_y_set_initial[1,40]:false,glob_log_10:log(10.0), glob_orig_start_sec:elapsed_time_seconds(), 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/sin_sqrt_linpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:40,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(2.0),"), omniout_str(always,"x_end:c(3.0),"), 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_h:c(0.0001),"), omniout_str(always,"glob_upper_ratio_limit:c(1.001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999),"), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,"glob_type_given_pole:1,"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,1]:c(-1.5),"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,2]:c(0.0),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,1]:c(0.5),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,2]:c(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:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), 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,""), omniout_str(always, " (sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0)))) "), 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:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(2.0),x_end:c(3.0), array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_max_h:c(1.0E-4), glob_upper_ratio_limit:c(1.001), glob_lower_ratio_limit:c(0.999),glob_type_given_pole:1, array_given_rad_poles[1,1]:c(-1.5), array_given_rad_poles[1,2]:c(0.0), array_given_ord_poles[1,1]:c(0.5), array_given_ord_poles[1,2]:c(0.0), glob_desired_digits_correct:8,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), found_h:false,glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), chk_data(),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:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(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,c(term_no-1)) /c(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 < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval, found_h:true), if glob_look_poles then check_for_pole(), if not found_h then (est_answer:est_size_answer(), 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 :test_suggested_h(), omniout_float(always, "estimated_step_error", 32, estimated_step_error, 32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(always, "Double H and LOOP"), glob_h:glob_h*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), 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 glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(always, "SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(x_start), glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(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 < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(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_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_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(), track_estimated_error(),atomall(), track_estimated_error(), 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:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_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,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_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 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; "), 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, "2015-04-24T22:28:58-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sin_sqrt_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; "), 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_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_min_good_digits # -16 then ( logitem_integer(html_log_file, glob_min_good_digits), 0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_good_digits # -16 then ( logitem_integer(html_log_file, glob_good_digits),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_str(html_log_file,"NA"), logitem_str(html_log_file,"NA"), logitem_integer(html_log_file, ats_max_terms), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 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 c(glob_percent_done) < glob__100 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 308.maple.seems.ok "), logitem_str(html_log_file, "sin_sqrt_lin diffeq.max"), logitem_str(html_log_file, "sin_sqrt_lin maxima results"), logitem_str(html_log_file, "Poor Accuracy & PROBLEM - found complex singularity instead of real - COULD BE RIGHT!!!"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i254) main():=(glob_iolevel:2,compile(all),main_prog()) (%i255) 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 ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. 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 ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_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 glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason 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 glob__0 in translation. 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__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 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 glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 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 glob__0 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. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. 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 ats_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. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms 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 always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles 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 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: encountered undefined variable glob__small 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__1 in translation. warning: encountered undefined variable glob__m1 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 glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error 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. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 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 closed_form_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 glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct 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 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 glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher 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 glob__0 in translation. warning: encountered undefined variable glob_large_float 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 always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio 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_const_2D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_3D0 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp4_g in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable glob__2 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: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_fact_1 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 array_m1 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. 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 glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_max_h (declared type convfloat) assigned type any. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. 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_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. 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__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. 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: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. 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_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 info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float 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: encountered undefined variable glob__100 in translation. 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 : $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__PI is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST 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: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. "##############ECHO OF PROBLEM#################" "##############temp/sin_sqrt_linpostode.ode#################" "diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:40," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(2.0)," "x_end:c(3.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_h:c(0.0001)," "glob_upper_ratio_limit:c(1.001)," "glob_lower_ratio_limit:c(0.999)," "" "" "" "" "" "" "" "" "glob_type_given_pole:1," "" "array_given_rad_poles[1,1]:c(-1.5)," "" "array_given_rad_poles[1,2]:c(0.0)," "" "array_given_ord_poles[1,1]:c(0.5)," "" "array_given_ord_poles[1,2]:c(0.0)," "" "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" "" " (sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0)))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 2. " " y[1] (closed_form) = 2.80289196959102 " " y[1] (numeric) = 2.80289196959102 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 15 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.009999999999999 " " y[1] (closed_form) = 2.807633062296781 " " y[1] (numeric) = 2.807634725094881 " " absolute error = 1.662798100099394000000E-6 " " relative error = 5.92241957266005500000E-5 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 8 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.019999999999998 " " y[1] (closed_form) = 2.8123408902813747 " " y[1] (numeric) = 2.812344216873596 " " absolute error = 3.3265922212422083000000E-6 " " relative error = 1.18285526222583310000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999999967 " " y[1] (closed_form) = 2.8170154339090177 " " y[1] (numeric) = 2.8170204252635203 " " absolute error = 4.991354502603684300000E-6 " " relative error = 1.77185912527197480000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999999956 " " y[1] (closed_form) = 2.821656674099206 " " y[1] (numeric) = 2.8216633311564765 " " absolute error = 6.657057270320621000000E-6 " " relative error = 2.35927259734596880000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999999945 " " y[1] (closed_form) = 2.8262645923230667 " " y[1] (numeric) = 2.826272915996097 " " absolute error = 8.323673030385947000000E-6 " " relative error = 2.945114570304350000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0599999999999934 " " y[1] (closed_form) = 2.8308391705997296 " " y[1] (numeric) = 2.8308491617741973 " " absolute error = 9.991174467760544000000E-6 " " relative error = 3.5294037794608646000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0699999999999923 " " y[1] (closed_form) = 2.8353803914927247 " " y[1] (numeric) = 2.8353920510271755 " " absolute error = 1.165953445081413500000E-5 " " relative error = 4.1121588079671430000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999991 " " y[1] (closed_form) = 2.839888238106417 " " y[1] (numeric) = 2.839901566832439 " " absolute error = 1.332872602199941500000E-5 " " relative error = 4.69339808628763340000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.08999999999999 " " y[1] (closed_form) = 2.844362694082461 " " y[1] (numeric) = 2.8443776928048625 " " absolute error = 1.499872240140476300000E-5 " " relative error = 5.2731398961914290000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999989 " " y[1] (closed_form) = 2.848803743596285 " " y[1] (numeric) = 2.84882041309327 " " absolute error = 1.666949698497788300000E-5 " " relative error = 5.8514023728200290000E-4 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999988 " " y[1] (closed_form) = 2.8532113713536 " " y[1] (numeric) = 2.8532297123769434 " " absolute error = 1.83410233436376300000E-5 " " relative error = 6.4282035070315920000E-4 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.119999999999987 " " y[1] (closed_form) = 2.857585562586939 " " y[1] (numeric) = 2.8576055758621566 " " absolute error = 2.001327521750084800000E-5 " " relative error = 7.0035611459987430000E-4 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999857 " " y[1] (closed_form) = 2.861926303052219 " " y[1] (numeric) = 2.861947989278741 " " absolute error = 2.168622652209961600000E-5 " " relative error = 7.5774929979753320000E-4 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999846 " " y[1] (closed_form) = 2.866233579025332 " " y[1] (numeric) = 2.8662569388766697 " " absolute error = 2.335985133772311400000E-5 " " relative error = 8.150016631117230000E-4 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999999835 " " y[1] (closed_form) = 2.8705073772987566 " " y[1] (numeric) = 2.8705324114226753 " " absolute error = 2.50341239187434900000E-5 " " relative error = 8.7211494792608530000E-4 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1599999999999824 " " y[1] (closed_form) = 2.874747685178202 " " y[1] (numeric) = 2.8747743941968853 " " absolute error = 2.67090186834018100000E-5 " " relative error = 9.2909088408383760000E-4 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999813 " " y[1] (closed_form) = 2.8789544904792708 " " y[1] (numeric) = 2.878982874989487 " " absolute error = 2.838451021602850000000E-5 " " relative error = 9.8593118821073210000E-4 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.17999999999998 " " y[1] (closed_form) = 2.8831277815241507 " " y[1] (numeric) = 2.8831578420974173 " " absolute error = 3.006057326659928000000E-5 " " relative error = 1.0426375639413356000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.189999999999979 " " y[1] (closed_form) = 2.8872675471383284 " " y[1] (numeric) = 2.88729928432108 " " absolute error = 3.173718275162329400000E-5 " " relative error = 1.0992117021880816000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999978 " " y[1] (closed_form) = 2.891373776647332 " " y[1] (numeric) = 2.8914071909610772 " " absolute error = 3.34143137452613800000E-5 " " relative error = 1.1556552810687336000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999977 " " y[1] (closed_form) = 2.8954464598734897 " " y[1] (numeric) = 2.895481551814975 " " absolute error = 3.5091941485099200000E-5 " " relative error = 1.2119699663392314000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999758 " " y[1] (closed_form) = 2.89948558713272 " " y[1] (numeric) = 2.899522357174089 " " absolute error = 3.67700413690386100000E-5 " " relative error = 1.2681574115152003000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999747 " " y[1] (closed_form) = 2.903491149231342 " " y[1] (numeric) = 2.903529597820296 " " absolute error = 3.84485889539654100000E-5 " " relative error = 1.3242192580522977000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999999736 " " y[1] (closed_form) = 2.9074631374629107 " " y[1] (numeric) = 2.9075032650228647 " " absolute error = 4.01275599539729900000E-5 " " relative error = 1.3801571355084769000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2499999999999725 " " y[1] (closed_form) = 2.91140154360507 " " y[1] (numeric) = 2.9114433505353117 " " absolute error = 4.18069302416945730000E-5 " " relative error = 1.4359726618103924000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2599999999999714 " " y[1] (closed_form) = 2.9153063599164413 " " y[1] (numeric) = 2.9153498465922816 " " absolute error = 4.34866758403096300000E-5 " " relative error = 1.491667443196469000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999703 " " y[1] (closed_form) = 2.9191775791335166 " " y[1] (numeric) = 2.9192227459064495 " " absolute error = 4.51667729328697500000E-5 " " relative error = 1.5472430747524565000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.279999999999969 " " y[1] (closed_form) = 2.9230151944675917 " " y[1] (numeric) = 2.923062041665444 " " absolute error = 4.68471978520845770000E-5 " " relative error = 1.6027011402729807000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999968 " " y[1] (closed_form) = 2.9268191996017094 " " y[1] (numeric) = 2.926867727528793 " " absolute error = 4.852792708343045500000E-5 " " relative error = 1.658043212578155800E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999967 " " y[1] (closed_form) = 2.9305895886876296 " " y[1] (numeric) = 2.9306397976248943 " " absolute error = 5.02089372647063200000E-5 " " relative error = 1.7132708537052704000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.309999999999966 " " y[1] (closed_form) = 2.934326356342824 " " y[1] (numeric) = 2.9343782465480057 " " absolute error = 5.18902051815928200000E-5 " " relative error = 1.7683856149615815000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999648 " " y[1] (closed_form) = 2.9380294976474834 " " y[1] (numeric) = 2.938083069355255 " " absolute error = 5.3571707771649100000E-5 " " relative error = 1.8233890372627176000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999637 " " y[1] (closed_form) = 2.9416990081415553 " " y[1] (numeric) = 2.941754261563673 " " absolute error = 5.525342211765150000000E-5 " " relative error = 1.8782826511050274000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999999626 " " y[1] (closed_form) = 2.9453348838218005 " " y[1] (numeric) = 2.9453918191472495 " " absolute error = 5.693532544892577000000E-5 " " relative error = 1.9330679768083883000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3499999999999615 " " y[1] (closed_form) = 2.9489371211388637 " " y[1] (numeric) = 2.9489957385340078 " " absolute error = 5.86173951440116500000E-5 " " relative error = 1.9877465248012452000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999604 " " y[1] (closed_form) = 2.9525057169943785 " " y[1] (numeric) = 2.9525660166030985 " " absolute error = 6.02996087200047300000E-5 " " relative error = 2.0423197954512050000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999593 " " y[1] (closed_form) = 2.9560406687380762 " " y[1] (numeric) = 2.9561026506819195 " " absolute error = 6.19819438432145400000E-5 " " relative error = 2.0967892796168605000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999958 " " y[1] (closed_form) = 2.9595419741649303 " " y[1] (numeric) = 2.95960563854325 " " absolute error = 6.36643783198387300000E-5 " " relative error = 2.151156458519308000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999957 " " y[1] (closed_form) = 2.96300963151231 " " y[1] (numeric) = 2.963074978402409 " " absolute error = 6.53468900990716900000E-5 " " relative error = 2.20542280403317030E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999956 " " y[1] (closed_form) = 2.9664436394571614 " " y[1] (numeric) = 2.966510668914429 " " absolute error = 6.70294572677754300000E-5 " " relative error = 2.2595897786900598000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.409999999999955 " " y[1] (closed_form) = 2.9698439971132 " " y[1] (numeric) = 2.9699127091712576 " " absolute error = 6.87120580575850700000E-5 " " relative error = 2.313658836099666300E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999537 " " y[1] (closed_form) = 2.973210704028132 " " y[1] (numeric) = 2.9732810986989677 " " absolute error = 7.03946708355829300000E-5 " " relative error = 2.36763142081426000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999999526 " " y[1] (closed_form) = 2.97654376018089 " " y[1] (numeric) = 2.976615837454996 " " absolute error = 7.2077274105630810000E-5 " " relative error = 2.421508968551181000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999999515 " " y[1] (closed_form) = 2.9798431659788855 " " y[1] (numeric) = 2.979916925825396 " " absolute error = 7.37598465105904200000E-5 " " relative error = 2.475292906442616000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999504 " " y[1] (closed_form) = 2.983108922255287 " " y[1] (numeric) = 2.9831843646221143 " " absolute error = 7.54423668274384300000E-5 " " relative error = 2.5289846530445353000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999493 " " y[1] (closed_form) = 2.9863410302663085 " " y[1] (numeric) = 2.986418155080279 " " absolute error = 7.71248139703750700000E-5 " " relative error = 2.582585618612266000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999482 " " y[1] (closed_form) = 2.9895394916885256 " " y[1] (numeric) = 2.9896182988555116 " " absolute error = 7.88071669859391500000E-5 " " relative error = 2.6360972051059267000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999947 " " y[1] (closed_form) = 2.9927043086162035 " " y[1] (numeric) = 2.992784798021257 " " absolute error = 8.04894050534521500000E-5 " " relative error = 2.6895208063729364000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999946 " " y[1] (closed_form) = 2.9958354835586456 " " y[1] (numeric) = 2.99591765506613 " " absolute error = 8.21715074845741400000E-5 " " relative error = 2.7428578082987903000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.499999999999945 " " y[1] (closed_form) = 2.99893301943756 " " y[1] (numeric) = 2.999016872891283 " " absolute error = 8.38534537228596800000E-5 " " relative error = 2.7961095889559456000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.509999999999944 " " y[1] (closed_form) = 3.0019969195844434 " " y[1] (numeric) = 3.0020824548077853 " " absolute error = 8.55352233419814900000E-5 " " relative error = 2.84927751870651000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999427 " " y[1] (closed_form) = 3.005027187737983 " " y[1] (numeric) = 3.005114404534027 " " absolute error = 8.72167960439540500000E-5 " " relative error = 2.902362960303397000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999999416 " " y[1] (closed_form) = 3.008023828041478 " " y[1] (numeric) = 3.00811272619314 " " absolute error = 8.88981516617981500000E-5 " " relative error = 2.955367269137614000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999999405 " " y[1] (closed_form) = 3.010986845040275 " " y[1] (numeric) = 3.0110774243104292 " " absolute error = 9.05792701542118600000E-5 " " relative error = 3.008291793217724000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999394 " " y[1] (closed_form) = 3.013916243679221 " " y[1] (numeric) = 3.0140085038108286 " " absolute error = 9.2260131607790900000E-5 " " relative error = 3.061137873399059000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999383 " " y[1] (closed_form) = 3.016812029300137 " " y[1] (numeric) = 3.0169059700163707 " " absolute error = 9.39407162339200900000E-5 " " relative error = 3.1139068434340994000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5699999999999372 " " y[1] (closed_form) = 3.019674207639305 " " y[1] (numeric) = 3.0197698286436765 " " absolute error = 9.56210043714378300000E-5 " " relative error = 3.166600030212915000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999936 " " y[1] (closed_form) = 3.022502784824975 " " y[1] (numeric) = 3.022600085801456 " " absolute error = 9.730097648086300000E-5 " " relative error = 3.2192187537222544000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.589999999999935 " " y[1] (closed_form) = 3.025297767374884 " " y[1] (numeric) = 3.0253967479880313 " " absolute error = 9.89806131470594200000E-5 " " relative error = 3.271764327282964000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.599999999999934 " " y[1] (closed_form) = 3.0280591621937942 " " y[1] (numeric) = 3.0281598220888744 " " absolute error = 1.00659895080124070000E-4 " " relative error = 3.3242380577266245000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.609999999999933 " " y[1] (closed_form) = 3.030786976571049 " " y[1] (numeric) = 3.0308893153741576 " " absolute error = 1.02338803108725780000E-4 " " relative error = 3.3766412453213446000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999999317 " " y[1] (closed_form) = 3.0334812181781436 " " y[1] (numeric) = 3.033585235496327 " " absolute error = 1.0401731818321380000E-4 " " relative error = 3.4289751840192640000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999999306 " " y[1] (closed_form) = 3.036141895066309 " " y[1] (numeric) = 3.0362475904876858 " " absolute error = 1.0569542137695010000E-4 " " relative error = 3.481241161643459000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999295 " " y[1] (closed_form) = 3.0387690156641187 " " y[1] (numeric) = 3.0388763887579966 " " absolute error = 1.07373093877871640000E-4 " " relative error = 3.5334404597516080000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999284 " " y[1] (closed_form) = 3.041362588775103 " " y[1] (numeric) = 3.0414716390921006 " " absolute error = 1.09050316997816310000E-4 " " relative error = 3.5855743540837043000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999273 " " y[1] (closed_form) = 3.0439226235753827 " " y[1] (numeric) = 3.0440333506475463 " " absolute error = 1.10727072163641080000E-4 " " relative error = 3.637644114408578000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999926 " " y[1] (closed_form) = 3.0464491296113216 " " y[1] (numeric) = 3.046561532952242 " " absolute error = 1.12403340920330660000E-4 " " relative error = 3.6896510047640785000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999925 " " y[1] (closed_form) = 3.048942116797189 " " y[1] (numeric) = 3.0490561959021165 " " absolute error = 1.14079104927444770000E-4 " " relative error = 3.741596283476875000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.689999999999924 " " y[1] (closed_form) = 3.0514015954128375 " " y[1] (numeric) = 3.0515173497588015 " " absolute error = 1.15754345964003140000E-4 " " relative error = 3.793481203457987000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.699999999999923 " " y[1] (closed_form) = 3.0538275761014013 " " y[1] (numeric) = 3.0539450051473223 " " absolute error = 1.17429045920935950000E-4 " " relative error = 3.84530701208904000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999922 " " y[1] (closed_form) = 3.0562200698670035 " " y[1] (numeric) = 3.0563391730538054 " " absolute error = 1.19103186801972070000E-4 " " relative error = 3.897074951384474400E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999999207 " " y[1] (closed_form) = 3.05857908807248 " " y[1] (numeric) = 3.058699864823209 " " absolute error = 1.2077675072896810000E-4 " " relative error = 3.948786258297533600E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999196 " " y[1] (closed_form) = 3.06090464243712 " " y[1] (numeric) = 3.0610270921570524 " " absolute error = 1.22449719932582470000E-4 " " relative error = 4.00044216454541000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999185 " " y[1] (closed_form) = 3.0631967450344173 " " y[1] (numeric) = 3.0633208671111745 " " absolute error = 1.24122076757160470000E-4 " " relative error = 4.0520438968984956000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999174 " " y[1] (closed_form) = 3.065455408289843 " " y[1] (numeric) = 3.0655812020935005 " " absolute error = 1.2579380365762560000E-4 " " relative error = 4.103592677206923700E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7599999999999163 " " y[1] (closed_form) = 3.0676806449786196 " " y[1] (numeric) = 3.0678081098618195 " " absolute error = 1.27464883199923660000E-4 " " relative error = 4.1550897225422256000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999915 " " y[1] (closed_form) = 3.069872468223526 " " y[1] (numeric) = 3.0700016035215842 " " absolute error = 1.29135298058358220000E-4 " " relative error = 4.2065362452364760000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999914 " " y[1] (closed_form) = 3.0720308914927 " " y[1] (numeric) = 3.0721616965237195 " " absolute error = 1.3080503101958740000E-4 " " relative error = 4.25793345313755000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.789999999999913 " " y[1] (closed_form) = 3.0741559285974667 " " y[1] (numeric) = 3.0742884026624426 " " absolute error = 1.3247406497596260000E-4 " " relative error = 4.309282549516013600E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.799999999999912 " " y[1] (closed_form) = 3.0762475936901765 " " y[1] (numeric) = 3.076381736073106 " " absolute error = 1.34142382929525180000E-4 " " relative error = 4.360584733318292300E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999911 " " y[1] (closed_form) = 3.078305901262056 " " y[1] (numeric) = 3.0784417112300417 " " absolute error = 1.35809967985789370000E-4 " " relative error = 4.4118411990864675000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999999097 " " y[1] (closed_form) = 3.080330866141069 " " y[1] (numeric) = 3.0804683429444313 " " absolute error = 1.37476803362179820000E-4 " " relative error = 4.463053137353585000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999086 " " y[1] (closed_form) = 3.082322503489803 " " y[1] (numeric) = 3.0824616463621806 " " absolute error = 1.39142872377373550000E-4 " " relative error = 4.514221734417345000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999075 " " y[1] (closed_form) = 3.0842808288033536 " " y[1] (numeric) = 3.084421636961811 " " absolute error = 1.40808158457517150000E-4 " " relative error = 4.565348172661314300E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8499999999999064 " " y[1] (closed_form) = 3.0862058579072325 " " y[1] (numeric) = 3.086348330552363 " " absolute error = 1.42472645130453660000E-4 " " relative error = 4.616433630485844400E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8599999999999053 " " y[1] (closed_form) = 3.088097606955285 " " y[1] (numeric) = 3.0882417432713174 " " absolute error = 1.44136316032383860000E-4 " " relative error = 4.667479282641435000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999904 " " y[1] (closed_form) = 3.089956092427622 " " y[1] (numeric) = 3.0901018915825214 " " absolute error = 1.45799154899428630000E-4 " " relative error = 4.718486300071714000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999903 " " y[1] (closed_form) = 3.091781331128562 " " y[1] (numeric) = 3.0919287922741323 " " absolute error = 1.47461145570293440000E-4 " " relative error = 4.769455850115608700E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.889999999999902 " " y[1] (closed_form) = 3.093573340184588 " " y[1] (numeric) = 3.0937224624565745 " " absolute error = 1.49122271986268370000E-4 " " relative error = 4.820389096622177000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999901 " " y[1] (closed_form) = 3.0953321370423184 " " y[1] (numeric) = 3.095482919560508 " " absolute error = 1.50782518189451760000E-4 " " relative error = 4.871287200007199400E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999998998 " " y[1] (closed_form) = 3.0970577394664853 " " y[1] (numeric) = 3.097210181334809 " " absolute error = 1.52441868323638370000E-4 " " relative error = 4.92215131739516030E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999998987 " " y[1] (closed_form) = 3.098750165537933 " " y[1] (numeric) = 3.098904265844563 " " absolute error = 1.5410030662987850000E-4 " " relative error = 4.972982602588330600E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999998976 " " y[1] (closed_form) = 3.1004094336516186 " " y[1] (numeric) = 3.100565191469073 " " absolute error = 1.5575781745447160000E-4 " " relative error = 5.023782206436593000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999998965 " " y[1] (closed_form) = 3.102035562514637 " " y[1] (numeric) = 3.1021929768998717 " " absolute error = 1.57414385234755370000E-4 " " relative error = 5.0745512764898420000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9499999999998954 " " y[1] (closed_form) = 3.103628571144247 " " y[1] (numeric) = 3.1037876411387577 " " absolute error = 1.59069994510652180000E-4 " " relative error = 5.125290957480978000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9599999999998943 " " y[1] (closed_form) = 3.105188478865915 " " y[1] (numeric) = 3.105349203495836 " " absolute error = 1.60724629921116250000E-4 " " relative error = 5.176002391320753000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999893 " " y[1] (closed_form) = 3.1067153053113716 " " y[1] (numeric) = 3.106877683587571 " " absolute error = 1.62378276199248720000E-4 " " relative error = 5.226686717049354000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999892 " " y[1] (closed_form) = 3.108209070416675 " " y[1] (numeric) = 3.1083731013348506 " " absolute error = 1.64030918175406270000E-4 " " relative error = 5.2773450710449430000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.989999999999891 " " y[1] (closed_form) = 3.1096697944202933 " " y[1] (numeric) = 3.1098354769610674 " " absolute error = 1.6568254077409250000E-4 " " relative error = 5.327978587031269000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999989 " " y[1] (closed_form) = 3.1110974978611883 " " y[1] (numeric) = 3.1112648309902062 " " absolute error = 1.67333129017954720000E-4 " " relative error = 5.378588396313281000E-3 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 6 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; " Iterations = 1001 "Total Elapsed Time "= 1 Minutes 10 Seconds "Elapsed Time(since restart) "= 1 Minutes 10 Seconds "Time to Timeout "= 1 Minutes 49 Seconds Percent Done = 100.19999999998896 "%" (%o255) temp/diffeq.sin_sqrt_lin.max