(%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 # 0.0 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 # 0.0 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 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_x array_x , 1 1 1 array_const_1D0 1 array_tmp2 : array_const_1D0 + array_tmp1 , array_tmp3 : ----------------, 1 1 1 1 array_tmp2 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_x array_x + array_x array_x , 2 2 1 1 2 - ats(2, array_tmp2, array_tmp3, 2) array_tmp2 : array_tmp1 , array_tmp3 : -----------------------------------, 2 2 2 array_tmp2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary array_y_higher : temporary, temporary : ---------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, array_tmp1 : array_x array_x , 2, 2 3 2 2 - ats(3, array_tmp2, array_tmp3, 2) array_tmp2 : array_tmp1 , array_tmp3 : -----------------------------------, 3 3 3 array_tmp2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, array_tmp2 : array_tmp1 , 2, 3 4 4 - ats(4, array_tmp2, array_tmp3, 2) array_tmp3 : -----------------------------------, array_tmp4 : array_tmp3 , 4 array_tmp2 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp2, array_tmp3, 2) array_tmp2 : array_tmp1 , array_tmp3 : -----------------------------------, 5 5 5 array_tmp2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp2 : array_tmp1 , kkk kkk - ats(kkk, array_tmp2, array_tmp3, 2) array_tmp3 : -------------------------------------, kkk array_tmp2 1 array_tmp4 : array_tmp3 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_x array_x , 1 1 1 array_const_1D0 1 array_tmp2 : array_const_1D0 + array_tmp1 , array_tmp3 : ----------------, 1 1 1 1 array_tmp2 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_x array_x + array_x array_x , 2 2 1 1 2 - ats(2, array_tmp2, array_tmp3, 2) array_tmp2 : array_tmp1 , array_tmp3 : -----------------------------------, 2 2 2 array_tmp2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary array_y_higher : temporary, temporary : ---------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, array_tmp1 : array_x array_x , 2, 2 3 2 2 - ats(3, array_tmp2, array_tmp3, 2) array_tmp2 : array_tmp1 , array_tmp3 : -----------------------------------, 3 3 3 array_tmp2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, array_tmp2 : array_tmp1 , 2, 3 4 4 - ats(4, array_tmp2, array_tmp3, 2) array_tmp3 : -----------------------------------, array_tmp4 : array_tmp3 , 4 array_tmp2 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp2, array_tmp3, 2) array_tmp2 : array_tmp1 , array_tmp3 : -----------------------------------, 5 5 5 array_tmp2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp2 : array_tmp1 , kkk kkk - ats(kkk, array_tmp2, array_tmp3, 2) array_tmp3 : -------------------------------------, kkk array_tmp2 1 array_tmp4 : array_tmp3 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, 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 # 0.0 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 # 0.0 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) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) omniabs(x) := abs(x) (%o49) omniabs(x) := abs(x) y (%i50) expt(x, y) := x y (%o50) expt(x, y) := x (%i51) 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) (%o51) 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) (%i52) exact_soln_y(x) := block(arctan(x)) (%o52) exact_soln_y(x) := block(arctan(x)) (%i53) 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], 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/sing2postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-2.0,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "glob_h:0.00001,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (arctan(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 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_tmp3, 1 + max_terms), array(array_tmp4, 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_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 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_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 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_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, 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), iiif, jjjf x_start : - 2.0, x_end : 1.0, glob_h : 1.0E-5, array_y_init : exact_soln_y(x_start), glob_look_poles : true, 1 + 0 glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 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(), 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 : 1, 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 display_alot(current_iter)), 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 ) = 1.0/ (x * x + 1.0) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T02:54:01-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing2"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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, " 151 "), logitem_str(html_log_file, "sing2 diffeq.max"), logitem_str(html_log_file, "sing2 maxima results" ), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o53) 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], 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/sing2postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-2.0,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "glob_h:0.00001,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (arctan(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 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_tmp3, 1 + max_terms), array(array_tmp4, 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_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 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_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 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_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, 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), iiif, jjjf x_start : - 2.0, x_end : 1.0, glob_h : 1.0E-5, array_y_init : exact_soln_y(x_start), glob_look_poles : true, 1 + 0 glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 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(), 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 : 1, 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 display_alot(current_iter)), 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 ) = 1.0/ (x * x + 1.0) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T02:54:01-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing2"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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, " 151 "), logitem_str(html_log_file, "sing2 diffeq.max"), logitem_str(html_log_file, "sing2 maxima results" ), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i54) main() "##############ECHO OF PROBLEM#################" "##############temp/sing2postode.ode#################" "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-2.0," "x_end:1.0," "glob_h:0.00001," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:100," "/* 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," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (arctan(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 = 3. "" estimated_steps = 3000. "" step_error = 3.333333333333333700000000000000E-14 "" est_needed_step_err = 3.333333333333333700000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.042650135480420700000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" max_value3 = 1.042650135480420700000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" value3 = 1.042650135480420700000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -2. " " y[1] (analytic) = -1.1071487177940906 " " y[1] (numeric) = -1.1071487177940906 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.243797808043561 " " Order of pole = 2.1818134489421936 " " x[1] = -1.999 " " y[1] (analytic) = -1.1069486377647475 " " y[1] (numeric) = -1.1069486377647477 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00591605924376220000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2428999321539482 " " Order of pole = 2.1817931899862693 " " x[1] = -1.9980000000000002 " " y[1] (analytic) = -1.1067483975592705 " " y[1] (numeric) = -1.1067483975592702 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.006278982781540300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.24200204397892 " " Order of pole = 2.1817716888804277 " " x[1] = -1.9970000000000003 " " y[1] (analytic) = -1.1065479970013126 " " y[1] (numeric) = -1.1065479970013123 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00664232845534600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2411041438369925 " " Order of pole = 2.1817489480425714 " " x[1] = -1.9960000000000004 " " y[1] (analytic) = -1.106347435914297 " " y[1] (numeric) = -1.1063474359142969 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.007006096972885600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.240206232056638 " " Order of pole = 2.181724970013658 " " x[1] = -1.9950000000000006 " " y[1] (analytic) = -1.1061467141214156 " " y[1] (numeric) = -1.1061467141214156 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.239308308976153 " " Order of pole = 2.1816997574559913 " " x[1] = -1.9940000000000007 " " y[1] (analytic) = -1.1059458314456285 " " y[1] (numeric) = -1.1059458314456285 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.238410374943555 " " Order of pole = 2.1816733131515598 " " x[1] = -1.9930000000000008 " " y[1] (analytic) = -1.1057447877096636 " " y[1] (numeric) = -1.1057447877096636 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.237512430316653 " " Order of pole = 2.181645640003694 " " x[1] = -1.9920000000000009 " " y[1] (analytic) = -1.1055435827360163 " " y[1] (numeric) = -1.1055435827360163 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2366144754638766 " " Order of pole = 2.1816167410483303 " " x[1] = -1.991000000000001 " " y[1] (analytic) = -1.1053422163469497 " " y[1] (numeric) = -1.10534221634695 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.008831307093901500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2357165107623467 " " Order of pole = 2.1815866194270868 " " x[1] = -1.990000000000001 " " y[1] (analytic) = -1.1051406883644945 " " y[1] (numeric) = -1.1051406883644945 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.234818536600195 " " Order of pole = 2.18155527842028 " " x[1] = -1.9890000000000012 " " y[1] (analytic) = -1.104938998610447 " " y[1] (numeric) = -1.104938998610447 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2339205533747784 " " Order of pole = 2.181522721421441 " " x[1] = -1.9880000000000013 " " y[1] (analytic) = -1.1047371469063707 " " y[1] (numeric) = -1.1047371469063707 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2330225614937187 " " Order of pole = 2.1814889519524776 " " x[1] = -1.9870000000000014 " " y[1] (analytic) = -1.1045351330735953 " " y[1] (numeric) = -1.104535133073595 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.010299159132645500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2321245613740164 " " Order of pole = 2.181453973651017 " " x[1] = -1.9860000000000015 " " y[1] (analytic) = -1.1043329569332156 " " y[1] (numeric) = -1.1043329569332154 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.010667195350753500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.231226553442698 " " Order of pole = 2.1814177902798946 " " x[1] = -1.9850000000000017 " " y[1] (analytic) = -1.1041306183060926 " " y[1] (numeric) = -1.1041306183060926 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.230328538137466 " " Order of pole = 2.18138040573605 " " x[1] = -1.9840000000000018 " " y[1] (analytic) = -1.1039281170128525 " " y[1] (numeric) = -1.1039281170128523 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.011404560705161700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2294305159047108 " " Order of pole = 2.181341824023118 " " x[1] = -1.9830000000000019 " " y[1] (analytic) = -1.1037254528738856 " " y[1] (numeric) = -1.1037254528738853 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.011773891295797500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2285324872015693 " " Order of pole = 2.1813020492801165 " " x[1] = -1.982000000000002 " " y[1] (analytic) = -1.1035226257093471 " " y[1] (numeric) = -1.103522625709347 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.012143654800919700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2276344524942244 " " Order of pole = 2.1812610857578747 " " x[1] = -1.981000000000002 " " y[1] (analytic) = -1.1033196353391566 " " y[1] (numeric) = -1.1033196353391563 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.012513851951665500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.226736412259509 " " Order of pole = 2.1812189378415496 " " x[1] = -1.9800000000000022 " " y[1] (analytic) = -1.1031164815829972 " " y[1] (numeric) = -1.1031164815829972 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2258383669838566 " " Order of pole = 2.181175610036238 " " x[1] = -1.9790000000000023 " " y[1] (analytic) = -1.1029131642603165 " " y[1] (numeric) = -1.1029131642603163 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.013255550122556600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2249403171630853 " " Order of pole = 2.181131106963811 " " x[1] = -1.9780000000000024 " " y[1] (analytic) = -1.1027096831903238 " " y[1] (numeric) = -1.1027096831903236 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.013627052612969600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.224042263303468 " " Order of pole = 2.181085433378133 " " x[1] = -1.9770000000000025 " " y[1] (analytic) = -1.1025060381919922 " " y[1] (numeric) = -1.1025060381919922 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2231442059207382 " " Order of pole = 2.1810385941514454 " " x[1] = -1.9760000000000026 " " y[1] (analytic) = -1.1023022290840578 " " y[1] (numeric) = -1.1023022290840578 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.222246145540586 " " Order of pole = 2.1809905942811447 " " x[1] = -1.9750000000000028 " " y[1] (analytic) = -1.1020982556850183 " " y[1] (numeric) = -1.1020982556850183 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.221348082698077 " " Order of pole = 2.180941438881888 " " x[1] = -1.9740000000000029 " " y[1] (analytic) = -1.1018941178131336 " " y[1] (numeric) = -1.1018941178131334 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.015117435835945500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.220450017938579 " " Order of pole = 2.180891133198834 " " x[1] = -1.973000000000003 " " y[1] (analytic) = -1.1016898152864247 " " y[1] (numeric) = -1.1016898152864245 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01549112866494700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2195519518169045 " " Order of pole = 2.180839682595561 " " x[1] = -1.972000000000003 " " y[1] (analytic) = -1.1014853479226747 " " y[1] (numeric) = -1.1014853479226745 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.015865261792107200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2186538848978263 " " Order of pole = 2.180787092561598 " " x[1] = -1.9710000000000032 " " y[1] (analytic) = -1.1012807155394273 " " y[1] (numeric) = -1.101280715539427 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.016239835964710000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2177558177555015 " " Order of pole = 2.1807333687043524 " " x[1] = -1.9700000000000033 " " y[1] (analytic) = -1.101075917953987 " " y[1] (numeric) = -1.1010759179539866 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.033229703863350000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2168577509739085 " " Order of pole = 2.1806785167554636 " " x[1] = -1.9690000000000034 " " y[1] (analytic) = -1.1008709549834184 " " y[1] (numeric) = -1.100870954983418 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.033980620887137600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.21595968514704 " " Order of pole = 2.180622542573598 " " x[1] = -1.9680000000000035 " " y[1] (analytic) = -1.1006658264445461 " " y[1] (numeric) = -1.1006658264445457 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.034732424505202400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.215061620877884 " " Order of pole = 2.1805654521304163 " " x[1] = -1.9670000000000036 " " y[1] (analytic) = -1.1004605321539547 " " y[1] (numeric) = -1.1004605321539542 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03548511622527200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.214163558779621 " " Order of pole = 2.180507251527228 " " x[1] = -1.9660000000000037 " " y[1] (analytic) = -1.1002550719279875 " " y[1] (numeric) = -1.1002550719279873 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01811934877919180000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2132654994747565 " " Order of pole = 2.1804479469833 " " x[1] = -1.9650000000000039 " " y[1] (analytic) = -1.100049445582748 " " y[1] (numeric) = -1.1000494455827476 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.036993170018895500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2123674435953036 " " Order of pole = 2.1803875448384034 " " x[1] = -1.964000000000004 " " y[1] (analytic) = -1.0998436529340971 " " y[1] (numeric) = -1.0998436529340967 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03774853512449700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2114693917832127 " " Order of pole = 2.180326051558957 " " x[1] = -1.963000000000004 " " y[1] (analytic) = -1.0996376937976549 " " y[1] (numeric) = -1.0996376937976544 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03850479439621500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.21057134468917 " " Order of pole = 2.180263473721446 " " x[1] = -1.9620000000000042 " " y[1] (analytic) = -1.0994315679887992 " " y[1] (numeric) = -1.0994315679887987 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03926194935842500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2096733029744846 " " Order of pole = 2.1801998180388082 " " x[1] = -1.9610000000000043 " " y[1] (analytic) = -1.099225275322666 " " y[1] (numeric) = -1.0992252753226652 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.06003000230828400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2087752673091203 " " Order of pole = 2.1801350913332485 " " x[1] = -1.9600000000000044 " " y[1] (analytic) = -1.0990188156141474 " " y[1] (numeric) = -1.0990188156141467 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.06116842870291400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2078772383723084 " " Order of pole = 2.1800693005449183 " " x[1] = -1.9590000000000045 " " y[1] (analytic) = -1.0988121886778943 " " y[1] (numeric) = -1.0988121886778934 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.08307760736430700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2069792168538473 " " Order of pole = 2.1800024527500277 " " x[1] = -1.9580000000000046 " " y[1] (analytic) = -1.098605394328313 " " y[1] (numeric) = -1.0986053943283123 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.0634493350760210000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2060812034512596 " " Order of pole = 2.179934555121662 " " x[1] = -1.9570000000000047 " " y[1] (analytic) = -1.098398432379567 " " y[1] (numeric) = -1.0983984323795664 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.06459181967315500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2051831988727395 " " Order of pole = 2.179865614970705 " " x[1] = -1.9560000000000048 " " y[1] (analytic) = -1.0981913026455756 " " y[1] (numeric) = -1.098191302645575 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.06573566163160800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2042852038349787 " " Order of pole = 2.179795639715916 " " x[1] = -1.955000000000005 " " y[1] (analytic) = -1.0979840049400142 " " y[1] (numeric) = -1.0979840049400131 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01114681054557900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2033872190645423 " " Order of pole = 2.17972463690311 " " x[1] = -1.954000000000005 " " y[1] (analytic) = -1.0977765390763126 " " y[1] (numeric) = -1.0977765390763115 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01133790448766250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.202489245296733 " " Order of pole = 2.1796526141896067 " " x[1] = -1.9530000000000052 " " y[1] (analytic) = -1.0975689048676565 " " y[1] (numeric) = -1.0975689048676553 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01152922582024670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2015912832762 " " Order of pole = 2.179579579352808 " " x[1] = -1.9520000000000053 " " y[1] (analytic) = -1.0973611021269865 " " y[1] (numeric) = -1.0973611021269853 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01172077493291880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.200693333756553 " " Order of pole = 2.179505540285014 " " x[1] = -1.9510000000000054 " " y[1] (analytic) = -1.097153130666997 " " y[1] (numeric) = -1.097153130666996 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01191255221612860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.199795397501121 " " Order of pole = 2.179430505004028 " " x[1] = -1.9500000000000055 " " y[1] (analytic) = -1.0969449903001374 " " y[1] (numeric) = -1.0969449903001363 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01210455806118970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.198897475281599 " " Order of pole = 2.1793544816347037 " " x[1] = -1.9490000000000056 " " y[1] (analytic) = -1.0967366808386099 " " y[1] (numeric) = -1.0967366808386088 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0122967928602830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.197999567879003 " " Order of pole = 2.1792774784221614 " " x[1] = -1.9480000000000057 " " y[1] (analytic) = -1.0965282020943707 " " y[1] (numeric) = -1.0965282020943696 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01248925700645800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.197101676083373 " " Order of pole = 2.1791995037279754 " " x[1] = -1.9470000000000058 " " y[1] (analytic) = -1.096319553879129 " " y[1] (numeric) = -1.096319553879128 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01268195089363550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1962038006933327 " " Order of pole = 2.179120566024203 " " x[1] = -1.946000000000006 " " y[1] (analytic) = -1.0961107360043472 " " y[1] (numeric) = -1.0961107360043458 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.21544984989993220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1953059425168293 " " Order of pole = 2.1790406739036854 " " x[1] = -1.945000000000006 " " y[1] (analytic) = -1.0959017482812388 " " y[1] (numeric) = -1.0959017482812377 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0130680294710530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1944081023705366 " " Order of pole = 2.1789598360720923 " " x[1] = -1.9440000000000062 " " y[1] (analytic) = -1.095692590520771 " " y[1] (numeric) = -1.0956925905207697 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.21591369794421550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1935102810800173 " " Order of pole = 2.178878061350172 " " x[1] = -1.9430000000000063 " " y[1] (analytic) = -1.0954832625336617 " " y[1] (numeric) = -1.0954832625336606 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01345503176142030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1926124794787833 " " Order of pole = 2.1787953586611515 " " x[1] = -1.9420000000000064 " " y[1] (analytic) = -1.095273764130381 " " y[1] (numeric) = -1.0952737641303798 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01364888029308820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1917146984102995 " " Order of pole = 2.178711737058318 " " x[1] = -1.9410000000000065 " " y[1] (analytic) = -1.0950640951211499 " " y[1] (numeric) = -1.0950640951211483 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.41938014532680070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.190816938725589 " " Order of pole = 2.178627205692294 " " x[1] = -1.9400000000000066 " " y[1] (analytic) = -1.0948542553159393 " " y[1] (numeric) = -1.094854255315938 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.21684472895046550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.189919201284855 " " Order of pole = 2.178541773833498 " " x[1] = -1.9390000000000067 " " y[1] (analytic) = -1.094644244524472 " " y[1] (numeric) = -1.0946442445244706 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2170781842725009000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.189021486956641 " " Order of pole = 2.1784554508607954 " " x[1] = -1.9380000000000068 " " y[1] (analytic) = -1.09443406255622 " " y[1] (numeric) = -1.0944340625562186 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.4201972395165430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1881237966181493 " " Order of pole = 2.1783682462658938 " " x[1] = -1.937000000000007 " " y[1] (analytic) = -1.0942237092204048 " " y[1] (numeric) = -1.0942237092204037 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0146216128109220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.187226131154364 " " Order of pole = 2.178280169641681 " " x[1] = -1.936000000000007 " " y[1] (analytic) = -1.0940131843259988 " " y[1] (numeric) = -1.0940131843259975 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.217780232119390100000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1863284914592582 " " Order of pole = 2.178191230698797 " " x[1] = -1.9350000000000072 " " y[1] (analytic) = -1.0938024876817218 " " y[1] (numeric) = -1.0938024876817203 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42101727869492460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.185430878435276 " " Order of pole = 2.178101439258672 " " x[1] = -1.9340000000000073 " " y[1] (analytic) = -1.0935916190960433 " " y[1] (numeric) = -1.0935916190960415 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.62433289390840170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.184533292992477 " " Order of pole = 2.17801080524206 " " x[1] = -1.9330000000000074 " " y[1] (analytic) = -1.0933805783771806 " " y[1] (numeric) = -1.093380578377179 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42156561513298800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1836357360492604 " " Order of pole = 2.177919338679036 " " x[1] = -1.9320000000000075 " " y[1] (analytic) = -1.0931693653331 " " y[1] (numeric) = -1.0931693653330985 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42184027815452400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1827382085325158 " " Order of pole = 2.1778270497112935 " " x[1] = -1.9310000000000076 " " y[1] (analytic) = -1.0929579797715152 " " y[1] (numeric) = -1.0929579797715137 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42211527180592130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1818407113766347 " " Order of pole = 2.177733948578691 " " x[1] = -1.9300000000000077 " " y[1] (analytic) = -1.0927464214998868 " " y[1] (numeric) = -1.0927464214998852 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42239059665992260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.18094324552487 " " Order of pole = 2.177640045638043 " " x[1] = -1.9290000000000078 " " y[1] (analytic) = -1.0925346903254232 " " y[1] (numeric) = -1.0925346903254216 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42266625329054820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1800458119276027 " " Order of pole = 2.177545351339642 " " x[1] = -1.928000000000008 " " y[1] (analytic) = -1.0923227860550795 " " y[1] (numeric) = -1.0923227860550775 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.82949716863684830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1791484115428563 " " Order of pole = 2.1774498762342986 " " x[1] = -1.927000000000008 " " y[1] (analytic) = -1.092110708495556 " " y[1] (numeric) = -1.0921107084955541 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6265355019247840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.178251045337146 " " Order of pole = 2.17735363098528 " " x[1] = -1.9260000000000081 " " y[1] (analytic) = -1.0918984574533006 " " y[1] (numeric) = -1.091898457453299 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42349521960167760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1773537142849424 " " Order of pole = 2.177256626360972 " " x[1] = -1.9250000000000083 " " y[1] (analytic) = -1.091686032734507 " " y[1] (numeric) = -1.091686032734505 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83056426884897570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1764564193675295 " " Order of pole = 2.177158873219593 " " x[1] = -1.9240000000000084 " " y[1] (analytic) = -1.0914734341451127 " " y[1] (numeric) = -1.0914734341451107 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83092082849502680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1755591615740246 " " Order of pole = 2.1770603825231376 " " x[1] = -1.9230000000000085 " " y[1] (analytic) = -1.0912606614908014 " " y[1] (numeric) = -1.0912606614907996 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6278025059324690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.174661941901704 " " Order of pole = 2.1769611653420817 " " x[1] = -1.9220000000000086 " " y[1] (analytic) = -1.0910477145770017 " " y[1] (numeric) = -1.091047714577 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6281202147872540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1737647613543314 " " Order of pole = 2.1768612328326746 " " x[1] = -1.9210000000000087 " " y[1] (analytic) = -1.0908345932088863 " " y[1] (numeric) = -1.0908345932088843 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83199309663129060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.172867620943583 " " Order of pole = 2.1767605962565533 " " x[1] = -1.9200000000000088 " " y[1] (analytic) = -1.0906212971913716 " " y[1] (numeric) = -1.0906212971913696 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83235138491397140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1719705216886465 " " Order of pole = 2.176659266975438 " " x[1] = -1.919000000000009 " " y[1] (analytic) = -1.0904078263291181 " " y[1] (numeric) = -1.090407826329116 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.03634456359827630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1710734646153793 " " Order of pole = 2.1765572564397786 " " x[1] = -1.918000000000009 " " y[1] (analytic) = -1.0901941804265292 " " y[1] (numeric) = -1.0901941804265272 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83306926436116570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1701764507572636 " " Order of pole = 2.176454576201941 " " x[1] = -1.9170000000000091 " " y[1] (analytic) = -1.089980359287752 " " y[1] (numeric) = -1.08998035928775 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8334288570402660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1692794811544944 " " Order of pole = 2.176351237903969 " " x[1] = -1.9160000000000093 " " y[1] (analytic) = -1.0897663627166758 " " y[1] (numeric) = -1.0897663627166738 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8337888860356010000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.168382556854532 " " Order of pole = 2.1762472532851795 " " x[1] = -1.9150000000000094 " " y[1] (analytic) = -1.0895521905169323 " " y[1] (numeric) = -1.0895521905169303 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83414935210873240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1674856789114143 " " Order of pole = 2.1761426341730505 " " x[1] = -1.9140000000000095 " " y[1] (analytic) = -1.0893378424918954 " " y[1] (numeric) = -1.0893378424918934 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8345102560229380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.166588848386827 " " Order of pole = 2.1760373924978857 " " x[1] = -1.9130000000000096 " " y[1] (analytic) = -1.0891233184446807 " " y[1] (numeric) = -1.0891233184446785 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.03874622060357170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.165692066348068 " " Order of pole = 2.1759315402652213 " " x[1] = -1.9120000000000097 " " y[1] (analytic) = -1.0889086181781442 " " y[1] (numeric) = -1.0889086181781422 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8352333804362870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.164795333869751 " " Order of pole = 2.1758250895792735 " " x[1] = -1.9110000000000098 " " y[1] (analytic) = -1.088693741494884 " " y[1] (numeric) = -1.0886937414948823 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6316405355294292000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1638986520332253 " " Order of pole = 2.1757180526350552 " " x[1] = -1.91000000000001 " " y[1] (analytic) = -1.0884786881972386 " " y[1] (numeric) = -1.0884786881972368 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6319629025923238000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1630020219261645 " " Order of pole = 2.175610441713072 " " x[1] = -1.90900000000001 " " y[1] (analytic) = -1.0882634580872865 " " y[1] (numeric) = -1.0882634580872848 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63228566226265220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.162105444642434 " " Order of pole = 2.1755022691775174 " " x[1] = -1.9080000000000101 " " y[1] (analytic) = -1.0880480509668462 " " y[1] (numeric) = -1.0880480509668444 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63260881522812230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.161208921282822 " " Order of pole = 2.1753935474865003 " " x[1] = -1.9070000000000102 " " y[1] (analytic) = -1.0878324666374757 " " y[1] (numeric) = -1.087832466637474 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63293236217799730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1603124529536912 " " Order of pole = 2.1752842891737743 " " x[1] = -1.9060000000000104 " " y[1] (analytic) = -1.0876167049004724 " " y[1] (numeric) = -1.0876167049004706 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63325630380309840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.159416040767828 " " Order of pole = 2.1751745068604187 " " x[1] = -1.9050000000000105 " " y[1] (analytic) = -1.0874007655568727 " " y[1] (numeric) = -1.0874007655568707 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83777822089528610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1585196858442592 " " Order of pole = 2.1750642132525932 " " x[1] = -1.9040000000000106 " " y[1] (analytic) = -1.0871846484074512 " " y[1] (numeric) = -1.0871846484074492 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83814354558134630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1576233893080206 " " Order of pole = 2.174953421138408 " " x[1] = -1.9030000000000107 " " y[1] (analytic) = -1.0869683532527208 " " y[1] (numeric) = -1.0869683532527192 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.42995169070376850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1567271522897022 " " Order of pole = 2.17484214338198 " " x[1] = -1.9020000000000108 " " y[1] (analytic) = -1.0867518798929332 " " y[1] (numeric) = -1.0867518798929314 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63455603092700160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.155830975926202 " " Order of pole = 2.1747303929337605 " " x[1] = -1.901000000000011 " " y[1] (analytic) = -1.0865352281280762 " " y[1] (numeric) = -1.0865352281280745 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63488195634542370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1549348613593438 " " Order of pole = 2.1746181828119404 " " x[1] = -1.900000000000011 " " y[1] (analytic) = -1.0863183977578759 " " y[1] (numeric) = -1.0863183977578739 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83960931569410430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1540388097377625 " " Order of pole = 2.1745055261281827 " " x[1] = -1.8990000000000111 " " y[1] (analytic) = -1.086101388581794 " " y[1] (numeric) = -1.086101388581792 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83997687999897320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.153142822214421 " " Order of pole = 2.1743924360539992 " " x[1] = -1.8980000000000112 " " y[1] (analytic) = -1.08588420039903 " " y[1] (numeric) = -1.085884200399028 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8403448945945880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1522468999487123 " " Order of pole = 2.17427892584951 " " x[1] = -1.8970000000000113 " " y[1] (analytic) = -1.085666833008519 " " y[1] (numeric) = -1.085666833008517 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8407133602741280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.151351044104358 " " Order of pole = 2.1741650088350006 " " x[1] = -1.8960000000000115 " " y[1] (analytic) = -1.0854492862089318 " " y[1] (numeric) = -1.0854492862089298 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8410822778325740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.150455255851428 " " Order of pole = 2.174050698418494 " " x[1] = -1.8950000000000116 " " y[1] (analytic) = -1.0852315597986748 " " y[1] (numeric) = -1.0852315597986726 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.04605738674079470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.149559536364223 " " Order of pole = 2.1739360080670913 " " x[1] = -1.8940000000000117 " " y[1] (analytic) = -1.085013653575889 " " y[1] (numeric) = -1.085013653575887 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8418214717751550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1486638868225945 " " Order of pole = 2.1738209513251086 " " x[1] = -1.8930000000000118 " " y[1] (analytic) = -1.084795567338451 " " y[1] (numeric) = -1.084795567338449 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.8421917497583120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1477683084110915 " " Order of pole = 2.173705541802555 " " x[1] = -1.892000000000012 " " y[1] (analytic) = -1.0845773008839714 " " y[1] (numeric) = -1.0845773008839694 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.842562482818430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1468728023195927 " " Order of pole = 2.173589793183883 " " x[1] = -1.891000000000012 " " y[1] (analytic) = -1.0843588540097948 " " y[1] (numeric) = -1.0843588540097928 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.84293367175958040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1459773697418156 " " Order of pole = 2.1734737192078875 " " x[1] = -1.8900000000000121 " " y[1] (analytic) = -1.0841402265129991 " " y[1] (numeric) = -1.0841402265129974 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63849361545570450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.145082011877076 " " Order of pole = 2.17335733369168 " " x[1] = -1.8890000000000122 " " y[1] (analytic) = -1.0839214181903971 " " y[1] (numeric) = -1.083921418190395 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.04853046723381450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1441867299290167 " " Order of pole = 2.1732406505135984 " " x[1] = -1.8880000000000123 " " y[1] (analytic) = -1.083702428838532 " " y[1] (numeric) = -1.0837024288385302 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63915553949996880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.143291525104997 " " Order of pole = 2.173123683605013 " " x[1] = -1.8870000000000124 " " y[1] (analytic) = -1.0834832582536826 " " y[1] (numeric) = -1.0834832582536804 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.0493588916446610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1423963986177896 " " Order of pole = 2.173006446973556 " " x[1] = -1.8860000000000126 " " y[1] (analytic) = -1.0832639062318576 " " y[1] (numeric) = -1.0832639062318554 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.049773869946570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1415013516836217 " " Order of pole = 2.1728889546765586 " " x[1] = -1.8850000000000127 " " y[1] (analytic) = -1.083044372568799 " " y[1] (numeric) = -1.0830443725687968 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.05018936018640550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1406063855233946 " " Order of pole = 2.172771220837795 " " x[1] = -1.8840000000000128 " " y[1] (analytic) = -1.08282465705998 " " y[1] (numeric) = -1.0828246570599778 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.05060536327195730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1397115013618278 " " Order of pole = 2.172653259635979 " " x[1] = -1.8830000000000129 " " y[1] (analytic) = -1.0826047595006052 " " y[1] (numeric) = -1.0826047595006028 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25612406812440100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.138816700426945 " " Order of pole = 2.172535085297884 " " x[1] = -1.882000000000013 " " y[1] (analytic) = -1.0823846796856098 " " y[1] (numeric) = -1.0823846796856074 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25658280278393440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1379219839519235 " " Order of pole = 2.1724167121235887 " " x[1] = -1.881000000000013 " " y[1] (analytic) = -1.0821644174096599 " " y[1] (numeric) = -1.0821644174096574 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25704210458319370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1370273531724173 " " Order of pole = 2.172298154450271 " " x[1] = -1.8800000000000132 " " y[1] (analytic) = -1.0819439724671516 " " y[1] (numeric) = -1.0819439724671491 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25750197452992380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1361328093284193 " " Order of pole = 2.172179426677552 " " x[1] = -1.8790000000000133 " " y[1] (analytic) = -1.081723344652211 " " y[1] (numeric) = -1.0817233446522085 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25796241363418030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1352383536624777 " " Order of pole = 2.172060543243454 " " x[1] = -1.8780000000000134 " " y[1] (analytic) = -1.0815025337586937 " " y[1] (numeric) = -1.0815025337586912 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25842342290833360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1343439874223185 " " Order of pole = 2.1719415186600983 " " x[1] = -1.8770000000000135 " " y[1] (analytic) = -1.0812815395801842 " " y[1] (numeric) = -1.0812815395801818 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25888500336707850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1334497118568256 " " Order of pole = 2.1718223674592316 " " x[1] = -1.8760000000000137 " " y[1] (analytic) = -1.081060361909996 " " y[1] (numeric) = -1.0810603619099937 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25934715602743970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.132555528219575 " " Order of pole = 2.1717031042403114 " " x[1] = -1.8750000000000138 " " y[1] (analytic) = -1.0808390005411712 " " y[1] (numeric) = -1.0808390005411688 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.25980988190877670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1316614377663052 " " Order of pole = 2.1715837436363365 " " x[1] = -1.8740000000000139 " " y[1] (analytic) = -1.08061745526648 " " y[1] (numeric) = -1.0806174552664771 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.67123194240238950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.130767441756242 " " Order of pole = 2.1714643003318415 " " x[1] = -1.873000000000014 " " y[1] (analytic) = -1.0803957258784191 " " y[1] (numeric) = -1.0803957258784165 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.46625860809840450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.129873541451049 " " Order of pole = 2.1713447890488666 " " x[1] = -1.872000000000014 " " y[1] (analytic) = -1.0801738121692148 " " y[1] (numeric) = -1.080173812169212 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.6723290562178610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1289797381155986 " " Order of pole = 2.1712252245574106 " " x[1] = -1.8710000000000142 " " y[1] (analytic) = -1.0799517139308186 " " y[1] (numeric) = -1.079951713930816 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.4672725870325950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1280860330161557 " " Order of pole = 2.1711056216509768 " " x[1] = -1.8700000000000143 " " y[1] (analytic) = -1.0797294309549095 " " y[1] (numeric) = -1.0797294309549068 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.46778052233314480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1271924274231364 " " Order of pole = 2.1709859951840897 " " x[1] = -1.8690000000000144 " " y[1] (analytic) = -1.079506963032893 " " y[1] (numeric) = -1.0795069630328902 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.6739798471660730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1262989226083753 " " Order of pole = 2.1708663600352764 " " x[1] = -1.8680000000000145 " " y[1] (analytic) = -1.0792843099559 " " y[1] (numeric) = -1.0792843099558969 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.88026467194492800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1254055198456943 " " Order of pole = 2.170746731114921 " " x[1] = -1.8670000000000146 " " y[1] (analytic) = -1.0790614715147866 " " y[1] (numeric) = -1.0790614715147837 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.67508380219824370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.124512220411515 " " Order of pole = 2.1706271233736487 " " x[1] = -1.8660000000000148 " " y[1] (analytic) = -1.0788384475001358 " " y[1] (numeric) = -1.0788384475001327 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.88145502800135100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1236190255842717 " " Order of pole = 2.1705075517944685 " " x[1] = -1.8650000000000149 " " y[1] (analytic) = -1.0786152377022542 " " y[1] (numeric) = -1.0786152377022509 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 3.08791212793424530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.12272593664428 " " Order of pole = 2.170388031391081 " " x[1] = -1.864000000000015 " " y[1] (analytic) = -1.0783918419111727 " " y[1] (numeric) = -1.0783918419111695 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.88264835483287740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1218329548731196 " " Order of pole = 2.170268577199572 " " x[1] = -1.863000000000015 " " y[1] (analytic) = -1.0781682599166476 " " y[1] (numeric) = -1.0781682599166444 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.8832461356177970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1209400815545623 " " Order of pole = 2.170149204291139 " " x[1] = -1.8620000000000152 " " y[1] (analytic) = -1.0779444915081582 " " y[1] (numeric) = -1.0779444915081549 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 3.08983356760375700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1200473179738895 " " Order of pole = 2.1700299277628687 " " x[1] = -1.8610000000000153 " " y[1] (analytic) = -1.0777205364749074 " " y[1] (numeric) = -1.0777205364749038 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.2965073584112950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.119154665417648 " " Order of pole = 2.1699107627345455 " " x[1] = -1.8600000000000154 " " y[1] (analytic) = -1.077496394605821 " " y[1] (numeric) = -1.0774963946058176 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 3.091118532321330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1182621251736173 " " Order of pole = 2.169791724348247 " " x[1] = -1.8590000000000155 " " y[1] (analytic) = -1.0772720656895485 " " y[1] (numeric) = -1.077272065689545 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.29787970184342750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.117369698530654 " " Order of pole = 2.169672827766359 " " x[1] = -1.8580000000000156 " " y[1] (analytic) = -1.0770475495144605 " " y[1] (numeric) = -1.077047549514457 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.2985671620552740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.116477386778874 " " Order of pole = 2.169554088174138 " " x[1] = -1.8570000000000157 " " y[1] (analytic) = -1.0768228458686504 " " y[1] (numeric) = -1.076822845868647 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 3.0930520156160773000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.115585191209324 " " Order of pole = 2.1694355207752594 " " x[1] = -1.8560000000000159 " " y[1] (analytic) = -1.0765979545399338 " " y[1] (numeric) = -1.0765979545399302 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.29994466719815970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1146931131134963 " " Order of pole = 2.1693171407853598 " " x[1] = -1.855000000000016 " " y[1] (analytic) = -1.0763728753158466 " " y[1] (numeric) = -1.0763728753158428 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 3.50692438493294700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.11380115378419 " " Order of pole = 2.1691989634438116 " " x[1] = -1.854000000000016 " " y[1] (analytic) = -1.076147607983646 " " y[1] (numeric) = -1.0761476079836423 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 3.50765848078983640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1129093145139612 " " Order of pole = 2.1690810039927158 " " x[1] = -1.8530000000000162 " " y[1] (analytic) = -1.0759221523303104 " " y[1] (numeric) = -1.0759221523303064 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.7147695862511960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1120175965965227 " " Order of pole = 2.168963277695987 " " x[1] = -1.8520000000000163 " " y[1] (analytic) = -1.075696508142537 " " y[1] (numeric) = -1.0756965081425334 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.3027100598617380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1111260013250965 " " Order of pole = 2.1688457998171096 " " x[1] = -1.8510000000000164 " " y[1] (analytic) = -1.0754706752067453 " " y[1] (numeric) = -1.0754706752067413 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.71632902764385500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.110234529994111 " " Order of pole = 2.168728585642107 " " x[1] = -1.8500000000000165 " " y[1] (analytic) = -1.0752446533090718 " " y[1] (numeric) = -1.0752446533090678 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.7171102189165780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1093431838969767 " " Order of pole = 2.1686116504496056 " " x[1] = -1.8490000000000166 " " y[1] (analytic) = -1.075018442235374 " " y[1] (numeric) = -1.07501844223537 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.71789239293391470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1084519643276267 " " Order of pole = 2.1684950095316005 " " x[1] = -1.8480000000000167 " " y[1] (analytic) = -1.0747920417712271 " " y[1] (numeric) = -1.0747920417712231 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.71867555147128200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.107560872579595 " " Order of pole = 2.1683786781811705 " " x[1] = -1.8470000000000169 " " y[1] (analytic) = -1.0745654517019256 " " y[1] (numeric) = -1.0745654517019216 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.7194596963082327000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.106669909946372 " " Order of pole = 2.1682626716972635 " " x[1] = -1.846000000000017 " " y[1] (analytic) = -1.0743386718124814 " " y[1] (numeric) = -1.0743386718124774 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.72024482922846730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1057790777203174 " " Order of pole = 2.1681470053700203 " " x[1] = -1.845000000000017 " " y[1] (analytic) = -1.0741117018876247 " " y[1] (numeric) = -1.0741117018876207 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.7210309520198440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.104888377193988 " " Order of pole = 2.1680316944988753 " " x[1] = -1.8440000000000172 " " y[1] (analytic) = -1.0738845417118028 " " y[1] (numeric) = -1.0738845417117988 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.7218180664743950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1039978096584218 " " Order of pole = 2.1679167543692444 " " x[1] = -1.8430000000000173 " " y[1] (analytic) = -1.0736571910691801 " " y[1] (numeric) = -1.0736571910691761 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.72260617438833200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1031073764047123 " " Order of pole = 2.16780220027405 " " x[1] = -1.8420000000000174 " " y[1] (analytic) = -1.073429649743638 " " y[1] (numeric) = -1.0734296497436338 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.9302505707599580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.10221707872194 " " Order of pole = 2.167688047485573 " " x[1] = -1.8410000000000175 " " y[1] (analytic) = -1.073201917518773 " " y[1] (numeric) = -1.073201917518769 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.7241853778002120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1013269178987986 " " Order of pole = 2.167574311277651 " " x[1] = -1.8400000000000176 " " y[1] (analytic) = -1.0729739941778993 " " y[1] (numeric) = -1.072973994177895 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.93191961451780400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.100436895222217 " " Order of pole = 2.1674610069069793 " " x[1] = -1.8390000000000177 " " y[1] (analytic) = -1.0727458795040454 " " y[1] (numeric) = -1.072745879504041 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.13974286301034400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.099547011978643 " " Order of pole = 2.167348149630577 " " x[1] = -1.8380000000000178 " " y[1] (analytic) = -1.072517573279955 " " y[1] (numeric) = -1.0725175732799508 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.93359288340011770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.098657269452052 " " Order of pole = 2.1672357546788064 " " x[1] = -1.837000000000018 " " y[1] (analytic) = -1.0722890752880878 " " y[1] (numeric) = -1.0722890752880834 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.14150642848572200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0977676689250617 " " Order of pole = 2.167123837270509 " " x[1] = -1.836000000000018 " " y[1] (analytic) = -1.0720603853106168 " " y[1] (numeric) = -1.0720603853106123 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.1423898871274220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0968782116787845 " " Order of pole = 2.1670124126110473 " " x[1] = -1.8350000000000182 " " y[1] (analytic) = -1.0718315031294297 " " y[1] (numeric) = -1.0718315031294252 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.1432744657481520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.095988898992075 " " Order of pole = 2.16690149588214 " " x[1] = -1.8340000000000183 " " y[1] (analytic) = -1.0716024285261276 " " y[1] (numeric) = -1.0716024285261232 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.14416016638613770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0950997321419678 " " Order of pole = 2.1667911022477746 " " x[1] = -1.8330000000000184 " " y[1] (analytic) = -1.0713731612820259 " " y[1] (numeric) = -1.0713731612820212 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 4.35229934063860350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.094210712403294 " " Order of pole = 2.166681246849116 " " x[1] = -1.8320000000000185 " " y[1] (analytic) = -1.0711437011781517 " " y[1] (numeric) = -1.071143701178147 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 4.35323168898523200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0933218410484726 " " Order of pole = 2.166571944801561 " " x[1] = -1.8310000000000186 " " y[1] (analytic) = -1.0709140479952457 " " y[1] (numeric) = -1.0709140479952413 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.14682402085768700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.092433119347347 " " Order of pole = 2.1664632111926814 " " x[1] = -1.8300000000000187 " " y[1] (analytic) = -1.0706842015137612 " " y[1] (numeric) = -1.0706842015137565 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 4.3550999415449260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.091544548567878 " " Order of pole = 2.1663550610915436 " " x[1] = -1.8290000000000188 " " y[1] (analytic) = -1.0704541615138623 " " y[1] (numeric) = -1.0704541615138576 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 4.3560358500836870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0906561299742528 " " Order of pole = 2.166247509523078 " " x[1] = -1.828000000000019 " " y[1] (analytic) = -1.0702239277754257 " " y[1] (numeric) = -1.0702239277754209 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.5644478520533943000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0897678648290863 " " Order of pole = 2.166140571498026 " " x[1] = -1.827000000000019 " " y[1] (analytic) = -1.0699935000780387 " " y[1] (numeric) = -1.0699935000780338 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.5654308255091340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0888797543905255 " " Order of pole = 2.1660342619735253 " " x[1] = -1.8260000000000192 " " y[1] (analytic) = -1.0697628782010002 " " y[1] (numeric) = -1.0697628782009951 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 4.7739793718250045000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.087991799914745 " " Order of pole = 2.1659285958871095 " " x[1] = -1.8250000000000193 " " y[1] (analytic) = -1.0695320619233186 " " y[1] (numeric) = -1.0695320619233135 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 4.775009646828030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0871040026549217 " " Order of pole = 2.16582358814275 " " x[1] = -1.8240000000000194 " " y[1] (analytic) = -1.069301051023713 " " y[1] (numeric) = -1.0693010510237082 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.5683872691174960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0862163638593287 " " Order of pole = 2.165719253584914 " " x[1] = -1.8230000000000195 " " y[1] (analytic) = -1.069069845280613 " " y[1] (numeric) = -1.069069845280608 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 4.777074141432929300000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0853288847738534 " " Order of pole = 2.165615607032823 " " x[1] = -1.8220000000000196 " " y[1] (analytic) = -1.0688384444721564 " " y[1] (numeric) = -1.068838444472151 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9858522078446580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.08444156664088 " " Order of pole = 2.1655126632652824 " " x[1] = -1.8210000000000197 " " y[1] (analytic) = -1.0686068483761901 " " y[1] (numeric) = -1.0686068483761848 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9869327772871580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.083554410699594 " " Order of pole = 2.1654104370247893 " " x[1] = -1.8200000000000198 " " y[1] (analytic) = -1.0683750567702703 " " y[1] (numeric) = -1.068375056770265 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9880147280026270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.082667418181302 " " Order of pole = 2.1653089429538355 " " x[1] = -1.81900000000002 " " y[1] (analytic) = -1.0681430694316616 " " y[1] (numeric) = -1.068143069431656 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.196977148463290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0817805905121434 " " Order of pole = 2.1652081983535645 " " x[1] = -1.81800000000002 " " y[1] (analytic) = -1.0679108861373359 " " y[1] (numeric) = -1.0679108861373303 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.1981070660346240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0808939283390013 " " Order of pole = 2.165108209927606 " " x[1] = -1.8170000000000202 " " y[1] (analytic) = -1.067678506663973 " " y[1] (numeric) = -1.0676785066639674 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.1992384303685050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.080007433459328 " " Order of pole = 2.165009000044588 " " x[1] = -1.8160000000000203 " " y[1] (analytic) = -1.0674459307879596 " " y[1] (numeric) = -1.0674459307879542 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9923563943580507000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.079121106901208 " " Order of pole = 2.1649105806101545 " " x[1] = -1.8150000000000204 " " y[1] (analytic) = -1.0672131582853899 " " y[1] (numeric) = -1.0672131582853848 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 4.7853850691653665000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.078234949876994 " " Order of pole = 2.164812966044792 " " x[1] = -1.8140000000000205 " " y[1] (analytic) = -1.0669801889320647 " " y[1] (numeric) = -1.0669801889320591 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2026412305573040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.077348963591736 " " Order of pole = 2.164716170676691 " " x[1] = -1.8130000000000206 " " y[1] (analytic) = -1.0667470225034892 " " y[1] (numeric) = -1.0667470225034839 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9956272722414097000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0764631492516203 " " Order of pole = 2.1646202088566042 " " x[1] = -1.8120000000000207 " " y[1] (analytic) = -1.0665136587748765 " " y[1] (numeric) = -1.0665136587748711 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9967203648590414000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.075577508052319 " " Order of pole = 2.1645250947992523 " " x[1] = -1.8110000000000208 " " y[1] (analytic) = -1.066280097521144 " " y[1] (numeric) = -1.0662800975211386 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9978148617700124000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0746920411880585 " " Order of pole = 2.1644308427067607 " " x[1] = -1.810000000000021 " " y[1] (analytic) = -1.0660463385169139 " " y[1] (numeric) = -1.0660463385169086 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.9989107655625614000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0738067498466135 " " Order of pole = 2.1643374667003883 " " x[1] = -1.809000000000021 " " y[1] (analytic) = -1.0658123815365137 " " y[1] (numeric) = -1.0658123815365084 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.000008078831070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.07292163520892 " " Order of pole = 2.1642449808153152 " " x[1] = -1.8080000000000211 " " y[1] (analytic) = -1.065578226353975 " " y[1] (numeric) = -1.0655782263539695 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2094862543500910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0720366984520324 " " Order of pole = 2.164153399040792 " " x[1] = -1.8070000000000213 " " y[1] (analytic) = -1.0653438727430329 " " y[1] (numeric) = -1.0653438727430273 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2106322335461950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.071151940746907 " " Order of pole = 2.164062735289974 " " x[1] = -1.8060000000000214 " " y[1] (analytic) = -1.065109320477126 " " y[1] (numeric) = -1.0651093204771207 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.0033085015287850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0702673632591013 " " Order of pole = 2.163973003409371 " " x[1] = -1.8050000000000215 " " y[1] (analytic) = -1.064874569329397 " " y[1] (numeric) = -1.0648745693293917 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.0044114787685500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0693829671467845 " " Order of pole = 2.1638842171516757 " " x[1] = -1.8040000000000216 " " y[1] (analytic) = -1.0646396190726906 " " y[1] (numeric) = -1.0646396190726852 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.0055158785490370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.068498753563358 " " Order of pole = 2.16379639021147 " " x[1] = -1.8030000000000217 " " y[1] (analytic) = -1.064404469479554 " " y[1] (numeric) = -1.0644044694795485 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2152309411478040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.067614723655534 " " Order of pole = 2.163709536198919 " " x[1] = -1.8020000000000218 " " y[1] (analytic) = -1.0641691203222365 " " y[1] (numeric) = -1.064169120322231 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2163843294427410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0667308785633427 " " Order of pole = 2.163623668639879 " " x[1] = -1.801000000000022 " " y[1] (analytic) = -1.0639335713726892 " " y[1] (numeric) = -1.0639335713726839 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.0088376394826740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.065847219421033 " " Order of pole = 2.163538800988057 " " x[1] = -1.800000000000022 " " y[1] (analytic) = -1.0636978224025646 " " y[1] (numeric) = -1.0636978224025593 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.0099477558053350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0649637473555917 " " Order of pole = 2.1634549466048263 " " x[1] = -1.7990000000000221 " " y[1] (analytic) = -1.0634618731832164 " " y[1] (numeric) = -1.0634618731832108 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2198534457186130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0640804634870533 " " Order of pole = 2.163372118763334 " " x[1] = -1.7980000000000222 " " y[1] (analytic) = -1.063225723485698 " " y[1] (numeric) = -1.0632257234856923 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 5.4298533232660930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.063197368929422 " " Order of pole = 2.1632903306610025 " " x[1] = -1.7970000000000224 " " y[1] (analytic) = -1.0629893730807636 " " y[1] (numeric) = -1.062989373080758 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2221736770871940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0623144647881038 " " Order of pole = 2.163209595384483 " " x[1] = -1.7960000000000225 " " y[1] (analytic) = -1.0627528217388675 " " y[1] (numeric) = -1.062752821738862 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.2233360472692910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.0614317521632044 " " Order of pole = 2.163129925954536 " " x[1] = -1.7950000000000226 " " y[1] (analytic) = -1.062516069230163 " " y[1] (numeric) = -1.0625160692301576 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.0155199272062630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.060549232145954 " " Order of pole = 2.1630513352771636 " " x[1] = -1.7940000000000227 " " y[1] (analytic) = -1.062279115324503 " " y[1] (numeric) = -1.0622791153244975 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.225665310599690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.059666905820963 " " Order of pole = 2.1629738361743414 " " x[1] = -1.7930000000000228 " " y[1] (analytic) = -1.0620419597914383 " " y[1] (numeric) = -1.062041959791433 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.0177589209820520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;" Iterations = 207 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 40 Minutes 32 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 40 Minutes 8 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 43 Minutes 10 Seconds "Time to Timeout " Unknown Percent Done = 6.93333333333257 "%" (%o54) true (%o54) diffeq.max