(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_y array_y , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : ats(2, array_y, array_y, 1), array_tmp2 : array_tmp1 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_y, array_y, 1), array_tmp2 : array_tmp1 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_y, array_y, 1), array_tmp2 : array_tmp1 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_y, array_y, 1), array_tmp2 : array_tmp1 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_y, array_y, 1), array_tmp2 : array_tmp1 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp2 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_y array_y , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : ats(2, array_y, array_y, 1), array_tmp2 : array_tmp1 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_y, array_y, 1), array_tmp2 : array_tmp1 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_y, array_y, 1), array_tmp2 : array_tmp1 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_y, array_y, 1), array_tmp2 : array_tmp1 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_y, array_y, 1), array_tmp2 : array_tmp1 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp2 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) 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)) (%o17) 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)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) 1.0 (%i55) exact_soln_y(x) := block(-------) 1.0 - x 1.0 (%o55) exact_soln_y(x) := block(-------) 1.0 - x (%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/nonlinear1postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:0.5,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0/(1.0 - x)) "), 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 : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 0.5, array_y_init : exact_soln_y(x_start), glob_h : 0.01, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), 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, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /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, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no 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_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(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 ) = y * y;"), 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, "2013-01-13T01:22:47-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "nonlinear1"), logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "nonlinear1 diffeq.max"), logitem_str(html_log_file, "nonlinear1 maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/nonlinear1postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:0.5,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0/(1.0 - x)) "), 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 : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 0.5, array_y_init : exact_soln_y(x_start), glob_h : 0.01, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), 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, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /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, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no 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_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(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 ) = y * y;"), 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, "2013-01-13T01:22:47-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "nonlinear1"), logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "nonlinear1 diffeq.max"), logitem_str(html_log_file, "nonlinear1 maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/nonlinear1postode.ode#################" "diff ( y , x , 1 ) = y * y;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.0," "x_end:0.5," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.01," "glob_look_poles:true," "glob_max_iter:1000000," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0/(1.0 - x)) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 0.5 "" estimated_steps = 500. "" step_error = 2.0000000000000E-13 "" est_needed_step_err = 2.0000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.0005002499999997000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" max_value3 = 1.0005002499999997000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" value3 = 1.0005002499999997000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.0 " " y[1] (analytic) = 1. " " y[1] (numeric) = 1. " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.0 " " y[1] (analytic) = 1. " " y[1] (numeric) = 1. " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 1.0000000000000304 " " Order of pole = 1.000000000000803 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.000E-3 " " y[1] (analytic) = 1.001001001001001 " " y[1] (numeric) = 1.001001001001001 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9990000000000294 " " Order of pole = 1.000000000000778 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.000E-3 " " y[1] (analytic) = 1.002004008016032 " " y[1] (numeric) = 1.0020040080160322 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.216005157151812700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9979999999999921 " " Order of pole = 0.9999999999997868 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.000E-3 " " y[1] (analytic) = 1.0030090270812437 " " y[1] (numeric) = 1.003009027081244 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.213784711102562100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9970000000000356 " " Order of pole = 1.000000000000945 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.000E-3 " " y[1] (analytic) = 1.0040160642570282 " " y[1] (numeric) = 1.0040160642570284 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.211564265053311800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9959999999999705 " " Order of pole = 0.9999999999992255 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.000E-3 " " y[1] (analytic) = 1.0050251256281406 " " y[1] (numeric) = 1.005025125628141 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.418687638008123600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9950000000000047 " " Order of pole = 1.000000000000128 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.000E-3 " " y[1] (analytic) = 1.0060362173038229 " " y[1] (numeric) = 1.0060362173038233 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.414246745909622400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9939999999999763 " " Order of pole = 0.9999999999993818 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.000E-3 " " y[1] (analytic) = 1.0070493454179255 " " y[1] (numeric) = 1.007049345417926 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.409805853811122000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9929999999999718 " " Order of pole = 0.9999999999992575 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.000E-3 " " y[1] (analytic) = 1.0080645161290323 " " y[1] (numeric) = 1.0080645161290327 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.40536496171262100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9920000000000111 " " Order of pole = 1.0000000000003126 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.000000000000001000E-3 " " y[1] (analytic) = 1.0090817356205852 " " y[1] (numeric) = 1.0090817356205857 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.40092406961412100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9909999999999947 " " Order of pole = 0.9999999999998721 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000000200E-2 " " y[1] (analytic) = 1.0101010101010102 " " y[1] (numeric) = 1.0101010101010106 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.3964831775156200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9900000000000106 " " Order of pole = 1.0000000000002949 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.100000000000000300E-2 " " y[1] (analytic) = 1.0111223458038423 " " y[1] (numeric) = 1.0111223458038427 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.39204228541711870000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9890000000000156 " " Order of pole = 1.0000000000004299 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.200000000000000400E-2 " " y[1] (analytic) = 1.0121457489878543 " " y[1] (numeric) = 1.0121457489878547 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.387601393318618600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9880000000000144 " " Order of pole = 1.0000000000003944 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000000600E-2 " " y[1] (analytic) = 1.0131712259371835 " " y[1] (numeric) = 1.013171225937184 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.383160501220117500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9870000000000078 " " Order of pole = 1.0000000000002132 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000000700E-2 " " y[1] (analytic) = 1.0141987829614605 " " y[1] (numeric) = 1.014198782961461 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.37871960912161740000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9860000000000169 " " Order of pole = 1.0000000000004547 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000000800E-2 " " y[1] (analytic) = 1.015228426395939 " " y[1] (numeric) = 1.0152284263959395 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.37427871702311700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9850000000000065 " " Order of pole = 1.0000000000001776 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.600000000000001000E-2 " " y[1] (analytic) = 1.016260162601626 " " y[1] (numeric) = 1.0162601626016263 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.18491891246230780000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9839999999999947 " " Order of pole = 0.9999999999998721 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.700000000000001000E-2 " " y[1] (analytic) = 1.017293997965412 " " y[1] (numeric) = 1.0172939979654123 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.182698466413057800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9830000000000113 " " Order of pole = 1.0000000000003162 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.80000000000000100E-2 " " y[1] (analytic) = 1.0183299389002036 " " y[1] (numeric) = 1.018329938900204 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.36095604072761500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.982000000000028 " " Order of pole = 1.0000000000007638 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.90000000000000100E-2 " " y[1] (analytic) = 1.019367991845056 " " y[1] (numeric) = 1.0193679918450564 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.356515148629115000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9809999999999884 " " Order of pole = 0.9999999999997016 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000000120E-2 " " y[1] (analytic) = 1.0204081632653061 " " y[1] (numeric) = 1.0204081632653066 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.352074256530613600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.980000000000005 " " Order of pole = 1.0000000000001492 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.10000000000000130E-2 " " y[1] (analytic) = 1.0214504596527068 " " y[1] (numeric) = 1.0214504596527074 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.5214500466481710000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9789999999999819 " " Order of pole = 0.999999999999531 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.200000000000001400E-2 " " y[1] (analytic) = 1.0224948875255624 " " y[1] (numeric) = 1.022494887525563 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.51478870850041900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9780000000000068 " " Order of pole = 1.000000000000199 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.300000000000001500E-2 " " y[1] (analytic) = 1.0235414534288638 " " y[1] (numeric) = 1.0235414534288645 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.50812737035266800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.977000000000004 " " Order of pole = 1.0000000000001137 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.400000000000001600E-2 " " y[1] (analytic) = 1.0245901639344261 " " y[1] (numeric) = 1.0245901639344268 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.50146603220491700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9760000000000221 " " Order of pole = 1.0000000000006146 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.500000000000001700E-2 " " y[1] (analytic) = 1.0256410256410258 " " y[1] (numeric) = 1.0256410256410262 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.3298697960381100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9750000000000272 " " Order of pole = 1.000000000000746 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.600000000000002000E-2 " " y[1] (analytic) = 1.026694045174538 " " y[1] (numeric) = 1.0266940451745385 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.325428903939609300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9739999999999954 " " Order of pole = 0.9999999999998934 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.700000000000002000E-2 " " y[1] (analytic) = 1.027749229188078 " " y[1] (numeric) = 1.0277492291880788 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.48148201776166400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9729999999999953 " " Order of pole = 0.9999999999998863 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.800000000000002000E-2 " " y[1] (analytic) = 1.02880658436214 " " y[1] (numeric) = 1.0288065843621406 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.47482067961391300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9720000000000044 " " Order of pole = 1.0000000000001315 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.90000000000000200E-2 " " y[1] (analytic) = 1.0298661174047374 " " y[1] (numeric) = 1.029866117404738 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.46815934146616200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.971000000000034 " " Order of pole = 1.000000000000938 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.00000000000000200E-2 " " y[1] (analytic) = 1.0309278350515465 " " y[1] (numeric) = 1.0309278350515472 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.4614980033184100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9700000000000296 " " Order of pole = 1.0000000000008242 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.10000000000000200E-2 " " y[1] (analytic) = 1.0319917440660475 " " y[1] (numeric) = 1.0319917440660482 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.4548366651706600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9690000000000257 " " Order of pole = 1.0000000000007176 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.20000000000000230E-2 " " y[1] (analytic) = 1.0330578512396695 " " y[1] (numeric) = 1.0330578512396702 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.44817532702290900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.968 " " Order of pole = 1.0000000000000178 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.30000000000000240E-2 " " y[1] (analytic) = 1.0341261633919339 " " y[1] (numeric) = 1.0341261633919345 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.44151398887515700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.967000000000002 " " Order of pole = 1.0000000000000675 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.40000000000000250E-2 " " y[1] (analytic) = 1.0351966873706004 " " y[1] (numeric) = 1.035196687370601 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.43485265072740700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9659999999999777 " " Order of pole = 0.9999999999993996 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.500000000000002600E-2 " " y[1] (analytic) = 1.0362694300518136 " " y[1] (numeric) = 1.0362694300518143 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.42819131257965500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9650000000000263 " " Order of pole = 1.000000000000746 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.600000000000002600E-2 " " y[1] (analytic) = 1.037344398340249 " " y[1] (numeric) = 1.0373443983402497 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.42152997443190500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9639999999999938 " " Order of pole = 0.9999999999998543 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.700000000000003000E-2 " " y[1] (analytic) = 1.0384215991692627 " " y[1] (numeric) = 1.0384215991692636 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.55315818171220600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9629999999999795 " " Order of pole = 0.9999999999994529 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.80000000000000300E-2 " " y[1] (analytic) = 1.0395010395010396 " " y[1] (numeric) = 1.0395010395010404 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.54427639751520400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9620000000000096 " " Order of pole = 1.0000000000002949 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.90000000000000300E-2 " " y[1] (analytic) = 1.040582726326743 " " y[1] (numeric) = 1.040582726326744 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.53539461331820300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9610000000000187 " " Order of pole = 1.0000000000005471 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.00000000000000300E-2 " " y[1] (analytic) = 1.0416666666666667 " " y[1] (numeric) = 1.0416666666666676 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.52651282912120200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9599999999999939 " " Order of pole = 0.9999999999998543 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.10000000000000300E-2 " " y[1] (analytic) = 1.0427528675703859 " " y[1] (numeric) = 1.0427528675703868 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.517631044924200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9590000000000172 " " Order of pole = 1.0000000000004974 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.20000000000000300E-2 " " y[1] (analytic) = 1.0438413361169103 " " y[1] (numeric) = 1.0438413361169112 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.508749260727200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9580000000000108 " " Order of pole = 1.0000000000003197 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.30000000000000300E-2 " " y[1] (analytic) = 1.044932079414838 " " y[1] (numeric) = 1.0449320794148391 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.06248343456627480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9570000000000066 " " Order of pole = 1.000000000000206 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.40000000000000340E-2 " " y[1] (analytic) = 1.0460251046025104 " " y[1] (numeric) = 1.0460251046025115 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.06137321154164970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9559999999999944 " " Order of pole = 0.9999999999998721 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.50000000000000340E-2 " " y[1] (analytic) = 1.0471204188481675 " " y[1] (numeric) = 1.0471204188481686 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.06026298851702450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9550000000000041 " " Order of pole = 1.000000000000135 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.600000000000003500E-2 " " y[1] (analytic) = 1.0482180293501049 " " y[1] (numeric) = 1.048218029350106 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05915276549239920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9540000000000213 " " Order of pole = 1.0000000000006253 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.700000000000003600E-2 " " y[1] (analytic) = 1.0493179433368311 " " y[1] (numeric) = 1.0493179433368323 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0580425424677740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9530000000000137 " " Order of pole = 1.0000000000004121 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.800000000000003700E-2 " " y[1] (analytic) = 1.050420168067227 " " y[1] (numeric) = 1.050420168067228 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0569323194431490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9520000000000192 " " Order of pole = 1.0000000000005507 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.90000000000000400E-2 " " y[1] (analytic) = 1.0515247108307046 " " y[1] (numeric) = 1.0515247108307058 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05582209641852370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9510000000000216 " " Order of pole = 1.0000000000006253 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000000300E-2 " " y[1] (analytic) = 1.0526315789473684 " " y[1] (numeric) = 1.0526315789473697 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26565424807267850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9499999999999789 " " Order of pole = 0.9999999999994493 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.10000000000000300E-2 " " y[1] (analytic) = 1.053740779768177 " " y[1] (numeric) = 1.0537407797681784 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26432198044312830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9489999999999772 " " Order of pole = 0.9999999999993996 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.20000000000000400E-2 " " y[1] (analytic) = 1.0548523206751055 " " y[1] (numeric) = 1.0548523206751068 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2629897128135780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9480000000000209 " " Order of pole = 1.0000000000006146 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.30000000000000400E-2 " " y[1] (analytic) = 1.0559662090813096 " " y[1] (numeric) = 1.0559662090813107 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05138120432002310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9469999999999997 " " Order of pole = 1.0000000000000178 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.40000000000000400E-2 " " y[1] (analytic) = 1.0570824524312896 " " y[1] (numeric) = 1.057082452431291 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26032517755447770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9460000000000142 " " Order of pole = 1.0000000000004334 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.50000000000000400E-2 " " y[1] (analytic) = 1.0582010582010584 " " y[1] (numeric) = 1.0582010582010595 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04916075827077280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9450000000000137 " " Order of pole = 1.0000000000004086 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.60000000000000400E-2 " " y[1] (analytic) = 1.0593220338983051 " " y[1] (numeric) = 1.0593220338983063 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04805053524614760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9439999999999902 " " Order of pole = 0.999999999999762 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.700000000000004000E-2 " " y[1] (analytic) = 1.0604453870625663 " " y[1] (numeric) = 1.0604453870625674 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04694031222152260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9430000000000403 " " Order of pole = 1.0000000000011546 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.800000000000004000E-2 " " y[1] (analytic) = 1.0615711252653928 " " y[1] (numeric) = 1.0615711252653939 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04583008919689750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9420000000000095 " " Order of pole = 1.0000000000002807 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.900000000000004000E-2 " " y[1] (analytic) = 1.0626992561105209 " " y[1] (numeric) = 1.0626992561105217 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.35775892937817800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9410000000000235 " " Order of pole = 1.0000000000006715 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.000000000000004000E-2 " " y[1] (analytic) = 1.0638297872340425 " " y[1] (numeric) = 1.0638297872340436 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04360964314764710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.940000000000017 " " Order of pole = 1.000000000000501 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.10000000000000400E-2 " " y[1] (analytic) = 1.0649627263045793 " " y[1] (numeric) = 1.0649627263045804 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0424994201230220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9390000000000103 " " Order of pole = 1.0000000000003126 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.20000000000000400E-2 " " y[1] (analytic) = 1.0660980810234542 " " y[1] (numeric) = 1.0660980810234553 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04138919709839680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9379999999999977 " " Order of pole = 0.999999999999968 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.30000000000000400E-2 " " y[1] (analytic) = 1.0672358591248667 " " y[1] (numeric) = 1.0672358591248676 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.32223179259017200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9369999999999895 " " Order of pole = 0.9999999999997264 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.40000000000000500E-2 " " y[1] (analytic) = 1.0683760683760684 " " y[1] (numeric) = 1.0683760683760695 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.03916875104914650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9360000000000094 " " Order of pole = 1.0000000000002842 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.50000000000000500E-2 " " y[1] (analytic) = 1.0695187165775402 " " y[1] (numeric) = 1.0695187165775413 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.03805852802452140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9350000000000012 " " Order of pole = 1.000000000000064 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.60000000000000500E-2 " " y[1] (analytic) = 1.0706638115631693 " " y[1] (numeric) = 1.0706638115631704 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.03694830499989610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9340000000000112 " " Order of pole = 1.0000000000003446 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.70000000000000500E-2 " " y[1] (analytic) = 1.0718113612004287 " " y[1] (numeric) = 1.0718113612004299 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0358380819752710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9330000000000053 " " Order of pole = 1.000000000000174 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.80000000000000500E-2 " " y[1] (analytic) = 1.072961373390558 " " y[1] (numeric) = 1.072961373390559 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.27782287160516600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9320000000000144 " " Order of pole = 1.0000000000004263 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.90000000000000500E-2 " " y[1] (analytic) = 1.0741138560687433 " " y[1] (numeric) = 1.0741138560687442 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.26894108740816600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9309999999999803 " " Order of pole = 0.9999999999994529 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000000500E-2 " " y[1] (analytic) = 1.0752688172043012 " " y[1] (numeric) = 1.075268817204302 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.19504447740837200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9300000000000056 " " Order of pole = 1.0000000000001847 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.10000000000000500E-2 " " y[1] (analytic) = 1.0764262648008611 " " y[1] (numeric) = 1.076426264800862 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.25117751901416300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9289999999999888 " " Order of pole = 0.9999999999997016 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.20000000000000500E-2 " " y[1] (analytic) = 1.0775862068965518 " " y[1] (numeric) = 1.0775862068965525 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.18172180111287200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9279999999999892 " " Order of pole = 0.9999999999997158 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.30000000000000500E-2 " " y[1] (analytic) = 1.0787486515641855 " " y[1] (numeric) = 1.0787486515641864 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.23341395062016100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9269999999999912 " " Order of pole = 0.9999999999997655 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.40000000000000500E-2 " " y[1] (analytic) = 1.0799136069114472 " " y[1] (numeric) = 1.0799136069114479 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.16839912481736900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9260000000000362 " " Order of pole = 1.0000000000010516 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.50000000000000600E-2 " " y[1] (analytic) = 1.0810810810810811 " " y[1] (numeric) = 1.0810810810810818 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.16173778666961900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9249999999999976 " " Order of pole = 0.9999999999999574 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.60000000000000600E-2 " " y[1] (analytic) = 1.0822510822510822 " " y[1] (numeric) = 1.082251082251083 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.15507644852186800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9240000000000076 " " Order of pole = 1.0000000000002451 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.70000000000000600E-2 " " y[1] (analytic) = 1.0834236186348862 " " y[1] (numeric) = 1.083423618634887 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.14841511037411700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9230000000000087 " " Order of pole = 1.0000000000002665 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.80000000000000600E-2 " " y[1] (analytic) = 1.0845986984815619 " " y[1] (numeric) = 1.0845986984815625 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.14175377222636500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9220000000000016 " " Order of pole = 1.000000000000064 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.90000000000000600E-2 " " y[1] (analytic) = 1.0857763300760044 " " y[1] (numeric) = 1.085776330076005 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.13509243407861500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9210000000000202 " " Order of pole = 1.0000000000005862 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000000600E-2 " " y[1] (analytic) = 1.0869565217391306 " " y[1] (numeric) = 1.086956521739131 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.085620730620575500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9199999999999554 " " Order of pole = 0.9999999999987281 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.10000000000000600E-2 " " y[1] (analytic) = 1.0881392818280742 " " y[1] (numeric) = 1.0881392818280746 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.08117983852207500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.91900000000003 " " Order of pole = 1.0000000000008775 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.20000000000000600E-2 " " y[1] (analytic) = 1.0893246187363834 " " y[1] (numeric) = 1.089324618736384 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.11510841963536200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9180000000000081 " " Order of pole = 1.0000000000002416 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.30000000000000600E-2 " " y[1] (analytic) = 1.0905125408942205 " " y[1] (numeric) = 1.090512540894221 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.07229805432507360000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9169999999999914 " " Order of pole = 0.9999999999997691 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.40000000000000600E-2 " " y[1] (analytic) = 1.091703056768559 " " y[1] (numeric) = 1.0917030567685595 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.06785716222657360000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9159999999999658 " " Order of pole = 0.9999999999990301 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.50000000000000600E-2 " " y[1] (analytic) = 1.092896174863388 " " y[1] (numeric) = 1.0928961748633885 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.06341627012807240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.915000000000024 " " Order of pole = 1.000000000000707 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.60000000000000700E-2 " " y[1] (analytic) = 1.0940919037199126 " " y[1] (numeric) = 1.094091903719913 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.05897537802957200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9140000000000196 " " Order of pole = 1.0000000000005826 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.70000000000000700E-2 " " y[1] (analytic) = 1.095290251916758 " " y[1] (numeric) = 1.0952902519167584 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.054534485931071700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9130000000000095 " " Order of pole = 1.0000000000002878 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.80000000000000700E-2 " " y[1] (analytic) = 1.0964912280701755 " " y[1] (numeric) = 1.096491228070176 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.050093593832570500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9119999999999914 " " Order of pole = 0.9999999999997691 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.90000000000000700E-2 " " y[1] (analytic) = 1.0976948408342482 " " y[1] (numeric) = 1.0976948408342486 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.0456527017340704000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9109999999999934 " " Order of pole = 0.9999999999998188 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000000700E-2 " " y[1] (analytic) = 1.098901098901099 " " y[1] (numeric) = 1.0989010989010994 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.04121180963556900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9099999999999917 " " Order of pole = 0.9999999999997762 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.10000000000000700E-2 " " y[1] (analytic) = 1.1001100110011002 " " y[1] (numeric) = 1.1001100110011006 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03677091753706860000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.908999999999988 " " Order of pole = 0.999999999999666 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.20000000000000700E-2 " " y[1] (analytic) = 1.1013215859030838 " " y[1] (numeric) = 1.1013215859030843 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03233002543856800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9080000000000101 " " Order of pole = 1.000000000000302 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.30000000000000700E-2 " " y[1] (analytic) = 1.1025358324145536 " " y[1] (numeric) = 1.102535832414554 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.027889133340067400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.907000000000001 " " Order of pole = 1.0000000000000462 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.40000000000000700E-2 " " y[1] (analytic) = 1.1037527593818985 " " y[1] (numeric) = 1.103752759381899 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.02344824124156730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9060000000000267 " " Order of pole = 1.0000000000007851 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.50000000000000700E-2 " " y[1] (analytic) = 1.1049723756906078 " " y[1] (numeric) = 1.1049723756906082 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.019007349143066700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9050000000000381 " " Order of pole = 1.0000000000011227 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.60000000000000700E-2 " " y[1] (analytic) = 1.106194690265487 " " y[1] (numeric) = 1.1061946902654873 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.014566457044565500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9040000000000099 " " Order of pole = 1.0000000000002913 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.70000000000000800E-2 " " y[1] (analytic) = 1.1074197120708749 " " y[1] (numeric) = 1.1074197120708755 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.01518834741909800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9030000000000045 " " Order of pole = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.80000000000000800E-2 " " y[1] (analytic) = 1.108647450110865 " " y[1] (numeric) = 1.1086474501108654 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.00568467284756400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9020000000000046 " " Order of pole = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.90000000000000800E-2 " " y[1] (analytic) = 1.109877913429523 " " y[1] (numeric) = 1.1098779134295234 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.00124378074906300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9010000000000178 " " Order of pole = 1.0000000000005365 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000007 " " y[1] (analytic) = 1.1111111111111112 " " y[1] (numeric) = 1.1111111111111116 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.996802888650563500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9000000000000167 " " Order of pole = 1.0000000000004974 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10100000000000008 " " y[1] (analytic) = 1.1123470522803116 " " y[1] (numeric) = 1.112347052280312 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.992361996552062400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8990000000000055 " " Order of pole = 1.0000000000001776 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000008 " " y[1] (analytic) = 1.11358574610245 " " y[1] (numeric) = 1.1135857461024505 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.987921104453562000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8979999999999712 " " Order of pole = 0.9999999999991651 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000008 " " y[1] (analytic) = 1.1148272017837237 " " y[1] (numeric) = 1.1148272017837242 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.98348021235506100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8969999999999857 " " Order of pole = 0.9999999999995843 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000008 " " y[1] (analytic) = 1.1160714285714286 " " y[1] (numeric) = 1.1160714285714293 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.96855898038484200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8960000000000088 " " Order of pole = 1.0000000000002665 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000008 " " y[1] (analytic) = 1.11731843575419 " " y[1] (numeric) = 1.1173184357541905 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.9745984281580600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8950000000000177 " " Order of pole = 1.000000000000533 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000008 " " y[1] (analytic) = 1.1185682326621924 " " y[1] (numeric) = 1.118568232662193 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.9552363040893400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8940000000000142 " " Order of pole = 1.0000000000004334 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000008 " " y[1] (analytic) = 1.1198208286674134 " " y[1] (numeric) = 1.1198208286674138 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.965716643961058600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8929999999999808 " " Order of pole = 0.9999999999994351 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000008 " " y[1] (analytic) = 1.1210762331838566 " " y[1] (numeric) = 1.121076233183857 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.96127575186255800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8919999999999947 " " Order of pole = 0.9999999999998472 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000008 " " y[1] (analytic) = 1.1223344556677892 " " y[1] (numeric) = 1.1223344556677897 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.95683485976405700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8909999999999655 " " Order of pole = 0.9999999999989875 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000008 " " y[1] (analytic) = 1.1235955056179776 " " y[1] (numeric) = 1.1235955056179783 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.92859095149833600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8900000000000287 " " Order of pole = 1.0000000000008775 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000008 " " y[1] (analytic) = 1.124859392575928 " " y[1] (numeric) = 1.1248593925759287 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.92192961335058500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.889000000000013 " " Order of pole = 1.0000000000003944 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000009 " " y[1] (analytic) = 1.1261261261261262 " " y[1] (numeric) = 1.1261261261261268 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.91526827520283400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8880000000000009 " " Order of pole = 1.0000000000000462 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000009 " " y[1] (analytic) = 1.1273957158962797 " " y[1] (numeric) = 1.1273957158962804 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.90860693705508200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8869999999999946 " " Order of pole = 0.9999999999998508 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000009 " " y[1] (analytic) = 1.1286681715575622 " " y[1] (numeric) = 1.1286681715575628 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.90194559890733100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8859999999999778 " " Order of pole = 0.9999999999993499 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000009 " " y[1] (analytic) = 1.1299435028248588 " " y[1] (numeric) = 1.1299435028248594 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.89528426075958100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8850000000000131 " " Order of pole = 1.000000000000405 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000009 " " y[1] (analytic) = 1.1312217194570138 " " y[1] (numeric) = 1.1312217194570142 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.92574861507455300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8840000000000086 " " Order of pole = 1.00000000000027 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000009 " " y[1] (analytic) = 1.1325028312570782 " " y[1] (numeric) = 1.1325028312570788 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.88196158446407900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8829999999999761 " " Order of pole = 0.9999999999993001 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000009 " " y[1] (analytic) = 1.1337868480725626 " " y[1] (numeric) = 1.133786848072563 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.91686683087755170000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8820000000000224 " " Order of pole = 1.0000000000006857 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000009 " " y[1] (analytic) = 1.135073779795687 " " y[1] (numeric) = 1.1350737797956874 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.91242593877905050000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8810000000000081 " " Order of pole = 1.000000000000263 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000009 " " y[1] (analytic) = 1.1363636363636365 " " y[1] (numeric) = 1.136363636363637 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.907985046680550500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8800000000000239 " " Order of pole = 1.0000000000007354 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1210000000000001 " " y[1] (analytic) = 1.137656427758817 " " y[1] (numeric) = 1.1376564277588175 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.9035441545820500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8790000000000066 " " Order of pole = 1.000000000000206 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1220000000000001 " " y[1] (analytic) = 1.1389521640091118 " " y[1] (numeric) = 1.1389521640091123 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.89910326248354900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.878000000000017 " " Order of pole = 1.0000000000005365 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1230000000000001 " " y[1] (analytic) = 1.1402508551881416 " " y[1] (numeric) = 1.140250855188142 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.894662370385048600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8769999999999814 " " Order of pole = 0.9999999999994458 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1240000000000001 " " y[1] (analytic) = 1.1415525114155252 " " y[1] (numeric) = 1.1415525114155258 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.83533221742982300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8759999999999788 " " Order of pole = 0.9999999999993676 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000008 " " y[1] (analytic) = 1.142857142857143 " " y[1] (numeric) = 1.1428571428571437 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.8286708792820710000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.874999999999973 " " Order of pole = 0.9999999999992006 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000008 " " y[1] (analytic) = 1.1441647597254005 " " y[1] (numeric) = 1.1441647597254012 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.82200954113432100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8739999999999922 " " Order of pole = 0.9999999999997833 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000009 " " y[1] (analytic) = 1.1454753722794961 " " y[1] (numeric) = 1.1454753722794968 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.8153482029865700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8730000000000058 " " Order of pole = 1.0000000000001883 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000009 " " y[1] (analytic) = 1.1467889908256883 " " y[1] (numeric) = 1.146788990825689 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.80868686483881800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8719999999999841 " " Order of pole = 0.9999999999995346 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1290000000000001 " " y[1] (analytic) = 1.1481056257175661 " " y[1] (numeric) = 1.148105625717567 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.7360340355880910000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8710000000000222 " " Order of pole = 1.0000000000006963 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1300000000000001 " " y[1] (analytic) = 1.149425287356322 " " y[1] (numeric) = 1.1494252873563229 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.72715225139108800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8700000000000211 " " Order of pole = 1.000000000000668 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1310000000000001 " " y[1] (analytic) = 1.1507479861910244 " " y[1] (numeric) = 1.1507479861910253 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.71827046719408700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8690000000000097 " " Order of pole = 1.0000000000003197 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1320000000000001 " " y[1] (analytic) = 1.1520737327188941 " " y[1] (numeric) = 1.152073732718895 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.70938868299708700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8680000000000142 " " Order of pole = 1.0000000000004512 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1330000000000001 " " y[1] (analytic) = 1.1534025374855825 " " y[1] (numeric) = 1.1534025374855834 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.70050689880008600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8670000000000163 " " Order of pole = 1.0000000000005222 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1340000000000001 " " y[1] (analytic) = 1.1547344110854505 " " y[1] (numeric) = 1.1547344110854514 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.69162511460308500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8659999999999706 " " Order of pole = 0.9999999999991225 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1350000000000001 " " y[1] (analytic) = 1.1560693641618498 " " y[1] (numeric) = 1.1560693641618507 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.68274333040608300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8649999999999952 " " Order of pole = 0.9999999999998757 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1360000000000001 " " y[1] (analytic) = 1.1574074074074077 " " y[1] (numeric) = 1.1574074074074083 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.7553961596568100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8640000000000143 " " Order of pole = 1.0000000000004512 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1370000000000001 " " y[1] (analytic) = 1.1587485515643108 " " y[1] (numeric) = 1.1587485515643114 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.74873482150905800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.86299999999997 " " Order of pole = 0.9999999999990941 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1380000000000001 " " y[1] (analytic) = 1.1600928074245942 " " y[1] (numeric) = 1.1600928074245949 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.74207348336130900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8619999999999769 " " Order of pole = 0.9999999999993108 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1390000000000001 " " y[1] (analytic) = 1.16144018583043 " " y[1] (numeric) = 1.1614401858304306 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.73541214521355800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8609999999999608 " " Order of pole = 0.999999999998817 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1400000000000001 " " y[1] (analytic) = 1.1627906976744187 " " y[1] (numeric) = 1.1627906976744196 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.63833440942107700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8600000000000154 " " Order of pole = 1.0000000000005045 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1410000000000001 " " y[1] (analytic) = 1.1641443538998837 " " y[1] (numeric) = 1.1641443538998846 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.62945262522407500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8589999999999998 " " Order of pole = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1420000000000001 " " y[1] (analytic) = 1.1655011655011658 " " y[1] (numeric) = 1.1655011655011664 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.71542813077030400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8580000000000112 " " Order of pole = 1.000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1430000000000001 " " y[1] (analytic) = 1.166861143523921 " " y[1] (numeric) = 1.1668611435239216 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.70876679262255400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8570000000000132 " " Order of pole = 1.0000000000004299 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1440000000000001 " " y[1] (analytic) = 1.1682242990654208 " " y[1] (numeric) = 1.1682242990654215 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.70210545447480300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8560000000000024 " " Order of pole = 1.0000000000000995 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1450000000000001 " " y[1] (analytic) = 1.169590643274854 " " y[1] (numeric) = 1.1695906432748546 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.69544411632705200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8550000000000041 " " Order of pole = 1.0000000000001492 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1460000000000001 " " y[1] (analytic) = 1.1709601873536302 " " y[1] (numeric) = 1.1709601873536308 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.688782778179301000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8540000000000092 " " Order of pole = 1.000000000000302 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1470000000000001 " " y[1] (analytic) = 1.172332942555686 " " y[1] (numeric) = 1.1723329425556868 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.6821214400315500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8530000000000111 " " Order of pole = 1.000000000000366 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1480000000000001 " " y[1] (analytic) = 1.1737089201877937 " " y[1] (numeric) = 1.1737089201877944 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.67546010188379900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8519999999999978 " " Order of pole = 0.9999999999999538 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1490000000000001 " " y[1] (analytic) = 1.175088131609871 " " y[1] (numeric) = 1.1750881316098718 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.55839835164806600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8510000000000156 " " Order of pole = 1.0000000000004974 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1500000000000001 " " y[1] (analytic) = 1.1764705882352944 " " y[1] (numeric) = 1.1764705882352953 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.54951656745106300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8500000000000211 " " Order of pole = 1.0000000000006857 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1510000000000001 " " y[1] (analytic) = 1.1778563015312133 " " y[1] (numeric) = 1.1778563015312142 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.54063478325406200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.848999999999994 " " Order of pole = 0.9999999999998295 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1520000000000001 " " y[1] (analytic) = 1.1792452830188682 " " y[1] (numeric) = 1.1792452830188689 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.648814749292795000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8480000000000252 " " Order of pole = 1.0000000000008136 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1530000000000001 " " y[1] (analytic) = 1.180637544273908 " " y[1] (numeric) = 1.1806375442739088 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.64215341114504400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8470000000000117 " " Order of pole = 1.0000000000003908 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1540000000000001 " " y[1] (analytic) = 1.182033096926714 " " y[1] (numeric) = 1.1820330969267148 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.635492072997293000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8460000000000212 " " Order of pole = 1.0000000000006715 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1550000000000001 " " y[1] (analytic) = 1.1834319526627222 " " y[1] (numeric) = 1.1834319526627226 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.752553823233028600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8450000000000125 " " Order of pole = 1.0000000000004121 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1560000000000001 " " y[1] (analytic) = 1.184834123222749 " " y[1] (numeric) = 1.1848341232227495 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.748112931134527400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8440000000000161 " " Order of pole = 1.0000000000005151 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1570000000000001 " " y[1] (analytic) = 1.1862396204033216 " " y[1] (numeric) = 1.186239620403322 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.74367203903602730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.843000000000025 " " Order of pole = 1.0000000000007923 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1580000000000001 " " y[1] (analytic) = 1.1876484560570073 " " y[1] (numeric) = 1.1876484560570078 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.73923114693752670000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8420000000000144 " " Order of pole = 1.000000000000476 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1590000000000001 " " y[1] (analytic) = 1.189060642092747 " " y[1] (numeric) = 1.1890606420927474 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.73479025483902550000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8409999999999958 " " Order of pole = 0.9999999999998721 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000011 " " y[1] (analytic) = 1.1904761904761907 " " y[1] (numeric) = 1.1904761904761911 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.730349362740525400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8400000000000275 " " Order of pole = 1.000000000000881 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000012 " " y[1] (analytic) = 1.191895113230036 " " y[1] (numeric) = 1.1918951132300364 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.72590847064202500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8390000000000031 " " Order of pole = 1.0000000000001066 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000012 " " y[1] (analytic) = 1.1933174224343677 " " y[1] (numeric) = 1.1933174224343681 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.721467578543525000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8380000000000118 " " Order of pole = 1.0000000000003837 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000012 " " y[1] (analytic) = 1.1947431302270013 " " y[1] (numeric) = 1.1947431302270017 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.717026686445023500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.83700000000001 " " Order of pole = 1.0000000000003268 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000012 " " y[1] (analytic) = 1.196172248803828 " " y[1] (numeric) = 1.1961722488038282 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.856292897173261200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.836000000000032 " " Order of pole = 1.0000000000010232 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000012 " " y[1] (analytic) = 1.1976047904191618 " " y[1] (numeric) = 1.1976047904191622 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.70814490224802230000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8349999999999973 " " Order of pole = 0.999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000012 " " y[1] (analytic) = 1.1990407673860914 " " y[1] (numeric) = 1.1990407673860917 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.851852005074760600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8340000000000027 " " Order of pole = 1.0000000000001066 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000012 " " y[1] (analytic) = 1.2004801920768309 " " y[1] (numeric) = 1.2004801920768313 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.69926311805102100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8330000000000171 " " Order of pole = 1.0000000000005578 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000012 " " y[1] (analytic) = 1.201923076923077 " " y[1] (numeric) = 1.2019230769230775 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.694822225952520400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8320000000000077 " " Order of pole = 1.0000000000002558 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000012 " " y[1] (analytic) = 1.2033694344163661 " " y[1] (numeric) = 1.2033694344163663 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.845190666927009600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.830999999999985 " " Order of pole = 0.9999999999995346 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000012 " " y[1] (analytic) = 1.204819277108434 " " y[1] (numeric) = 1.2048192771084343 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.842970220877759300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8300000000000031 " " Order of pole = 1.0000000000001101 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000012 " " y[1] (analytic) = 1.2062726176115803 " " y[1] (numeric) = 1.2062726176115808 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.68149954965701850000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8289999999999945 " " Order of pole = 0.999999999999833 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000013 " " y[1] (analytic) = 1.207729468599034 " " y[1] (numeric) = 1.2077294685990343 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.83852932877925900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8279999999999821 " " Order of pole = 0.9999999999994422 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000013 " " y[1] (analytic) = 1.2091898428053207 " " y[1] (numeric) = 1.209189842805321 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.836308882730008400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.827000000000016 " " Order of pole = 1.0000000000005116 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000013 " " y[1] (analytic) = 1.2106537530266346 " " y[1] (numeric) = 1.2106537530266348 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.834088436680758000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8259999999999962 " " Order of pole = 0.9999999999998899 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000013 " " y[1] (analytic) = 1.2121212121212124 " " y[1] (numeric) = 1.2121212121212126 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.83186799063150800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8250000000000042 " " Order of pole = 1.0000000000001386 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000013 " " y[1] (analytic) = 1.2135922330097089 " " y[1] (numeric) = 1.2135922330097093 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.659295089164515400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8239999999999815 " " Order of pole = 0.9999999999994102 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000013 " " y[1] (analytic) = 1.2150668286755775 " " y[1] (numeric) = 1.2150668286755777 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.827427098533007400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8230000000000167 " " Order of pole = 1.0000000000005471 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000013 " " y[1] (analytic) = 1.2165450121654504 " " y[1] (numeric) = 1.2165450121654506 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.825206652483756800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8220000000000198 " " Order of pole = 1.0000000000006501 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000013 " " y[1] (analytic) = 1.2180267965895253 " " y[1] (numeric) = 1.2180267965895255 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.822986206434506500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8209999999999983 " " Order of pole = 0.9999999999999538 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000013 " " y[1] (analytic) = 1.2195121951219514 " " y[1] (numeric) = 1.2195121951219519 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.64153152077051300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8200000000000086 " " Order of pole = 1.0000000000002913 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000013 " " y[1] (analytic) = 1.2210012210012213 " " y[1] (numeric) = 1.2210012210012215 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.81854531433600590000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8190000000000123 " " Order of pole = 1.0000000000004086 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000013 " " y[1] (analytic) = 1.2224938875305627 " " y[1] (numeric) = 1.2224938875305629 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.816324868286755800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8179999999999963 " " Order of pole = 0.9999999999998934 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000013 " " y[1] (analytic) = 1.2239902080783356 " " y[1] (numeric) = 1.2239902080783358 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.814104422237505500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.816999999999992 " " Order of pole = 0.9999999999997513 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000014 " " y[1] (analytic) = 1.2254901960784317 " " y[1] (numeric) = 1.225490196078432 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.81188397618825500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8160000000000168 " " Order of pole = 1.0000000000005613 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000014 " " y[1] (analytic) = 1.226993865030675 " " y[1] (numeric) = 1.2269938650306753 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.80966353013900500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8150000000000047 " " Order of pole = 1.0000000000001599 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000014 " " y[1] (analytic) = 1.2285012285012287 " " y[1] (numeric) = 1.228501228501229 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.807443084089754600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8140000000000208 " " Order of pole = 1.0000000000006786 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000014 " " y[1] (analytic) = 1.2300123001230014 " " y[1] (numeric) = 1.2300123001230017 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.80522263804050430000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8130000000000018 " " Order of pole = 1.0000000000000604 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000014 " " y[1] (analytic) = 1.2315270935960594 " " y[1] (numeric) = 1.2315270935960596 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.80300219199125400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8120000000000193 " " Order of pole = 1.000000000000643 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000014 " " y[1] (analytic) = 1.2330456226880397 " " y[1] (numeric) = 1.23304562268804 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.800781745942003400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8110000000000257 " " Order of pole = 1.0000000000008562 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000014 " " y[1] (analytic) = 1.234567901234568 " " y[1] (numeric) = 1.2345679012345685 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.597122599785506600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8100000000000247 " " Order of pole = 1.0000000000008136 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19100000000000014 " " y[1] (analytic) = 1.236093943139679 " " y[1] (numeric) = 1.2360939431396791 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.796340853843502700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8090000000000004 " " Order of pole = 1.0000000000000213 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19200000000000014 " " y[1] (analytic) = 1.2376237623762378 " " y[1] (numeric) = 1.237623762376238 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.794120407794252700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8080000000000174 " " Order of pole = 1.000000000000579 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19300000000000014 " " y[1] (analytic) = 1.2391573729863696 " " y[1] (numeric) = 1.2391573729863696 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8070000000000366 " " Order of pole = 1.0000000000011973 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19400000000000014 " " y[1] (analytic) = 1.240694789081886 " " y[1] (numeric) = 1.2406947890818862 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.789679515695752300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8059999999999924 " " Order of pole = 0.9999999999997549 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19500000000000015 " " y[1] (analytic) = 1.2422360248447208 " " y[1] (numeric) = 1.2422360248447208 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.805000000000011 " " Order of pole = 1.000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19600000000000015 " " y[1] (analytic) = 1.2437810945273635 " " y[1] (numeric) = 1.2437810945273635 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8039999999999767 " " Order of pole = 0.9999999999992397 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19700000000000015 " " y[1] (analytic) = 1.2453300124533004 " " y[1] (numeric) = 1.2453300124533004 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8030000000000147 " " Order of pole = 1.0000000000004974 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19800000000000015 " " y[1] (analytic) = 1.2468827930174566 " " y[1] (numeric) = 1.2468827930174566 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8019999999999831 " " Order of pole = 0.9999999999994422 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19900000000000015 " " y[1] (analytic) = 1.248439450686642 " " y[1] (numeric) = 1.248439450686642 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8010000000000025 " " Order of pole = 1.0000000000000888 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000015 " " y[1] (analytic) = 1.2500000000000002 " " y[1] (numeric) = 1.2500000000000004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.7763568394002502000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8000000000000215 " " Order of pole = 1.0000000000007319 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20100000000000015 " " y[1] (analytic) = 1.251564455569462 " " y[1] (numeric) = 1.2515644555694623 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.77413639335100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7990000000000228 " " Order of pole = 1.0000000000007638 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20200000000000015 " " y[1] (analytic) = 1.2531328320802009 " " y[1] (numeric) = 1.2531328320802009 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7979999999999956 " " Order of pole = 0.9999999999998685 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20300000000000015 " " y[1] (analytic) = 1.254705144291092 " " y[1] (numeric) = 1.254705144291092 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.796999999999976 " " Order of pole = 0.9999999999992042 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20400000000000015 " " y[1] (analytic) = 1.2562814070351762 " " y[1] (numeric) = 1.2562814070351762 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7960000000000098 " " Order of pole = 1.0000000000003268 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20500000000000015 " " y[1] (analytic) = 1.2578616352201262 " " y[1] (numeric) = 1.2578616352201262 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7950000000000265 " " Order of pole = 1.0000000000008882 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20600000000000016 " " y[1] (analytic) = 1.2594458438287157 " " y[1] (numeric) = 1.2594458438287157 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7940000000000146 " " Order of pole = 1.0000000000004903 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20700000000000016 " " y[1] (analytic) = 1.261034047919294 " " y[1] (numeric) = 1.261034047919294 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7929999999999995 " " Order of pole = 0.9999999999999893 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20800000000000016 " " y[1] (analytic) = 1.262626262626263 " " y[1] (numeric) = 1.262626262626263 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.792000000000021 " " Order of pole = 1.0000000000007105 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20900000000000016 " " y[1] (analytic) = 1.2642225031605565 " " y[1] (numeric) = 1.2642225031605565 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7909999999999994 " " Order of pole = 0.9999999999999893 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000016 " " y[1] (analytic) = 1.2658227848101269 " " y[1] (numeric) = 1.2658227848101269 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7900000000000131 " " Order of pole = 1.0000000000004547 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21100000000000016 " " y[1] (analytic) = 1.2674271229404312 " " y[1] (numeric) = 1.2674271229404312 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.789000000000022 " " Order of pole = 1.0000000000007496 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21200000000000016 " " y[1] (analytic) = 1.269035532994924 " " y[1] (numeric) = 1.269035532994924 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7879999999999847 " " Order of pole = 0.999999999999492 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21300000000000016 " " y[1] (analytic) = 1.270648030495553 " " y[1] (numeric) = 1.270648030495553 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7869999999999804 " " Order of pole = 0.9999999999993392 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21400000000000016 " " y[1] (analytic) = 1.2722646310432573 " " y[1] (numeric) = 1.2722646310432573 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7859999999999887 " " Order of pole = 0.9999999999996305 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21500000000000016 " " y[1] (analytic) = 1.2738853503184717 " " y[1] (numeric) = 1.2738853503184715 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.74305014866149520000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7850000000000045 " " Order of pole = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21600000000000016 " " y[1] (analytic) = 1.275510204081633 " " y[1] (numeric) = 1.2755102040816328 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.74082970261224500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7839999999999991 " " Order of pole = 0.9999999999999609 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21700000000000016 " " y[1] (analytic) = 1.2771392081736912 " " y[1] (numeric) = 1.2771392081736912 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7829999999999963 " " Order of pole = 0.9999999999998757 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21800000000000017 " " y[1] (analytic) = 1.2787723785166243 " " y[1] (numeric) = 1.2787723785166243 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7820000000000036 " " Order of pole = 1.0000000000001208 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21900000000000017 " " y[1] (analytic) = 1.2804097311139568 " " y[1] (numeric) = 1.2804097311139566 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.73416836446449400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7809999999999784 " " Order of pole = 0.9999999999992681 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000017 " " y[1] (analytic) = 1.2820512820512824 " " y[1] (numeric) = 1.2820512820512822 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.73194791841524400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7800000000000197 " " Order of pole = 1.0000000000006715 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22100000000000017 " " y[1] (analytic) = 1.283697047496791 " " y[1] (numeric) = 1.2836970474967908 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.729727472365993300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7790000000000038 " " Order of pole = 1.0000000000001315 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000017 " " y[1] (analytic) = 1.2853470437017998 " " y[1] (numeric) = 1.2853470437017995 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.727507026316743300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7780000000000176 " " Order of pole = 1.0000000000006004 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000017 " " y[1] (analytic) = 1.2870012870012872 " " y[1] (numeric) = 1.287001287001287 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.72528658026749300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7770000000000211 " " Order of pole = 1.0000000000007105 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000017 " " y[1] (analytic) = 1.2886597938144333 " " y[1] (numeric) = 1.288659793814433 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.723066134218242400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7760000000000195 " " Order of pole = 1.000000000000668 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000017 " " y[1] (analytic) = 1.2903225806451617 " " y[1] (numeric) = 1.2903225806451615 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.72084568816899200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7750000000000172 " " Order of pole = 1.000000000000579 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000017 " " y[1] (analytic) = 1.2919896640826878 " " y[1] (numeric) = 1.2919896640826876 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.718625242119741800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7739999999999931 " " Order of pole = 0.9999999999997584 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000017 " " y[1] (analytic) = 1.2936610608020702 " " y[1] (numeric) = 1.29366106080207 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.716404796070491700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7729999999999939 " " Order of pole = 0.9999999999997868 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000017 " " y[1] (analytic) = 1.2953367875647672 " " y[1] (numeric) = 1.295336787564767 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.71418435002124110000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7719999999999766 " " Order of pole = 0.9999999999992006 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000018 " " y[1] (analytic) = 1.2970168612191961 " " y[1] (numeric) = 1.297016861219196 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.71196390397199080000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7709999999999945 " " Order of pole = 0.9999999999998082 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000018 " " y[1] (analytic) = 1.2987012987012991 " " y[1] (numeric) = 1.2987012987012987 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.41948691584548100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7700000000000121 " " Order of pole = 1.0000000000004121 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000018 " " y[1] (analytic) = 1.3003901170351109 " " y[1] (numeric) = 1.3003901170351104 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.415046023746980400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7690000000000172 " " Order of pole = 1.0000000000005933 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000018 " " y[1] (analytic) = 1.3020833333333337 " " y[1] (numeric) = 1.3020833333333333 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.4106051316484803000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7679999999999905 " " Order of pole = 0.999999999999666 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000018 " " y[1] (analytic) = 1.3037809647979144 " " y[1] (numeric) = 1.303780964797914 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.40616423954997900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.767000000000009 " " Order of pole = 1.0000000000003126 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000018 " " y[1] (analytic) = 1.305483028720627 " " y[1] (numeric) = 1.3054830287206267 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.700861673725739300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7659999999999962 " " Order of pole = 0.9999999999998721 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000018 " " y[1] (analytic) = 1.3071895424836606 " " y[1] (numeric) = 1.3071895424836601 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.39728245535297800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7650000000000068 " " Order of pole = 1.000000000000238 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000018 " " y[1] (analytic) = 1.3089005235602098 " " y[1] (numeric) = 1.3089005235602094 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.392841563254477000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.763999999999983 " " Order of pole = 0.9999999999993996 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000018 " " y[1] (analytic) = 1.3106159895150724 " " y[1] (numeric) = 1.310615989515072 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.38840067115597700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7629999999999942 " " Order of pole = 0.9999999999998153 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000018 " " y[1] (analytic) = 1.3123359580052496 " " y[1] (numeric) = 1.3123359580052492 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.383959779057476600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.761999999999992 " " Order of pole = 0.9999999999997158 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000018 " " y[1] (analytic) = 1.3140604467805523 " " y[1] (numeric) = 1.3140604467805517 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.06927833043846400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7610000000000058 " " Order of pole = 1.0000000000001847 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000019 " " y[1] (analytic) = 1.3157894736842108 " " y[1] (numeric) = 1.3157894736842104 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.37507799486047530000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7599999999999776 " " Order of pole = 0.9999999999992149 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2410000000000002 " " y[1] (analytic) = 1.317523056653492 " " y[1] (numeric) = 1.3175230566534912 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.055955654142962000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7589999999999858 " " Order of pole = 0.9999999999994991 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2420000000000002 " " y[1] (analytic) = 1.319261213720317 " " y[1] (numeric) = 1.3192612137203164 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.0492943159952100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7580000000000052 " " Order of pole = 1.000000000000167 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2430000000000002 " " y[1] (analytic) = 1.3210039630118895 " " y[1] (numeric) = 1.3210039630118888 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.04263297784745900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7569999999999975 " " Order of pole = 0.9999999999999147 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2440000000000002 " " y[1] (analytic) = 1.3227513227513232 " " y[1] (numeric) = 1.3227513227513226 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.035971639699709000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7560000000000239 " " Order of pole = 1.0000000000008349 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2450000000000002 " " y[1] (analytic) = 1.3245033112582785 " " y[1] (numeric) = 1.324503311258278 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.35287353436797200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7550000000000341 " " Order of pole = 1.0000000000011937 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2460000000000002 " " y[1] (analytic) = 1.3262599469496026 " " y[1] (numeric) = 1.326259946949602 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.022648963404207000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7539999999999903 " " Order of pole = 0.9999999999996483 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2470000000000002 " " y[1] (analytic) = 1.3280212483399738 " " y[1] (numeric) = 1.3280212483399731 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.01598762525645600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7530000000000203 " " Order of pole = 1.000000000000714 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2480000000000002 " " y[1] (analytic) = 1.3297872340425536 " " y[1] (numeric) = 1.329787234042553 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.00932628710870500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7520000000000029 " " Order of pole = 1.0000000000000995 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2490000000000002 " " y[1] (analytic) = 1.3315579227696408 " " y[1] (numeric) = 1.3315579227696401 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.002664948960954000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7510000000000067 " " Order of pole = 1.000000000000231 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25000000000000017 " " y[1] (analytic) = 1.3333333333333337 " " y[1] (numeric) = 1.333333333333333 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.99600361081320330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7499999999999772 " " Order of pole = 0.9999999999991829 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25100000000000017 " " y[1] (analytic) = 1.3351134846461952 " " y[1] (numeric) = 1.3351134846461947 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.326228181776968400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7490000000000144 " " Order of pole = 1.0000000000005045 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25200000000000017 " " y[1] (analytic) = 1.3368983957219256 " " y[1] (numeric) = 1.336898395721925 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.98268093451770100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7479999999999815 " " Order of pole = 0.9999999999993392 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25300000000000017 " " y[1] (analytic) = 1.3386880856760377 " " y[1] (numeric) = 1.3386880856760373 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.31734639757996700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.746999999999983 " " Order of pole = 0.9999999999993889 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25400000000000017 " " y[1] (analytic) = 1.340482573726542 " " y[1] (numeric) = 1.3404825737265413 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.96935825822219900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7459999999999841 " " Order of pole = 0.9999999999994351 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25500000000000017 " " y[1] (analytic) = 1.3422818791946312 " " y[1] (numeric) = 1.3422818791946307 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.30846461338296600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7450000000000289 " " Order of pole = 1.0000000000010196 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25600000000000017 " " y[1] (analytic) = 1.3440860215053767 " " y[1] (numeric) = 1.3440860215053763 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.30402372128446500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7440000000000199 " " Order of pole = 1.0000000000006963 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000002 " " y[1] (analytic) = 1.3458950201884254 " " y[1] (numeric) = 1.3458950201884252 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.649791414592982600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7429999999999991 " " Order of pole = 0.999999999999968 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000002 " " y[1] (analytic) = 1.3477088948787066 " " y[1] (numeric) = 1.3477088948787062 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.295141937087463500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7419999999999948 " " Order of pole = 0.9999999999998082 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000002 " " y[1] (analytic) = 1.3495276653171393 " " y[1] (numeric) = 1.3495276653171389 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.29070104498896300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7409999999999892 " " Order of pole = 0.9999999999996128 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000002 " " y[1] (analytic) = 1.3513513513513518 " " y[1] (numeric) = 1.3513513513513513 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.28626015289046200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7399999999999962 " " Order of pole = 0.9999999999998579 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000002 " " y[1] (analytic) = 1.3531799729364007 " " y[1] (numeric) = 1.3531799729364005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.640909630395981000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7389999999999883 " " Order of pole = 0.9999999999995701 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000002 " " y[1] (analytic) = 1.3550135501355018 " " y[1] (numeric) = 1.3550135501355012 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.916067553040191500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7380000000000149 " " Order of pole = 1.0000000000005258 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000002 " " y[1] (analytic) = 1.35685210312076 " " y[1] (numeric) = 1.3568521031207597 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.27293747659496100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7369999999999997 " " Order of pole = 0.9999999999999893 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000002 " " y[1] (analytic) = 1.3586956521739135 " " y[1] (numeric) = 1.3586956521739129 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.902744876744689600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.736000000000008 " " Order of pole = 1.0000000000002913 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000002 " " y[1] (analytic) = 1.360544217687075 " " y[1] (numeric) = 1.3605442176870746 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.264055692397959700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7349999999999962 " " Order of pole = 0.9999999999998579 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000002 " " y[1] (analytic) = 1.362397820163488 " " y[1] (numeric) = 1.3623978201634874 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.88942220044918800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7340000000000116 " " Order of pole = 1.0000000000004086 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000002 " " y[1] (analytic) = 1.3642564802182813 " " y[1] (numeric) = 1.3642564802182808 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.25517390820095840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7330000000000139 " " Order of pole = 1.0000000000005045 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000002 " " y[1] (analytic) = 1.3661202185792354 " " y[1] (numeric) = 1.3661202185792347 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.87609952415368600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7320000000000029 " " Order of pole = 1.000000000000096 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2690000000000002 " " y[1] (analytic) = 1.3679890560875516 " " y[1] (numeric) = 1.367989056087551 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.869438186005935500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.731 " " Order of pole = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2700000000000002 " " y[1] (analytic) = 1.3698630136986305 " " y[1] (numeric) = 1.3698630136986298 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.862776847858184500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7300000000000104 " " Order of pole = 1.0000000000003801 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2710000000000002 " " y[1] (analytic) = 1.3717421124828535 " " y[1] (numeric) = 1.3717421124828528 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.85611550971043360000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7290000000000156 " " Order of pole = 1.0000000000005578 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2720000000000002 " " y[1] (analytic) = 1.373626373626374 " " y[1] (numeric) = 1.3736263736263732 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.4659388954169110000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7279999999999989 " " Order of pole = 0.9999999999999503 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2730000000000002 " " y[1] (analytic) = 1.3755158184319123 " " y[1] (numeric) = 1.3755158184319116 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.842792833414931000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7270000000000323 " " Order of pole = 1.0000000000011688 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2740000000000002 " " y[1] (analytic) = 1.3774104683195596 " " y[1] (numeric) = 1.377410468319559 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.83613149526718100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7259999999999927 " " Order of pole = 0.9999999999997264 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2750000000000002 " " y[1] (analytic) = 1.3793103448275865 " " y[1] (numeric) = 1.3793103448275859 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.8294701571194300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7250000000000008 " " Order of pole = 1.0000000000000213 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2760000000000002 " " y[1] (analytic) = 1.3812154696132601 " " y[1] (numeric) = 1.3812154696132593 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.43041175862890400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7240000000000019 " " Order of pole = 1.0000000000000497 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2770000000000002 " " y[1] (analytic) = 1.3831258644536655 " " y[1] (numeric) = 1.3831258644536648 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.816147480823928500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7230000000000062 " " Order of pole = 1.0000000000002203 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2780000000000002 " " y[1] (analytic) = 1.385041551246538 " " y[1] (numeric) = 1.3850415512465368 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.01581023779362800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7219999999999924 " " Order of pole = 0.9999999999997087 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = y * y;" Iterations = 279 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 21 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 21 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 5 Minutes 22 Seconds "Time to Timeout " Unknown Percent Done = 56.000000000000036 "%" (%o57) true (%o57) diffeq.max