(%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) 2.0 (%i55) exact_soln_y(x) := block(-----------) 1.0 - 2.0 x 2.0 (%o55) exact_soln_y(x) := block(-----------) 1.0 - 2.0 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/nonlinear2postode.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:0.2,"), 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, " (2.0/(1.0 - 2.0*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 : 0.2, 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, "2013-01-13T01:25:58-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "nonlinear2"), 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, "nonlinear2 diffeq.max"), logitem_str(html_log_file, "nonlinear2 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/nonlinear2postode.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:0.2,"), 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, " (2.0/(1.0 - 2.0*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 : 0.2, 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, "2013-01-13T01:25:58-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "nonlinear2"), 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, "nonlinear2 diffeq.max"), logitem_str(html_log_file, "nonlinear2 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/nonlinear2postode.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:0.2," "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(" " (2.0/(1.0 - 2.0*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 = 0.2 "" estimated_steps = 200. "" step_error = 5.0000000000000E-13 "" est_needed_step_err = 5.0000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.34352079945727950000000000000000000000000000000000000000000000000000000000000000000000E-70 "" max_value3 = 1.34352079945727950000000000000000000000000000000000000000000000000000000000000000000000E-70 "" value3 = 1.34352079945727950000000000000000000000000000000000000000000000000000000000000000000000E-70 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.0 " " y[1] (analytic) = 2. " " y[1] (numeric) = 2. " " 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) = 2. " " y[1] (numeric) = 2. " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.5000000000000152 " " Order of pole = 1.000000000000803 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.000E-3 " " y[1] (analytic) = 2.004008016032064 " " y[1] (numeric) = 2.004008016032064 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4990000000000116 " " Order of pole = 1.0000000000006146 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.000E-3 " " y[1] (analytic) = 2.0080321285140563 " " y[1] (numeric) = 2.008032128514056 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.211564265053311800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.49800000000000416 " " Order of pole = 1.0000000000002132 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.000E-3 " " y[1] (analytic) = 2.0120724346076457 " " y[1] (numeric) = 2.0120724346076457 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4970000000000139 " " Order of pole = 1.000000000000746 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.000E-3 " " y[1] (analytic) = 2.0161290322580645 " " y[1] (numeric) = 2.0161290322580645 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4959999999999868 " " Order of pole = 0.9999999999992895 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.000E-3 " " y[1] (analytic) = 2.0202020202020203 " " y[1] (numeric) = 2.0202020202020203 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4950000000000121 " " Order of pole = 1.000000000000643 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.000E-3 " " y[1] (analytic) = 2.0242914979757085 " " y[1] (numeric) = 2.0242914979757085 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.49400000000000044 " " Order of pole = 1.0000000000000284 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.000E-3 " " y[1] (analytic) = 2.028397565922921 " " y[1] (numeric) = 2.028397565922921 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.49299999999999666 " " Order of pole = 0.9999999999998153 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.000E-3 " " y[1] (analytic) = 2.032520325203252 " " y[1] (numeric) = 2.032520325203252 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4920000000000024 " " Order of pole = 1.000000000000128 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.000000000000001000E-3 " " y[1] (analytic) = 2.0366598778004072 " " y[1] (numeric) = 2.0366598778004077 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.180478020363807400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4909999999999989 " " Order of pole = 0.9999999999999503 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000000200E-2 " " y[1] (analytic) = 2.0408163265306123 " " y[1] (numeric) = 2.0408163265306127 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.176037128265306800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4900000000000058 " " Order of pole = 1.0000000000003162 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.100000000000000300E-2 " " y[1] (analytic) = 2.044989775051125 " " y[1] (numeric) = 2.0449897750511252 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.17159623616680620000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4890000000000117 " " Order of pole = 1.000000000000636 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.200000000000000400E-2 " " y[1] (analytic) = 2.0491803278688523 " " y[1] (numeric) = 2.0491803278688527 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.167155344068305800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.48800000000001104 " " Order of pole = 1.0000000000006004 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000000600E-2 " " y[1] (analytic) = 2.053388090349076 " " y[1] (numeric) = 2.053388090349076 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.48699999999999116 " " Order of pole = 0.9999999999995097 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000000700E-2 " " y[1] (analytic) = 2.05761316872428 " " y[1] (numeric) = 2.0576131687242802 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.158273559871304300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4860000000000055 " " Order of pole = 1.0000000000003055 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000000800E-2 " " y[1] (analytic) = 2.061855670103093 " " y[1] (numeric) = 2.061855670103093 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4850000000000017 " " Order of pole = 1.000000000000096 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.600000000000001000E-2 " " y[1] (analytic) = 2.066115702479339 " " y[1] (numeric) = 2.066115702479339 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.48400000000000326 " " Order of pole = 1.000000000000174 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.700000000000001000E-2 " " y[1] (analytic) = 2.070393374741201 " " y[1] (numeric) = 2.070393374741201 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.48299999999999693 " " Order of pole = 0.9999999999998366 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.80000000000000100E-2 " " y[1] (analytic) = 2.074688796680498 " " y[1] (numeric) = 2.074688796680498 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.48199999999999527 " " Order of pole = 0.9999999999997407 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.90000000000000100E-2 " " y[1] (analytic) = 2.079002079002079 " " y[1] (numeric) = 2.079002079002079 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.481 " " Order of pole = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000000120E-2 " " y[1] (analytic) = 2.0833333333333335 " " y[1] (numeric) = 2.0833333333333335 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.47999999999999693 " " Order of pole = 0.9999999999998366 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.10000000000000130E-2 " " y[1] (analytic) = 2.0876826722338206 " " y[1] (numeric) = 2.0876826722338206 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4790000000000054 " " Order of pole = 1.0000000000002949 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.200000000000001400E-2 " " y[1] (analytic) = 2.092050209205021 " " y[1] (numeric) = 2.0920502092050213 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.122746423083299600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4779999999999861 " " Order of pole = 0.9999999999992326 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.300000000000001500E-2 " " y[1] (analytic) = 2.0964360587002098 " " y[1] (numeric) = 2.09643605870021 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.118305530984798400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.47700000000001225 " " Order of pole = 1.0000000000006892 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.400000000000001600E-2 " " y[1] (analytic) = 2.100840336134454 " " y[1] (numeric) = 2.1008403361344543 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.11386463888629800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.47600000000000325 " " Order of pole = 1.0000000000001883 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.500000000000001700E-2 " " y[1] (analytic) = 2.1052631578947367 " " y[1] (numeric) = 2.105263157894737 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.109423746787797400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.47499999999999415 " " Order of pole = 0.9999999999996838 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.600000000000002000E-2 " " y[1] (analytic) = 2.109704641350211 " " y[1] (numeric) = 2.1097046413502114 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.104982854689296800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4740000000000089 " " Order of pole = 1.0000000000004938 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.700000000000002000E-2 " " y[1] (analytic) = 2.1141649048625792 " " y[1] (numeric) = 2.1141649048625797 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.100541962590796500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4730000000000164 " " Order of pole = 1.0000000000009308 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.800000000000002000E-2 " " y[1] (analytic) = 2.1186440677966103 " " y[1] (numeric) = 2.1186440677966107 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.096101070492295300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4719999999999997 " " Order of pole = 0.9999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.90000000000000200E-2 " " y[1] (analytic) = 2.1231422505307855 " " y[1] (numeric) = 2.123142250530786 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.09166017839379500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.47099999999998626 " " Order of pole = 0.9999999999992291 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.00000000000000200E-2 " " y[1] (analytic) = 2.127659574468085 " " y[1] (numeric) = 2.1276595744680855 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.087219286295294300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4700000000000024 " " Order of pole = 1.000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.10000000000000200E-2 " " y[1] (analytic) = 2.1321961620469083 " " y[1] (numeric) = 2.1321961620469088 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.082778394196793700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.46899999999999736 " " Order of pole = 0.9999999999998472 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.20000000000000230E-2 " " y[1] (analytic) = 2.1367521367521367 " " y[1] (numeric) = 2.136752136752137 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.078337502098293300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4679999999999956 " " Order of pole = 0.9999999999997549 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.30000000000000240E-2 " " y[1] (analytic) = 2.1413276231263385 " " y[1] (numeric) = 2.141327623126339 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.073896609999792100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.466999999999998 " " Order of pole = 0.9999999999998899 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.40000000000000250E-2 " " y[1] (analytic) = 2.145922746781116 " " y[1] (numeric) = 2.1459227467811166 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.069455717901291500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4659999999999876 " " Order of pole = 0.9999999999993072 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.500000000000002600E-2 " " y[1] (analytic) = 2.1505376344086025 " " y[1] (numeric) = 2.150537634408603 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.06501482580279100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4649999999999923 " " Order of pole = 0.9999999999995701 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.600000000000002600E-2 " " y[1] (analytic) = 2.1551724137931036 " " y[1] (numeric) = 2.155172413793104 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.060573933704290500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4640000000000051 " " Order of pole = 1.0000000000002878 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.700000000000003000E-2 " " y[1] (analytic) = 2.1598272138228944 " " y[1] (numeric) = 2.159827213822895 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.056133041605790000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.46300000000000024 " " Order of pole = 1.0000000000000213 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.80000000000000300E-2 " " y[1] (analytic) = 2.1645021645021645 " " y[1] (numeric) = 2.1645021645021654 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.10338429901457860000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.46199999999999786 " " Order of pole = 0.9999999999998899 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.90000000000000300E-2 " " y[1] (analytic) = 2.1691973969631237 " " y[1] (numeric) = 2.1691973969631246 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.09450251481757700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4610000000000141 " " Order of pole = 1.0000000000008242 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.00000000000000300E-2 " " y[1] (analytic) = 2.173913043478261 " " y[1] (numeric) = 2.173913043478262 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.085620730620575500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4599999999999777 " " Order of pole = 0.9999999999987281 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.10000000000000300E-2 " " y[1] (analytic) = 2.178649237472767 " " y[1] (numeric) = 2.178649237472768 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.11510841963536200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.45900000000000407 " " Order of pole = 1.0000000000002416 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.20000000000000300E-2 " " y[1] (analytic) = 2.183406113537118 " " y[1] (numeric) = 2.183406113537119 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.06785716222657360000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4579999999999829 " " Order of pole = 0.9999999999990301 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.30000000000000300E-2 " " y[1] (analytic) = 2.188183807439825 " " y[1] (numeric) = 2.188183807439826 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.05897537802957200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4570000000000098 " " Order of pole = 1.0000000000005826 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.40000000000000340E-2 " " y[1] (analytic) = 2.192982456140351 " " y[1] (numeric) = 2.192982456140352 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.050093593832570500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4559999999999957 " " Order of pole = 0.9999999999997691 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.50000000000000340E-2 " " y[1] (analytic) = 2.197802197802198 " " y[1] (numeric) = 2.197802197802199 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.04121180963556900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.45499999999999585 " " Order of pole = 0.9999999999997762 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.600000000000003500E-2 " " y[1] (analytic) = 2.2026431718061676 " " y[1] (numeric) = 2.2026431718061685 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.03233002543856800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.45400000000000507 " " Order of pole = 1.000000000000302 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.700000000000003600E-2 " " y[1] (analytic) = 2.207505518763797 " " y[1] (numeric) = 2.207505518763798 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.02344824124156730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.45300000000001334 " " Order of pole = 1.0000000000007851 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.800000000000003700E-2 " " y[1] (analytic) = 2.212389380530974 " " y[1] (numeric) = 2.2123893805309747 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.014566457044565500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.45200000000000495 " " Order of pole = 1.0000000000002913 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.90000000000000400E-2 " " y[1] (analytic) = 2.21729490022173 " " y[1] (numeric) = 2.217294900221731 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.00568467284756400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4510000000000023 " " Order of pole = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000000300E-2 " " y[1] (analytic) = 2.2222222222222223 " " y[1] (numeric) = 2.2222222222222237 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.99520433297584500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4499999999999957 " " Order of pole = 0.999999999999762 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.10000000000000300E-2 " " y[1] (analytic) = 2.2271714922049 " " y[1] (numeric) = 2.227171492204901 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.987921104453562000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4489999999999856 " " Order of pole = 0.9999999999991651 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.20000000000000400E-2 " " y[1] (analytic) = 2.232142857142857 " " y[1] (numeric) = 2.2321428571428585 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.96855898038484200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4480000000000044 " " Order of pole = 1.0000000000002665 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.30000000000000400E-2 " " y[1] (analytic) = 2.237136465324385 " " y[1] (numeric) = 2.237136465324386 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.9552363040893400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4470000000000071 " " Order of pole = 1.0000000000004334 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.40000000000000400E-2 " " y[1] (analytic) = 2.2421524663677133 " " y[1] (numeric) = 2.2421524663677146 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.94191362779383700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.446000000000007 " " Order of pole = 1.0000000000004334 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.50000000000000400E-2 " " y[1] (analytic) = 2.247191011235955 " " y[1] (numeric) = 2.2471910112359565 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.92859095149833600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.44500000000001433 " " Order of pole = 1.0000000000008775 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.60000000000000400E-2 " " y[1] (analytic) = 2.2522522522522523 " " y[1] (numeric) = 2.2522522522522537 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.91526827520283400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.44400000000000045 " " Order of pole = 1.0000000000000462 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.700000000000004000E-2 " " y[1] (analytic) = 2.2573363431151243 " " y[1] (numeric) = 2.2573363431151257 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.90194559890733100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4429999999999889 " " Order of pole = 0.9999999999993499 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.800000000000004000E-2 " " y[1] (analytic) = 2.2624434389140275 " " y[1] (numeric) = 2.2624434389140284 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.92574861507455300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4420000000000043 " " Order of pole = 1.00000000000027 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.900000000000004000E-2 " " y[1] (analytic) = 2.267573696145125 " " y[1] (numeric) = 2.267573696145126 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.91686683087755170000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4410000000000112 " " Order of pole = 1.0000000000006857 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.000000000000004000E-2 " " y[1] (analytic) = 2.272727272727273 " " y[1] (numeric) = 2.2727272727272743 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.86197757002082700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.43999999999999584 " " Order of pole = 0.999999999999762 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.10000000000000400E-2 " " y[1] (analytic) = 2.2779043280182236 " " y[1] (numeric) = 2.277904328018225 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.84865489372532500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4389999999999951 " " Order of pole = 0.9999999999997158 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.20000000000000400E-2 " " y[1] (analytic) = 2.2831050228310503 " " y[1] (numeric) = 2.283105022831052 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.78044295657309700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4380000000000133 " " Order of pole = 1.0000000000008313 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.30000000000000400E-2 " " y[1] (analytic) = 2.288329519450801 " " y[1] (numeric) = 2.288329519450803 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.76267938817909300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4370000000000001 " " Order of pole = 1.0000000000000249 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.40000000000000500E-2 " " y[1] (analytic) = 2.2935779816513766 " " y[1] (numeric) = 2.293577981651378 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.80868686483881800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.43599999999999206 " " Order of pole = 0.9999999999995346 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.50000000000000500E-2 " " y[1] (analytic) = 2.298850574712644 " " y[1] (numeric) = 2.2988505747126453 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.79536418854331600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4349999999999948 " " Order of pole = 0.9999999999996945 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.60000000000000500E-2 " " y[1] (analytic) = 2.3041474654377883 " " y[1] (numeric) = 2.3041474654377896 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.78204151224781500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.43399999999999794 " " Order of pole = 0.9999999999998899 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.70000000000000500E-2 " " y[1] (analytic) = 2.309468822170901 " " y[1] (numeric) = 2.3094688221709023 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.76871883595231200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4330000000000087 " " Order of pole = 1.0000000000005613 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.80000000000000500E-2 " " y[1] (analytic) = 2.3148148148148153 " " y[1] (numeric) = 2.3148148148148167 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.7553961596568100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.43200000000000716 " " Order of pole = 1.0000000000004512 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.90000000000000500E-2 " " y[1] (analytic) = 2.3201856148491884 " " y[1] (numeric) = 2.3201856148491897 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.74207348336130900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.43099999999998845 " " Order of pole = 0.9999999999993108 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000000500E-2 " " y[1] (analytic) = 2.3255813953488373 " " y[1] (numeric) = 2.325581395348839 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.63833440942107700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4300000000000077 " " Order of pole = 1.0000000000005045 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.10000000000000500E-2 " " y[1] (analytic) = 2.3310023310023316 " " y[1] (numeric) = 2.331002331002333 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.71542813077030400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4290000000000056 " " Order of pole = 1.000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.20000000000000500E-2 " " y[1] (analytic) = 2.3364485981308416 " " y[1] (numeric) = 2.336448598130843 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.70210545447480300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4280000000000012 " " Order of pole = 1.0000000000000995 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.30000000000000500E-2 " " y[1] (analytic) = 2.3419203747072603 " " y[1] (numeric) = 2.3419203747072617 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.688782778179301000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4270000000000046 " " Order of pole = 1.000000000000302 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.40000000000000500E-2 " " y[1] (analytic) = 2.3474178403755874 " " y[1] (numeric) = 2.3474178403755888 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.67546010188379900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4259999999999989 " " Order of pole = 0.9999999999999538 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.50000000000000600E-2 " " y[1] (analytic) = 2.3529411764705888 " " y[1] (numeric) = 2.35294117647059 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.66213742558829700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.42500000000000804 " " Order of pole = 1.0000000000005187 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.60000000000000600E-2 " " y[1] (analytic) = 2.3584905660377364 " " y[1] (numeric) = 2.3584905660377378 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.648814749292795000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4240000000000126 " " Order of pole = 1.0000000000008136 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.70000000000000600E-2 " " y[1] (analytic) = 2.364066193853428 " " y[1] (numeric) = 2.36406619385343 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.51398943066306000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.42299999999999194 " " Order of pole = 0.9999999999995204 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.80000000000000600E-2 " " y[1] (analytic) = 2.369668246445498 " " y[1] (numeric) = 2.3696682464455 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.49622586226905500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4220000000000105 " " Order of pole = 1.0000000000006786 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.90000000000000600E-2 " " y[1] (analytic) = 2.3752969121140146 " " y[1] (numeric) = 2.3752969121140164 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.47846229387505300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.42100000000000476 " " Order of pole = 1.0000000000003233 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000000600E-2 " " y[1] (analytic) = 2.3809523809523814 " " y[1] (numeric) = 2.380952380952383 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.46069872548105100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4200000000000027 " " Order of pole = 1.0000000000001883 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.10000000000000600E-2 " " y[1] (analytic) = 2.3866348448687353 " " y[1] (numeric) = 2.386634844868737 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.44293515708705000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4189999999999974 " " Order of pole = 0.999999999999865 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.20000000000000600E-2 " " y[1] (analytic) = 2.392344497607656 " " y[1] (numeric) = 2.3923444976076573 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.56887869151978400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.41799999999999904 " " Order of pole = 0.9999999999999574 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.30000000000000600E-2 " " y[1] (analytic) = 2.398081534772183 " " y[1] (numeric) = 2.398081534772184 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.55555601522428200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.41700000000001103 " " Order of pole = 1.0000000000007212 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.40000000000000600E-2 " " y[1] (analytic) = 2.403846153846154 " " y[1] (numeric) = 2.403846153846156 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.38964445190504100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4160000000000015 " " Order of pole = 1.0000000000001172 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.50000000000000600E-2 " " y[1] (analytic) = 2.409638554216868 " " y[1] (numeric) = 2.4096385542168695 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.52891066263327800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.41500000000001347 " " Order of pole = 1.000000000000881 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.60000000000000700E-2 " " y[1] (analytic) = 2.415458937198068 " " y[1] (numeric) = 2.4154589371980695 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.515587986337777000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.41399999999999104 " " Order of pole = 0.9999999999994422 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.70000000000000700E-2 " " y[1] (analytic) = 2.421307506053269 " " y[1] (numeric) = 2.4213075060532705 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.50226531004227500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4130000000000028 " " Order of pole = 1.000000000000199 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.80000000000000700E-2 " " y[1] (analytic) = 2.4271844660194177 " " y[1] (numeric) = 2.427184466019419 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.48894263374677300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.41200000000000253 " " Order of pole = 1.0000000000001776 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.90000000000000700E-2 " " y[1] (analytic) = 2.433090024330901 " " y[1] (numeric) = 2.4330900243309017 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.650413304967513600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.41100000000000053 " " Order of pole = 1.0000000000000462 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000000700E-2 " " y[1] (analytic) = 2.439024390243903 " " y[1] (numeric) = 2.4390243902439037 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.64153152077051300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4100000000000043 " " Order of pole = 1.0000000000002913 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.10000000000000700E-2 " " y[1] (analytic) = 2.4449877750611253 " " y[1] (numeric) = 2.444987775061126 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.632649736573511600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4089999999999958 " " Order of pole = 0.9999999999997407 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.20000000000000700E-2 " " y[1] (analytic) = 2.4509803921568634 " " y[1] (numeric) = 2.4509803921568643 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.6237679523765100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4080000000000084 " " Order of pole = 1.0000000000005542 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.30000000000000700E-2 " " y[1] (analytic) = 2.4570024570024573 " " y[1] (numeric) = 2.4570024570024587 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.422329252269263000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.40699999999999437 " " Order of pole = 0.9999999999996447 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.40000000000000700E-2 " " y[1] (analytic) = 2.4630541871921188 " " y[1] (numeric) = 2.46305418719212 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.40900657597376200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.40600000000000736 " " Order of pole = 1.000000000000501 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.50000000000000700E-2 " " y[1] (analytic) = 2.469135802469136 " " y[1] (numeric) = 2.469135802469138 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.19424519957101300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4049999999999918 " " Order of pole = 0.9999999999994955 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.60000000000000700E-2 " " y[1] (analytic) = 2.4752475247524757 " " y[1] (numeric) = 2.4752475247524774 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.1764816311770110000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4040000000000019 " " Order of pole = 1.0000000000001386 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.70000000000000800E-2 " " y[1] (analytic) = 2.481389578163772 " " y[1] (numeric) = 2.481389578163774 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.15871806278300900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.40300000000001196 " " Order of pole = 1.00000000000081 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.80000000000000800E-2 " " y[1] (analytic) = 2.487562189054727 " " y[1] (numeric) = 2.4875621890547284 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.355715870791754000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4020000000000063 " " Order of pole = 1.0000000000004476 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.90000000000000800E-2 " " y[1] (analytic) = 2.4937655860349133 " " y[1] (numeric) = 2.4937655860349146 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.34239319449625200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4010000000000049 " " Order of pole = 1.0000000000003446 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000007 " " y[1] (analytic) = 2.5000000000000004 " " y[1] (numeric) = 2.5000000000000018 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.32907051820075000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.4000000000000152 " " Order of pole = 1.0000000000010232 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10100000000000008 " " y[1] (analytic) = 2.5062656641604018 " " y[1] (numeric) = 2.5062656641604026 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.54383189460349900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.39900000000000224 " " Order of pole = 1.0000000000001563 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000008 " " y[1] (analytic) = 2.5125628140703524 " " y[1] (numeric) = 2.5125628140703533 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.534950110406497300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3979999999999895 " " Order of pole = 0.9999999999993214 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000008 " " y[1] (analytic) = 2.5188916876574314 " " y[1] (numeric) = 2.5188916876574323 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.52606832620949600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.39699999999999414 " " Order of pole = 0.9999999999996128 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000008 " " y[1] (analytic) = 2.525252525252526 " " y[1] (numeric) = 2.525252525252527 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.51718654201249500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3959999999999909 " " Order of pole = 0.9999999999994102 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000008 " " y[1] (analytic) = 2.5316455696202538 " " y[1] (numeric) = 2.5316455696202547 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.50830475781549400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.39500000000001306 " " Order of pole = 1.0000000000008953 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000008 " " y[1] (analytic) = 2.538071065989848 " " y[1] (numeric) = 2.538071065989849 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.499422973618493000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.39399999999999236 " " Order of pole = 0.999999999999492 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000008 " " y[1] (analytic) = 2.5445292620865145 " " y[1] (numeric) = 2.5445292620865154 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.49054118942149100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3929999999999901 " " Order of pole = 0.9999999999993463 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000008 " " y[1] (analytic) = 2.551020408163266 " " y[1] (numeric) = 2.5510204081632666 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.74082970261224500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3920000000000124 " " Order of pole = 1.0000000000008527 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000008 " " y[1] (analytic) = 2.5575447570332486 " " y[1] (numeric) = 2.5575447570332495 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.47277762102748900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3909999999999975 " " Order of pole = 0.9999999999998472 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000008 " " y[1] (analytic) = 2.5641025641025648 " " y[1] (numeric) = 2.5641025641025657 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.46389583683048800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.39000000000000984 " " Order of pole = 1.0000000000006857 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000008 " " y[1] (analytic) = 2.5706940874035995 " " y[1] (numeric) = 2.5706940874036004 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.455014052633486600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3889999999999962 " " Order of pole = 0.9999999999997584 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000009 " " y[1] (analytic) = 2.5773195876288666 " " y[1] (numeric) = 2.5773195876288675 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.44613226843648500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.387999999999993 " " Order of pole = 0.9999999999995488 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000009 " " y[1] (analytic) = 2.5839793281653756 " " y[1] (numeric) = 2.583979328165376 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.718625242119741800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3870000000000111 " " Order of pole = 1.0000000000007745 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000009 " " y[1] (analytic) = 2.5906735751295344 " " y[1] (numeric) = 2.590673575129535 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.71418435002124110000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.38600000000001106 " " Order of pole = 1.000000000000771 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000009 " " y[1] (analytic) = 2.5974025974025983 " " y[1] (numeric) = 2.5974025974025987 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.709743457922740500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3850000000000081 " " Order of pole = 1.0000000000005649 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000009 " " y[1] (analytic) = 2.6041666666666674 " " y[1] (numeric) = 2.604166666666668 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.7053025658242402000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.38400000000000545 " " Order of pole = 1.0000000000003908 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000009 " " y[1] (analytic) = 2.610966057441254 " " y[1] (numeric) = 2.6109660574412543 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.700861673725739300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3830000000000062 " " Order of pole = 1.0000000000004476 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000009 " " y[1] (analytic) = 2.6178010471204196 " " y[1] (numeric) = 2.61780104712042 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.696420781627238600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3820000000000118 " " Order of pole = 1.0000000000008278 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000009 " " y[1] (analytic) = 2.624671916010499 " " y[1] (numeric) = 2.6246719160105 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.383959779057476600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.38099999999999395 " " Order of pole = 0.9999999999995985 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000009 " " y[1] (analytic) = 2.6315789473684217 " " y[1] (numeric) = 2.6315789473684226 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.37507799486047530000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.38000000000001083 " " Order of pole = 1.0000000000007638 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1210000000000001 " " y[1] (analytic) = 2.638522427440634 " " y[1] (numeric) = 2.638522427440635 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.36619621066347400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3790000000000066 " " Order of pole = 1.000000000000469 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1220000000000001 " " y[1] (analytic) = 2.6455026455026465 " " y[1] (numeric) = 2.6455026455026474 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.35731442646647170000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.37799999999999806 " " Order of pole = 0.9999999999998757 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1230000000000001 " " y[1] (analytic) = 2.652519893899205 " " y[1] (numeric) = 2.652519893899206 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.34843264226947100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.377000000000005 " " Order of pole = 1.0000000000003766 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1240000000000001 " " y[1] (analytic) = 2.6595744680851072 " " y[1] (numeric) = 2.659574468085108 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.3395508580724700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3759999999999897 " " Order of pole = 0.9999999999992859 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000008 " " y[1] (analytic) = 2.6666666666666674 " " y[1] (numeric) = 2.6666666666666683 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.33066907387546900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.37500000000000033 " " Order of pole = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000008 " " y[1] (analytic) = 2.673796791443851 " " y[1] (numeric) = 2.673796791443852 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.32178728967846670000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3739999999999946 " " Order of pole = 0.9999999999996305 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000009 " " y[1] (analytic) = 2.680965147453084 " " y[1] (numeric) = 2.680965147453085 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.31290550548146600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3729999999999998 " " Order of pole = 0.9999999999999893 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000009 " " y[1] (analytic) = 2.6881720430107534 " " y[1] (numeric) = 2.6881720430107543 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.30402372128446500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.37199999999999456 " " Order of pole = 0.9999999999996341 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1290000000000001 " " y[1] (analytic) = 2.695417789757413 " " y[1] (numeric) = 2.695417789757414 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.295141937087463500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3709999999999897 " " Order of pole = 0.9999999999992788 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1300000000000001 " " y[1] (analytic) = 2.7027027027027035 " " y[1] (numeric) = 2.7027027027027044 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.28626015289046200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3700000000000057 " " Order of pole = 1.0000000000004121 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1310000000000001 " " y[1] (analytic) = 2.7100271002710037 " " y[1] (numeric) = 2.7100271002710046 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.27737836869346040000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3689999999999999 " " Order of pole = 1.0000000000000107 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1320000000000001 " " y[1] (analytic) = 2.717391304347827 " " y[1] (numeric) = 2.717391304347828 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.2684965844964600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.368000000000004 " " Order of pole = 1.0000000000003055 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1330000000000001 " " y[1] (analytic) = 2.724795640326976 " " y[1] (numeric) = 2.7247956403269775 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.88942220044918800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3670000000000002 " " Order of pole = 1.000000000000039 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1340000000000001 " " y[1] (analytic) = 2.7322404371584708 " " y[1] (numeric) = 2.732240437158472 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.87609952415368600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.36599999999999033 " " Order of pole = 0.999999999999325 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1350000000000001 " " y[1] (analytic) = 2.739726027397261 " " y[1] (numeric) = 2.7397260273972623 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.862776847858184500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.36500000000000704 " " Order of pole = 1.000000000000533 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1360000000000001 " " y[1] (analytic) = 2.747252747252748 " " y[1] (numeric) = 2.7472527472527495 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.84945417156268200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3639999999999903 " " Order of pole = 0.9999999999993072 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1370000000000001 " " y[1] (analytic) = 2.754820936639119 " " y[1] (numeric) = 2.7548209366391205 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.83613149526718100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.36300000000000915 " " Order of pole = 1.000000000000675 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1380000000000001 " " y[1] (analytic) = 2.7624309392265203 " " y[1] (numeric) = 2.7624309392265216 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.822808818971678300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.36200000000000637 " " Order of pole = 1.0000000000004938 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1390000000000001 " " y[1] (analytic) = 2.770083102493076 " " y[1] (numeric) = 2.770083102493077 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.80948614267617600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.36100000000000526 " " Order of pole = 1.0000000000004121 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1400000000000001 " " y[1] (analytic) = 2.7777777777777786 " " y[1] (numeric) = 2.7777777777777803 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.394884621840901000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3599999999999959 " " Order of pole = 0.9999999999997087 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1410000000000001 " " y[1] (analytic) = 2.785515320334263 " " y[1] (numeric) = 2.7855153203342646 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.37712105344689600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.35900000000000004 " " Order of pole = 1.0000000000000355 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1420000000000001 " " y[1] (analytic) = 2.7932960893854757 " " y[1] (numeric) = 2.7932960893854775 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.35935748505289400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3580000000000004 " " Order of pole = 1.0000000000000533 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1430000000000001 " " y[1] (analytic) = 2.801120448179273 " " y[1] (numeric) = 2.801120448179274 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.756195437494168400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3570000000000048 " " Order of pole = 1.0000000000003766 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1440000000000001 " " y[1] (analytic) = 2.808988764044945 " " y[1] (numeric) = 2.8089887640449462 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.74287276119866650000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3559999999999956 " " Order of pole = 0.999999999999698 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1450000000000001 " " y[1] (analytic) = 2.8169014084507054 " " y[1] (numeric) = 2.8169014084507067 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.72955008490316500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.35500000000000925 " " Order of pole = 1.000000000000714 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1460000000000001 " " y[1] (analytic) = 2.824858757062148 " " y[1] (numeric) = 2.8248587570621493 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.71622740860766330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.35400000000000503 " " Order of pole = 1.0000000000003944 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1470000000000001 " " y[1] (analytic) = 2.832861189801701 " " y[1] (numeric) = 2.832861189801702 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.702904732312161400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.352999999999999 " " Order of pole = 0.999999999999936 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1480000000000001 " " y[1] (analytic) = 2.840909090909092 " " y[1] (numeric) = 2.8409090909090935 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.68958205601665900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3520000000000003 " " Order of pole = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1490000000000001 " " y[1] (analytic) = 2.8490028490028503 " " y[1] (numeric) = 2.8490028490028516 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.676259379721157000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.35099999999999726 " " Order of pole = 0.9999999999998046 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1500000000000001 " " y[1] (analytic) = 2.857142857142858 " " y[1] (numeric) = 2.85714285714286 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.21724893790087400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3499999999999992 " " Order of pole = 0.9999999999999574 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1510000000000001 " " y[1] (analytic) = 2.8653295128939837 " " y[1] (numeric) = 2.8653295128939855 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.19948536950687300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.34899999999999903 " " Order of pole = 0.9999999999999467 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1520000000000001 " " y[1] (analytic) = 2.8735632183908058 " " y[1] (numeric) = 2.8735632183908075 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.18172180111286800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.34799999999999875 " " Order of pole = 0.9999999999999325 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1530000000000001 " " y[1] (analytic) = 2.8818443804034595 " " y[1] (numeric) = 2.8818443804034612 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.16395823271886600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3470000000000006 " " Order of pole = 1.0000000000000675 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1540000000000001 " " y[1] (analytic) = 2.8901734104046253 " " y[1] (numeric) = 2.8901734104046275 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.68274333040608100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.34599999999999353 " " Order of pole = 0.9999999999995381 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1550000000000001 " " y[1] (analytic) = 2.8985507246376825 " " y[1] (numeric) = 2.8985507246376843 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.12843109593086200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3450000000000031 " " Order of pole = 1.000000000000263 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1560000000000001 " " y[1] (analytic) = 2.9069767441860477 " " y[1] (numeric) = 2.9069767441860495 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.11066752753685800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.34400000000000763 " " Order of pole = 1.0000000000006075 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1570000000000001 " " y[1] (analytic) = 2.915451895043733 " " y[1] (numeric) = 2.9154518950437347 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.09290395914285700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.34299999999999825 " " Order of pole = 0.9999999999998899 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1580000000000001 " " y[1] (analytic) = 2.923976608187136 " " y[1] (numeric) = 2.9239766081871372 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.5563552930616400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.34200000000000164 " " Order of pole = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1590000000000001 " " y[1] (analytic) = 2.9325513196480952 " " y[1] (numeric) = 2.9325513196480966 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.543032616766138300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.34099999999999064 " " Order of pole = 0.9999999999992895 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000011 " " y[1] (analytic) = 2.9411764705882364 " " y[1] (numeric) = 2.941176470588238 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.03961325396084900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.339999999999998 " " Order of pole = 0.9999999999998685 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000012 " " y[1] (analytic) = 2.9498525073746324 " " y[1] (numeric) = 2.9498525073746342 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.02184968556684600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3390000000000064 " " Order of pole = 1.0000000000005222 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000012 " " y[1] (analytic) = 2.958579881656806 " " y[1] (numeric) = 2.958579881656808 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.00408611717284300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3380000000000062 " " Order of pole = 1.0000000000005116 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000012 " " y[1] (analytic) = 2.967359050445105 " " y[1] (numeric) = 2.967359050445107 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.98632254877884200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3369999999999978 " " Order of pole = 0.9999999999998508 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000012 " " y[1] (analytic) = 2.9761904761904776 " " y[1] (numeric) = 2.9761904761904794 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.96855898038483900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.33599999999999025 " " Order of pole = 0.9999999999992646 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000012 " " y[1] (analytic) = 2.985074626865673 " " y[1] (numeric) = 2.985074626865675 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.95079541199083700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3349999999999965 " " Order of pole = 0.9999999999997478 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000012 " " y[1] (analytic) = 2.9940119760479056 " " y[1] (numeric) = 2.9940119760479074 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.93303184359683300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.33400000000000357 " " Order of pole = 1.0000000000003055 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000012 " " y[1] (analytic) = 3.003003003003004 " " y[1] (numeric) = 3.0030030030030064 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.3940853440035400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3330000000000029 " " Order of pole = 1.0000000000002665 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000012 " " y[1] (analytic) = 3.012048192771086 " " y[1] (numeric) = 3.0120481927710876 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.89750470680882800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3319999999999867 " " Order of pole = 0.9999999999989697 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000012 " " y[1] (analytic) = 3.021148036253778 " " y[1] (numeric) = 3.0211480362537797 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.87974113841482700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.33099999999999974 " " Order of pole = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000012 " " y[1] (analytic) = 3.0303030303030316 " " y[1] (numeric) = 3.0303030303030334 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.86197757002082400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.32999999999999485 " " Order of pole = 0.9999999999996163 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000012 " " y[1] (analytic) = 3.0395136778115517 " " y[1] (numeric) = 3.0395136778115535 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.84421400162682100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.32899999999999396 " " Order of pole = 0.999999999999531 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000013 " " y[1] (analytic) = 3.0487804878048794 " " y[1] (numeric) = 3.048780487804881 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.82645043323281800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3280000000000027 " " Order of pole = 1.0000000000002451 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000013 " " y[1] (analytic) = 3.0581039755351695 " " y[1] (numeric) = 3.0581039755351713 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.80868686483881700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3269999999999965 " " Order of pole = 0.9999999999997513 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000013 " " y[1] (analytic) = 3.0674846625766885 " " y[1] (numeric) = 3.0674846625766903 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.79092329644481400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.32599999999999896 " " Order of pole = 0.9999999999999503 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000013 " " y[1] (analytic) = 3.0769230769230784 " " y[1] (numeric) = 3.07692307692308 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.77315972805081200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.32500000000000906 " " Order of pole = 1.0000000000007674 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000013 " " y[1] (analytic) = 3.086419753086421 " " y[1] (numeric) = 3.0864197530864232 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.19424519957101200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.32399999999999857 " " Order of pole = 0.9999999999999147 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000013 " " y[1] (analytic) = 3.095975232198144 " " y[1] (numeric) = 3.0959752321981457 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.73763259126280600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3230000000000064 " " Order of pole = 1.0000000000005507 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000013 " " y[1] (analytic) = 3.1055900621118027 " " y[1] (numeric) = 3.1055900621118044 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.71986902286880400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3220000000000037 " " Order of pole = 1.000000000000334 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000013 " " y[1] (analytic) = 3.11526479750779 " " y[1] (numeric) = 3.115264797507791 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.27657909085610100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.32100000000001 " " Order of pole = 1.000000000000849 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000013 " " y[1] (analytic) = 3.1250000000000018 " " y[1] (numeric) = 3.125000000000003 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.263256414560598300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3199999999999969 " " Order of pole = 0.9999999999997726 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000013 " " y[1] (analytic) = 3.134796238244516 " " y[1] (numeric) = 3.134796238244517 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.24993373826509700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.31899999999999834 " " Order of pole = 0.9999999999998863 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000013 " " y[1] (analytic) = 3.144654088050316 " " y[1] (numeric) = 3.1446540880503173 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.23661106196959500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3179999999999973 " " Order of pole = 0.9999999999998046 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000013 " " y[1] (analytic) = 3.1545741324921153 " " y[1] (numeric) = 3.1545741324921166 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.223288385674093000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3170000000000034 " " Order of pole = 1.0000000000002984 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000014 " " y[1] (analytic) = 3.164556962025318 " " y[1] (numeric) = 3.1645569620253196 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.20996570937859100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3160000000000039 " " Order of pole = 1.0000000000003517 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000014 " " y[1] (analytic) = 3.174603174603176 " " y[1] (numeric) = 3.1746031746031775 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.1966430330830900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3150000000000039 " " Order of pole = 1.0000000000003482 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000014 " " y[1] (analytic) = 3.18471337579618 " " y[1] (numeric) = 3.184713375796181 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.18332035678758800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.31400000000000006 " " Order of pole = 1.0000000000000355 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000014 " " y[1] (analytic) = 3.1948881789137396 " " y[1] (numeric) = 3.194888178913741 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.16999768049208600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3130000000000041 " " Order of pole = 1.0000000000003695 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000014 " " y[1] (analytic) = 3.205128205128207 " " y[1] (numeric) = 3.205128205128208 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.77111666946438900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3120000000000011 " " Order of pole = 1.0000000000001137 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000014 " " y[1] (analytic) = 3.215434083601288 " " y[1] (numeric) = 3.215434083601289 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.14335232790108200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3109999999999977 " " Order of pole = 0.999999999999833 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000014 " " y[1] (analytic) = 3.225806451612905 " " y[1] (numeric) = 3.225806451612906 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.130029651605580700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3100000000000072 " " Order of pole = 1.000000000000636 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19100000000000014 " " y[1] (analytic) = 3.2362459546925586 " " y[1] (numeric) = 3.2362459546925595 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.744471316873385300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3089999999999984 " " Order of pole = 0.9999999999998757 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19200000000000014 " " y[1] (analytic) = 3.2467532467532485 " " y[1] (numeric) = 3.24675324675325 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.10338429901457640000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3079999999999999 " " Order of pole = 1.000000000000007 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19300000000000014 " " y[1] (analytic) = 3.257328990228015 " " y[1] (numeric) = 3.2573289902280163 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.090061622719074500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.30699999999999855 " " Order of pole = 0.9999999999999112 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19400000000000014 " " y[1] (analytic) = 3.267973856209152 " " y[1] (numeric) = 3.2679738562091534 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.07673894642357260000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3060000000000024 " " Order of pole = 1.000000000000231 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19500000000000015 " " y[1] (analytic) = 3.278688524590166 " " y[1] (numeric) = 3.278688524590167 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.063416270128070000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.30500000000001154 " " Order of pole = 1.0000000000010196 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19600000000000015 " " y[1] (analytic) = 3.2894736842105283 " " y[1] (numeric) = 3.2894736842105297 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.050093593832569000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.30400000000000804 " " Order of pole = 1.0000000000007212 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19700000000000015 " " y[1] (analytic) = 3.300330033003302 " " y[1] (numeric) = 3.300330033003304 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.38236122338275600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.3029999999999989 " " Order of pole = 0.999999999999936 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19800000000000015 " " y[1] (analytic) = 3.311258278145697 " " y[1] (numeric) = 3.311258278145699 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.36459765498875400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.30199999999999594 " " Order of pole = 0.999999999999666 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19900000000000015 " " y[1] (analytic) = 3.3222591362126264 " " y[1] (numeric) = 3.322259136212628 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.34683408659475100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.30100000000000054 " " Order of pole = 1.0000000000000675 " " "Finished!" "diff ( y , x , 1 ) = y * y;" Iterations = 200 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 1 Minutes 15 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 1 Minutes 14 Seconds "Time to Timeout "= 0 Years 0 Days 0 Hours 1 Minutes 44 Seconds Percent Done = 100.50000000000007 "%" (%o57) true (%o57) diffeq.max