(%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_m1 array_const_2D0 , 1 1 1 array_tmp2 : array_tmp1 array_x , array_tmp3 : array_x array_x , 1 1 1 1 1 1 array_tmp2 1 array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 , 1 1 1 1 1 1 array_tmp5 1 array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 , 1 array_tmp7 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp9 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_m1 array_const_2D0 , 2 2 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 2 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp4 : array_tmp3 , array_tmp5 : 2 2 2 array_tmp2 - ats(2, array_tmp4, array_tmp5, 2) 2 -----------------------------------------------, array_tmp4 1 array_tmp6 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp7 : array_tmp6 , array_tmp8 : 2 2 2 array_tmp5 - ats(2, array_tmp7, array_tmp8, 2) 2 -----------------------------------------------, array_tmp9 : array_tmp8 , array_tmp7 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 3 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 , 3 2 2 3 3 array_tmp2 - ats(3, array_tmp4, array_tmp5, 2) 3 array_tmp5 : -----------------------------------------------, 3 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 , 3 2 2 3 3 array_tmp5 - ats(3, array_tmp7, array_tmp8, 2) 3 array_tmp8 : -----------------------------------------------, 3 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp9 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, 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 4 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 4 4 4 array_tmp2 - ats(4, array_tmp4, array_tmp5, 2) 4 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 4 4 1 array_tmp5 - ats(4, array_tmp7, array_tmp8, 2) 4 array_tmp8 : -----------------------------------------------, 4 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 5 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 5 5 5 array_tmp2 - ats(5, array_tmp4, array_tmp5, 2) 5 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 5 5 1 array_tmp5 - ats(5, array_tmp7, array_tmp8, 2) 5 array_tmp8 : -----------------------------------------------, 5 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp9 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_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , kkk kkk 1 kkk - 1 2 array_tmp4 : array_tmp3 , array_tmp5 : kkk kkk kkk array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2) kkk ---------------------------------------------------, array_tmp4 1 array_tmp7 : array_tmp6 , array_tmp8 : kkk kkk kkk array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2) kkk ---------------------------------------------------, array_tmp7 1 array_tmp9 : array_tmp8 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp9 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_m1 array_const_2D0 , 1 1 1 array_tmp2 : array_tmp1 array_x , array_tmp3 : array_x array_x , 1 1 1 1 1 1 array_tmp2 1 array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 , 1 1 1 1 1 1 array_tmp5 1 array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 , 1 array_tmp7 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp9 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_m1 array_const_2D0 , 2 2 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 2 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp4 : array_tmp3 , array_tmp5 : 2 2 2 array_tmp2 - ats(2, array_tmp4, array_tmp5, 2) 2 -----------------------------------------------, array_tmp4 1 array_tmp6 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp7 : array_tmp6 , array_tmp8 : 2 2 2 array_tmp5 - ats(2, array_tmp7, array_tmp8, 2) 2 -----------------------------------------------, array_tmp9 : array_tmp8 , array_tmp7 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 3 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 , 3 2 2 3 3 array_tmp2 - ats(3, array_tmp4, array_tmp5, 2) 3 array_tmp5 : -----------------------------------------------, 3 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 , 3 2 2 3 3 array_tmp5 - ats(3, array_tmp7, array_tmp8, 2) 3 array_tmp8 : -----------------------------------------------, 3 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp9 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, 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 4 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 4 4 4 array_tmp2 - ats(4, array_tmp4, array_tmp5, 2) 4 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 4 4 1 array_tmp5 - ats(4, array_tmp7, array_tmp8, 2) 4 array_tmp8 : -----------------------------------------------, 4 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , 5 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 5 5 5 array_tmp2 - ats(5, array_tmp4, array_tmp5, 2) 5 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 5 5 1 array_tmp5 - ats(5, array_tmp7, array_tmp8, 2) 5 array_tmp8 : -----------------------------------------------, 5 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp9 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_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , kkk kkk 1 kkk - 1 2 array_tmp4 : array_tmp3 , array_tmp5 : kkk kkk kkk array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2) kkk ---------------------------------------------------, array_tmp4 1 array_tmp7 : array_tmp6 , array_tmp8 : kkk kkk kkk array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2) kkk ---------------------------------------------------, array_tmp7 1 array_tmp9 : array_tmp8 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp9 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) 1.0 (%i52) exact_soln_y(x) := block(---------) 1.0 + x x 1.0 (%o52) exact_soln_y(x) := block(---------) 1.0 + x 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/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms: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, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.1,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:50,"), 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, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 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_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 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_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 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_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, 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, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.1, glob_look_poles : true, glob_max_iter : 50, 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 )\ = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T03:11:27-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 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/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms: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, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.1,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:50,"), 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, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 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_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 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_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 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_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, 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, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.1, glob_look_poles : true, glob_max_iter : 50, 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 )\ = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T03:11:27-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 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/sing4postode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-2.0," "x_end:1.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.1," "glob_look_poles:true," "glob_max_iter:50," "/* 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(" " (1.0 / (x * x + 1.0)) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" 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 = 1.183046327334381200000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" max_value3 = 1.183046327334381200000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" value3 = 1.183046327334381200000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -2. " " y[1] (analytic) = 0.2 " " y[1] (numeric) = 0.2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.259037444896596 " " Order of pole = 3.571602884033478 " " x[1] = -1.999 " " y[1] (analytic) = 0.2001600880384131 " " y[1] (numeric) = 0.20016008803841315 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.773337670625154000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2581061217122853 " " Order of pole = 3.5712012087996676 " " x[1] = -1.9980000000000002 " " y[1] (analytic) = 0.20032035230740997 " " y[1] (numeric) = 0.20032035230741002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.771118889910440500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.257174751806302 " " Order of pole = 3.5707978287454267 " " x[1] = -1.9970000000000003 " " y[1] (analytic) = 0.20048079303786334 " " y[1] (numeric) = 0.20048079303786343 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.153351829128128500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2562433385915934 " " Order of pole = 3.5703927882327093 " " x[1] = -1.9960000000000004 " " y[1] (analytic) = 0.2006414104609615 " " y[1] (numeric) = 0.20064141046096162 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.533369318300176000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2553118854965537 " " Order of pole = 3.569986131854151 " " x[1] = -1.9950000000000006 " " y[1] (analytic) = 0.2008022048082087 " " y[1] (numeric) = 0.20080220480820882 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.52893841820889700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2543803959650996 " " Order of pole = 3.5695779044345244 " " x[1] = -1.9940000000000007 " " y[1] (analytic) = 0.2009631763114253 " " y[1] (numeric) = 0.20096317631142543 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.90563717320458500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2534488734548783 " " Order of pole = 3.569168151005691 " " x[1] = -1.9930000000000008 " " y[1] (analytic) = 0.20112432520274826 " " y[1] (numeric) = 0.20112432520274845 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.66014573888785600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2525173214400165 " " Order of pole = 3.5687569168462225 " " x[1] = -1.9920000000000009 " " y[1] (analytic) = 0.20128565171463156 " " y[1] (numeric) = 0.20128565171463175 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.65240332106987600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.251585743407358 " " Order of pole = 3.5683442474282394 " " x[1] = -1.991000000000001 " " y[1] (analytic) = 0.20144715607984626 " " y[1] (numeric) = 0.20144715607984645 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.64466478903248200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2506541428580236 " " Order of pole = 3.5679301884400374 " " x[1] = -1.990000000000001 " " y[1] (analytic) = 0.20160883853148104 " " y[1] (numeric) = 0.20160883853148126 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.10136344488864880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.249722523306552 " " Order of pole = 3.5675147857742893 " " x[1] = -1.9890000000000012 " " y[1] (analytic) = 0.20177069930294256 " " y[1] (numeric) = 0.2017706993029428 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.23803992058135870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.248790888281442 " " Order of pole = 3.5670980855363013 " " x[1] = -1.9880000000000013 " " y[1] (analytic) = 0.20193273862795566 " " y[1] (numeric) = 0.20193273862795594 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.3744960725148320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.247859241323284 " " Order of pole = 3.566680134017684 " " x[1] = -1.9870000000000014 " " y[1] (analytic) = 0.20209495674056382 " " y[1] (numeric) = 0.20209495674056407 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.23605350954569940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.246927585986066 " " Order of pole = 3.5662609777154977 " " x[1] = -1.9860000000000015 " " y[1] (analytic) = 0.2022573538751293 " " y[1] (numeric) = 0.20225735387512958 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.37229005936490180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2459959258355973 " " Order of pole = 3.5658406633101407 " " x[1] = -1.9850000000000017 " " y[1] (analytic) = 0.20241993026633373 " " y[1] (numeric) = 0.20241993026633406 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.64542546254864670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.245064264450119 " " Order of pole = 3.565419237674522 " " x[1] = -1.9840000000000018 " " y[1] (analytic) = 0.20258268614917835 " " y[1] (numeric) = 0.20258268614917868 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.64410351999322550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.244132605419085 " " Order of pole = 3.564996747857087 " " x[1] = -1.9830000000000019 " " y[1] (analytic) = 0.2027456217589842 " " y[1] (numeric) = 0.20274562175898456 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.7796807638692540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.24320095234371 " " Order of pole = 3.5645732410900344 " " x[1] = -1.982000000000002 " " y[1] (analytic) = 0.20290873733139267 " " y[1] (numeric) = 0.20290873733139303 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.77825010272414650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.24226930883625 " " Order of pole = 3.5641487647794996 " " x[1] = -1.981000000000002 " " y[1] (analytic) = 0.20307203310236563 " " y[1] (numeric) = 0.20307203310236602 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.91349863731815920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2413376785194035 " " Order of pole = 3.563723366497392 " " x[1] = -1.9800000000000022 " " y[1] (analytic) = 0.20323550930818596 " " y[1] (numeric) = 0.20323550930818637 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.04852801388711120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.240406065026422 " " Order of pole = 3.5632970939834117 " " x[1] = -1.9790000000000023 " " y[1] (analytic) = 0.20339916618545775 " " y[1] (numeric) = 0.2033991661854582 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.1833383989644560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.239474472000969 " " Order of pole = 3.5628699951433838 " " x[1] = -1.9780000000000024 " " y[1] (analytic) = 0.2035630039711067 " " y[1] (numeric) = 0.20356300397110713 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.18158113796107940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2385429030958544 " " Order of pole = 3.562442118031708 " " x[1] = -1.9770000000000025 " " y[1] (analytic) = 0.20372702290238032 " " y[1] (numeric) = 0.2037270229023808 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.31606381295713040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.237611361973436 " " Order of pole = 3.562013510857355 " " x[1] = -1.9760000000000026 " " y[1] (analytic) = 0.2038912232168485 " " y[1] (numeric) = 0.20389122321684897 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.31419861052018420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.236679852305863 " " Order of pole = 3.561584221987829 " " x[1] = -1.9750000000000028 " " y[1] (analytic) = 0.2040556051524036 " " y[1] (numeric) = 0.2040556051524041 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.4483540195241510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.23574837777254 " " Order of pole = 3.5611542999133547 " " x[1] = -1.9740000000000029 " " y[1] (analytic) = 0.2042201689472609 " " y[1] (numeric) = 0.20422016894726142 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.58229115868147730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.234816942063366 " " Order of pole = 3.5607237932933984 " " x[1] = -1.973000000000003 " " y[1] (analytic) = 0.20438491483995896 " " y[1] (numeric) = 0.20438491483995952 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.71601019452561540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2338855488748903 " " Order of pole = 3.560292750902338 " " x[1] = -1.972000000000003 " " y[1] (analytic) = 0.20454984306935992 " " y[1] (numeric) = 0.20454984306936047 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.7138202796095420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.232954201911582 " " Order of pole = 3.559861221647804 " " x[1] = -1.9710000000000032 " " y[1] (analytic) = 0.20471495387464966 " " y[1] (numeric) = 0.20471495387465025 " " absolute error = 5.8286708792820720000000000000000E-16 " " relative error = 2.84721304866231900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.232022904885352 " " Order of pole = 3.5594292545643427 " " x[1] = -1.9700000000000033 " " y[1] (analytic) = 0.20488024749533842 " " y[1] (numeric) = 0.20488024749533906 " " absolute error = 6.383782391594650000000000000000E-16 " " relative error = 3.11586034751344100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.231091661515796 " " Order of pole = 3.5589968988171954 " " x[1] = -1.9690000000000034 " " y[1] (analytic) = 0.205045724171261 " " y[1] (numeric) = 0.20504572417126166 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.2487086354393660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.230160475528719 " " Order of pole = 3.558564203681609 " " x[1] = -1.9680000000000035 " " y[1] (analytic) = 0.20521138414257703 " " y[1] (numeric) = 0.20521138414257767 " " absolute error = 6.383782391594650000000000000000E-16 " " relative error = 3.11083248050182170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.229229350656085 " " Order of pole = 3.5581312185424885 " " x[1] = -1.9670000000000036 " " y[1] (analytic) = 0.20537722764977123 " " y[1] (numeric) = 0.20537722764977193 " " absolute error = 6.9388939039072280000000000000000E-16 " " relative error = 3.37860919796818400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2282982906367583 " " Order of pole = 3.557697992905325 " " x[1] = -1.9660000000000037 " " y[1] (analytic) = 0.2055432549336541 " " y[1] (numeric) = 0.20554325493365483 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 3.51091533623560940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.227367299214293 " " Order of pole = 3.557264576364968 " " x[1] = -1.9650000000000039 " " y[1] (analytic) = 0.20570946623536185 " " y[1] (numeric) = 0.20570946623536257 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 3.50807854987423840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.226436380139121 " " Order of pole = 3.556831018637265 " " x[1] = -1.964000000000004 " " y[1] (analytic) = 0.2058758617963568 " " y[1] (numeric) = 0.20587586179635756 " " absolute error = 7.4940054162198070000000000000000E-16 " " relative error = 3.6400602532182920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.225505537165172 " " Order of pole = 3.556397369511078 " " x[1] = -1.963000000000004 " " y[1] (analytic) = 0.206042441858428 " " y[1] (numeric) = 0.20604244185842874 " " absolute error = 7.4940054162198070000000000000000E-16 " " relative error = 3.63711735729134230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2245747740521695 " " Order of pole = 3.5559636788814366 " " x[1] = -1.9620000000000042 " " y[1] (analytic) = 0.20620920666369108 " " y[1] (numeric) = 0.20620920666369183 " " absolute error = 7.4940054162198070000000000000000E-16 " " relative error = 3.63417596016547660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.223644094563458 " " Order of pole = 3.555529996718853 " " x[1] = -1.9610000000000043 " " y[1] (analytic) = 0.20637615645458895 " " y[1] (numeric) = 0.2063761564545898 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 4.03470673537854930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2227135024671894 " " Order of pole = 3.555096373086542 " " x[1] = -1.9600000000000044 " " y[1] (analytic) = 0.2065432914738922 " " y[1] (numeric) = 0.206543291473893 " " absolute error = 8.0491169285323850000000000000000E-16 " " relative error = 3.89706045211825340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2217830015345257 " " Order of pole = 3.554662858115144 " " x[1] = -1.9590000000000045 " " y[1] (analytic) = 0.20671061196469886 " " y[1] (numeric) = 0.2067106119646997 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 4.02817862399375340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2208525955399776 " " Order of pole = 3.554229502007818 " " x[1] = -1.9580000000000046 " " y[1] (analytic) = 0.20687811817043536 " " y[1] (numeric) = 0.2068781181704362 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 4.02491706630316140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2199222882621417 " " Order of pole = 3.5537963550510696 " " x[1] = -1.9570000000000047 " " y[1] (analytic) = 0.20704581033485644 " " y[1] (numeric) = 0.20704581033485733 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.2897676522102474000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.218992083480817 " " Order of pole = 3.55336346757397 " " x[1] = -1.9560000000000048 " " y[1] (analytic) = 0.2072136887020458 " " y[1] (numeric) = 0.20721368870204668 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.28629221005396100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.218061984978816 " " Order of pole = 3.5529308899742205 " " x[1] = -1.955000000000005 " " y[1] (analytic) = 0.20738175351641602 " " y[1] (numeric) = 0.20738175351641694 " " absolute error = 9.1593399531575410000000000000000E-16 " " relative error = 4.41665662376246700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.21713199654096 " " Order of pole = 3.5524986727041252 " " x[1] = -1.954000000000005 " " y[1] (analytic) = 0.2075500050227093 " " y[1] (numeric) = 0.2075500050227102 " " absolute error = 9.1593399531575410000000000000000E-16 " " relative error = 4.4130762377747780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.216202121953881 " " Order of pole = 3.5520668662680563 " " x[1] = -1.9530000000000052 " " y[1] (analytic) = 0.20771844346599738 " " y[1] (numeric) = 0.20771844346599833 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 4.54311882558402160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.215272365004457 " " Order of pole = 3.551635521200428 " " x[1] = -1.9520000000000053 " " y[1] (analytic) = 0.20788706909168228 " " y[1] (numeric) = 0.20788706909168325 " " absolute error = 9.714451465470120000000000000000E-16 " " relative error = 4.6729464742156984000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2143427294821905 " " Order of pole = 3.5512046880998867 " " x[1] = -1.9510000000000054 " " y[1] (analytic) = 0.20805588214549633 " " y[1] (numeric) = 0.20805588214549728 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 4.53575049741418930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2134132191755618 " " Order of pole = 3.5507744175775073 " " x[1] = -1.9500000000000055 " " y[1] (analytic) = 0.20822488287350244 " " y[1] (numeric) = 0.20822488287350344 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 4.7986614681861050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2124838378739624 " " Order of pole = 3.5503447602847196 " " x[1] = -1.9490000000000056 " " y[1] (analytic) = 0.20839407152209477 " " y[1] (numeric) = 0.20839407152209577 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 4.7947655845703930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2115545893669917 " " Order of pole = 3.549915766903453 " " x[1] = -1.9480000000000057 " " y[1] (analytic) = 0.2085634483379986 " " y[1] (numeric) = 0.20856344833799964 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.9239514687826846000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2106254774429974 " " Order of pole = 3.5494874881255996 " " x[1] = -1.9470000000000058 " " y[1] (analytic) = 0.2087330135682711 " " y[1] (numeric) = 0.20873301356827212 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.9199514740028390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2096965058901077 " " Order of pole = 3.5490599746679905 " " x[1] = -1.946000000000006 " " y[1] (analytic) = 0.2089027674603012 " " y[1] (numeric) = 0.20890276746030223 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.9159535331355880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2087676784954424 " " Order of pole = 3.548633277261345 " " x[1] = -1.945000000000006 " " y[1] (analytic) = 0.2090727102618103 " " y[1] (numeric) = 0.20907271026181132 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.9119576461809320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2078389990436706 " " Order of pole = 3.5482074466299665 " " x[1] = -1.9440000000000062 " " y[1] (analytic) = 0.20924284222085224 " " y[1] (numeric) = 0.20924284222085332 " " absolute error = 1.0824674490095276000000000000000E-15 " " relative error = 5.1732591543896240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2069104713185417 " " Order of pole = 3.547782533513736 " " x[1] = -1.9430000000000063 " " y[1] (analytic) = 0.20941316358581402 " " y[1] (numeric) = 0.2094131635858151 " " absolute error = 1.0824674490095276000000000000000E-15 " " relative error = 5.1690516034153240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2059820991015386 " " Order of pole = 3.547358588649221 " " x[1] = -1.9420000000000064 " " y[1] (analytic) = 0.20958367460541572 " " y[1] (numeric) = 0.20958367460541683 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.2972781716676130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.205053886170718 " " Order of pole = 3.5469356627532704 " " x[1] = -1.9410000000000065 " " y[1] (analytic) = 0.209754375528711 " " y[1] (numeric) = 0.20975437552871212 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.2929671756629940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2041258363022913 " " Order of pole = 3.5465138065457538 " " x[1] = -1.9400000000000066 " " y[1] (analytic) = 0.20992526660508748 " " y[1] (numeric) = 0.2099252666050886 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.2886584001044230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.203197953268376 " " Order of pole = 3.5460930707177525 " " x[1] = -1.9390000000000067 " " y[1] (analytic) = 0.21009634808426683 " " y[1] (numeric) = 0.21009634808426797 " " absolute error = 1.1379786002407855000000000000000E-15 " " relative error = 5.4164606411167020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.20227024083794 " " Order of pole = 3.5456735059451923 " " x[1] = -1.9380000000000068 " " y[1] (analytic) = 0.21026762021630535 " " y[1] (numeric) = 0.21026762021630652 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 5.5440498858417030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.201342702775898 " " Order of pole = 3.5452551628760745 " " x[1] = -1.937000000000007 " " y[1] (analytic) = 0.21043908325159408 " " y[1] (numeric) = 0.2104390832515953 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 5.8033199357155120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.2004153428425512 " " Order of pole = 3.5448380921227987 " " x[1] = -1.936000000000007 " " y[1] (analytic) = 0.2106107374408593 " " y[1] (numeric) = 0.2106107374408605 " " absolute error = 1.1934897514720433000000000000000E-15 " " relative error = 5.6668039150054350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.199488164794251 " " Order of pole = 3.544422344271677 " " x[1] = -1.9350000000000072 " " y[1] (analytic) = 0.21078258303516256 " " y[1] (numeric) = 0.2107825830351638 " " absolute error = 1.2490009027033011000000000000000E-15 " " relative error = 5.9255413076276030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.198561172381365 " " Order of pole = 3.544007969854153 " " x[1] = -1.9340000000000073 " " y[1] (analytic) = 0.2109546202859013 " " y[1] (numeric) = 0.2109546202859026 " " absolute error = 1.27675647831893000000000000000E-15 " " relative error = 6.0522802325380450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1976343693496903 " " Order of pole = 3.543595019367075 " " x[1] = -1.9330000000000074 " " y[1] (analytic) = 0.21112684944480897 " " y[1] (numeric) = 0.21112684944481028 " " absolute error = 1.304512053934559000000000000000E-15 " " relative error = 6.1788069938284830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1967077594384117 " " Order of pole = 3.543183543243785 " " x[1] = -1.9320000000000075 " " y[1] (analytic) = 0.21129927076395547 " " y[1] (numeric) = 0.21129927076395674 " " absolute error = 1.27675647831893000000000000000E-15 " " relative error = 6.0424083514476850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.195781346381864 " " Order of pole = 3.542773591879328 " " x[1] = -1.9310000000000076 " " y[1] (analytic) = 0.21147188449574716 " " y[1] (numeric) = 0.21147188449574847 " " absolute error = 1.304512053934559000000000000000E-15 " " relative error = 6.1687257246756780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1948551339068794 " " Order of pole = 3.5423652155928274 " " x[1] = -1.9300000000000077 " " y[1] (analytic) = 0.21164469089292762 " " y[1] (numeric) = 0.21164469089292895 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.2948313228617230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1939291257338533 " " Order of pole = 3.54195846464275 " " x[1] = -1.9290000000000078 " " y[1] (analytic) = 0.21181769020857766 " " y[1] (numeric) = 0.211817690208579 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.2896901020792880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1930033255764516 " " Order of pole = 3.541553389222912 " " x[1] = -1.928000000000008 " " y[1] (analytic) = 0.21199088269611563 " " y[1] (numeric) = 0.211990882696117 " " absolute error = 1.3600232051658168000000000000000E-15 " " relative error = 6.415479703036949000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1920777371400306 " " Order of pole = 3.541150039440005 " " x[1] = -1.927000000000008 " " y[1] (analytic) = 0.2121642686092979 " " y[1] (numeric) = 0.21216426860929927 " " absolute error = 1.3600232051658168000000000000000E-15 " " relative error = 6.4102368135810360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1911523641226855 " " Order of pole = 3.540748465328729 " " x[1] = -1.9260000000000081 " " y[1] (analytic) = 0.21233784820221896 " " y[1] (numeric) = 0.21233784820222035 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 6.5357108613995230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.190227210214212 " " Order of pole = 3.54034871683702 " " x[1] = -1.9250000000000083 " " y[1] (analytic) = 0.2125116217293119 " " y[1] (numeric) = 0.2125116217293133 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 6.5303665253147340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1893022790961627 " " Order of pole = 3.5399508438269756 " " x[1] = -1.9240000000000084 " " y[1] (analytic) = 0.21268558944534854 " " y[1] (numeric) = 0.21268558944535 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 6.7860259633790090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1883775744399694 " " Order of pole = 3.539554896048159 " " x[1] = -1.9230000000000085 " " y[1] (analytic) = 0.21285975160544 " " y[1] (numeric) = 0.21285975160544143 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 6.7804736270105550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1874530999093746 " " Order of pole = 3.539160923172375 " " x[1] = -1.9220000000000086 " " y[1] (analytic) = 0.21303410846503662 " " y[1] (numeric) = 0.2130341084650381 " " absolute error = 1.4710455076283324000000000000000E-15 " " relative error = 6.9052111806300810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.186528859157747 " " Order of pole = 3.538768974755463 " " x[1] = -1.9210000000000087 " " y[1] (analytic) = 0.21320866027992863 " " y[1] (numeric) = 0.21320866027993016 " " absolute error = 1.5265566588595902000000000000000E-15 " " relative error = 7.1599186302063160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.185604855827894 " " Order of pole = 3.5383791002345824 " " x[1] = -1.9200000000000088 " " y[1] (analytic) = 0.21338340730624633 " " y[1] (numeric) = 0.21338340730624783 " " absolute error = 1.4988010832439613000000000000000E-15 " " relative error = 7.0239813965145510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1846810935541896 " " Order of pole = 3.5379913489588404 " " x[1] = -1.919000000000009 " " y[1] (analytic) = 0.21355834980046018 " " y[1] (numeric) = 0.2135583498004617 " " absolute error = 1.5265566588595902000000000000000E-15 " " relative error = 7.1481946750662750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1837575759584924 " " Order of pole = 3.537605770130895 " " x[1] = -1.918000000000009 " " y[1] (analytic) = 0.2137334880193815 " " y[1] (numeric) = 0.21373348801938302 " " absolute error = 1.5265566588595902000000000000000E-15 " " relative error = 7.142337277166230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1828343066521025 " " Order of pole = 3.5372224128350283 " " x[1] = -1.9170000000000091 " " y[1] (analytic) = 0.21390882222016236 " " y[1] (numeric) = 0.2139088222201639 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.2662371675136770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1819112892353325 " " Order of pole = 3.5368413260310483 " " x[1] = -1.9160000000000093 " " y[1] (analytic) = 0.21408435266029616 " " y[1] (numeric) = 0.21408435266029777 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 7.5195751847446110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1809885272965763 " " Order of pole = 3.536462558541036 " " x[1] = -1.9150000000000094 " " y[1] (analytic) = 0.21426007959761792 " " y[1] (numeric) = 0.21426007959761953 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 7.513407951353970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1800660244122034 " " Order of pole = 3.5360861590478585 " " x[1] = -1.9140000000000095 " " y[1] (analytic) = 0.21443600329030438 " " y[1] (numeric) = 0.214436003290306 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 7.50724393761010000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1791437841463246 " " Order of pole = 3.5357121760918098 " " x[1] = -1.9130000000000096 " " y[1] (analytic) = 0.2146121239968744 " " y[1] (numeric) = 0.21461212399687607 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 7.7597411829444860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.178221810049192 " " Order of pole = 3.535340658047815 " " x[1] = -1.9120000000000097 " " y[1] (analytic) = 0.2147884419761894 " " y[1] (numeric) = 0.2147884419761911 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 7.8825941329797110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.17730010566063 " " Order of pole = 3.534971653174466 " " x[1] = -1.9110000000000098 " " y[1] (analytic) = 0.21496495748745348 " " y[1] (numeric) = 0.21496495748745514 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 7.7470047044059850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1763786745030984 " " Order of pole = 3.5346052095148366 " " x[1] = -1.91000000000001 " " y[1] (analytic) = 0.21514167079021362 " " y[1] (numeric) = 0.21514167079021532 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 7.8696521521593530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.175457520088683 " " Order of pole = 3.534241374996416 " " x[1] = -1.90900000000001 " " y[1] (analytic) = 0.21531858214436028 " " y[1] (numeric) = 0.21531858214436203 " " absolute error = 1.7486012637846216000000000000000E-15 " " relative error = 8.1209956259709730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1745366459139306 " " Order of pole = 3.533880197357284 " " x[1] = -1.9080000000000101 " " y[1] (analytic) = 0.21549569181012754 " " y[1] (numeric) = 0.2154956918101293 " " absolute error = 1.7486012637846216000000000000000E-15 " " relative error = 8.1143212149471080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1736160554580093 " " Order of pole = 3.533521724119744 " " x[1] = -1.9070000000000102 " " y[1] (analytic) = 0.21567300004809326 " " y[1] (numeric) = 0.21567300004809503 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 8.2363431630484020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1726957521923214 " " Order of pole = 3.533166002727828 " " x[1] = -1.9060000000000104 " " y[1] (analytic) = 0.2158505071191796 " " y[1] (numeric) = 0.21585050711918138 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 8.2295699144197680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1717757395694073 " " Order of pole = 3.5328130803884683 " " x[1] = -1.9050000000000105 " " y[1] (analytic) = 0.21602821328465313 " " y[1] (numeric) = 0.21602821328465494 " " absolute error = 1.8041124150158794000000000000000E-15 " " relative error = 8.3512814719189520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.170856021012943 " " Order of pole = 3.5324630039284344 " " x[1] = -1.9040000000000106 " " y[1] (analytic) = 0.2162061188061252 " " y[1] (numeric) = 0.21620611880612706 " " absolute error = 1.8596235662471372000000000000000E-15 " " relative error = 8.6011606725833960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.169936599963982 " " Order of pole = 3.5321158204558003 " " x[1] = -1.9030000000000107 " " y[1] (analytic) = 0.21638422394555237 " " y[1] (numeric) = 0.2163842239455542 " " absolute error = 1.8318679906315083000000000000000E-15 " " relative error = 8.4658112187164410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1690174798100754 " " Order of pole = 3.5317715763458324 " " x[1] = -1.9020000000000108 " " y[1] (analytic) = 0.21656252896523634 " " y[1] (numeric) = 0.21656252896523817 " " absolute error = 1.8318679906315083000000000000000E-15 " " relative error = 8.458840961012090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.168098663946387 " " Order of pole = 3.531430318115291 " " x[1] = -1.901000000000011 " " y[1] (analytic) = 0.21674103412782456 " " y[1] (numeric) = 0.21674103412782642 " " absolute error = 1.8596235662471372000000000000000E-15 " " relative error = 8.5799330695746840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1671801557397288 " " Order of pole = 3.531092091907812 " " x[1] = -1.900000000000011 " " y[1] (analytic) = 0.2169197396963104 " " y[1] (numeric) = 0.21691973969631229 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 8.7008178439874310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1662619585455816 " " Order of pole = 3.530756943737334 " " x[1] = -1.8990000000000111 " " y[1] (analytic) = 0.21709864593403347 " " y[1] (numeric) = 0.21709864593403536 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 8.6936476906274950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1653440757001445 " " Order of pole = 3.5304249193742905 " " x[1] = -1.8980000000000112 " " y[1] (analytic) = 0.2172777531046798 " " y[1] (numeric) = 0.21727775310468173 " " absolute error = 1.915134717478395000000000000000E-15 " " relative error = 8.8142236842615160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1644265105176625 " " Order of pole = 3.530096064307191 " " x[1] = -1.8970000000000113 " " y[1] (analytic) = 0.2174570614722823 " " y[1] (numeric) = 0.21745706147228425 " " absolute error = 1.942890293094024000000000000000E-15 " " relative error = 8.93459278783490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.163509266298621 " " Order of pole = 3.5297704238598833 " " x[1] = -1.8960000000000115 " " y[1] (analytic) = 0.21763657130122088 " " y[1] (numeric) = 0.21763657130122285 " " absolute error = 1.970645868709652900000000000000E-15 " " relative error = 9.0547551678810980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1625923463245633 " " Order of pole = 3.5294480431171387 " " x[1] = -1.8950000000000116 " " y[1] (analytic) = 0.21781628285622284 " " y[1] (numeric) = 0.2178162828562248 " " absolute error = 1.970645868709652900000000000000E-15 " " relative error = 9.047284449392820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1616757538550373 " " Order of pole = 3.529128966880993 " " x[1] = -1.8940000000000117 " " y[1] (analytic) = 0.21799619640236306 " " y[1] (numeric) = 0.21799619640236506 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 9.1671390478610160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.160759492132907 " " Order of pole = 3.52881323974648 " " x[1] = -1.8930000000000118 " " y[1] (analytic) = 0.21817631220506442 " " y[1] (numeric) = 0.21817631220506642 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 9.1595711015913560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1598435643795524 " " Order of pole = 3.528500906032903 " " x[1] = -1.892000000000012 " " y[1] (analytic) = 0.21835663053009785 " " y[1] (numeric) = 0.2183566305300999 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 9.4062295730169390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1589279737970677 " " Order of pole = 3.5281920098150543 " " x[1] = -1.891000000000012 " " y[1] (analytic) = 0.21853715164358298 " " y[1] (numeric) = 0.218537151643585 " " absolute error = 2.0261570199409107000000000000000E-15 " " relative error = 9.2714534105643260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.15801272356735 " " Order of pole = 3.5278865949101004 " " x[1] = -1.8900000000000121 " " y[1] (analytic) = 0.21871787581198796 " " y[1] (numeric) = 0.21871787581198998 " " absolute error = 2.0261570199409107000000000000000E-15 " " relative error = 9.263792510871929000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.15709781685003 " " Order of pole = 3.527584704847765 " " x[1] = -1.8890000000000122 " " y[1] (analytic) = 0.21889880330213002 " " y[1] (numeric) = 0.2188988033021321 " " absolute error = 2.0816681711721685000000000000000E-15 " " relative error = 9.5097284213975080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1561832567852766 " " Order of pole = 3.5272863829102263 " " x[1] = -1.8880000000000123 " " y[1] (analytic) = 0.21907993438117582 " " y[1] (numeric) = 0.21907993438117793 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 9.6285575068578580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.155269046491079 " " Order of pole = 3.5269916720931818 " " x[1] = -1.8870000000000124 " " y[1] (analytic) = 0.2192612693166415 " " y[1] (numeric) = 0.2192612693166436 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 9.6205944322137360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.154355189063753 " " Order of pole = 3.526700615112759 " " x[1] = -1.8860000000000126 " " y[1] (analytic) = 0.21944280837639302 " " y[1] (numeric) = 0.21944280837639518 " " absolute error = 2.1649348980190553000000000000000E-15 " " relative error = 9.8655996705333460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.153441687576869 " " Order of pole = 3.5264132543900537 " " x[1] = -1.8850000000000127 " " y[1] (analytic) = 0.21962455182864665 " " y[1] (numeric) = 0.2196245518286488 " " absolute error = 2.1371793224034263000000000000000E-15 " " relative error = 9.731058320250441000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.152528545082078 " " Order of pole = 3.5261296320626982 " " x[1] = -1.8840000000000128 " " y[1] (analytic) = 0.21980649994196877 " " y[1] (numeric) = 0.21980649994197093 " " absolute error = 2.1649348980190553000000000000000E-15 " " relative error = 9.8492760614022820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.151615764607696 " " Order of pole = 3.525849789964404 " " x[1] = -1.8830000000000129 " " y[1] (analytic) = 0.21998865298527664 " " y[1] (numeric) = 0.21998865298527887 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.0093457181170716000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1507033491591643 " " Order of pole = 3.5255737696313325 " " x[1] = -1.882000000000013 " " y[1] (analytic) = 0.22017101122783853 " " y[1] (numeric) = 0.22017101122784072 " " absolute error = 2.192690473634684200000000000000E-15 " " relative error = 9.9590334867728460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1497913017180075 " " Order of pole = 3.5253016122869063 " " x[1] = -1.881000000000013 " " y[1] (analytic) = 0.22035357493927366 " " y[1] (numeric) = 0.2203535749392759 " " absolute error = 2.248201624865942000000000000000E-15 " " relative error = 1.020270093410336000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.148879625242314 " " Order of pole = 3.525033358848461 " " x[1] = -1.8800000000000132 " " y[1] (analytic) = 0.220536344389553 " " y[1] (numeric) = 0.22053634438955524 " " absolute error = 2.248201624865942000000000000000E-15 " " relative error = 1.0194245447792238000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1479683226655806 " " Order of pole = 3.524769049910475 " " x[1] = -1.8790000000000133 " " y[1] (analytic) = 0.22071931984899906 " " y[1] (numeric) = 0.22071931984900134 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 1.0311545006747139000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.147057396897171 " " Order of pole = 3.5245087257508168 " " x[1] = -1.8780000000000134 " " y[1] (analytic) = 0.22090250158828653 " " y[1] (numeric) = 0.22090250158828884 " " absolute error = 2.3037127760971998000000000000E-15 " " relative error = 1.0428640506710113000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.146146850819687 " " Order of pole = 3.5242524262929074 " " x[1] = -1.8770000000000135 " " y[1] (analytic) = 0.2210858898784423 " " y[1] (numeric) = 0.2210858898784446 " " absolute error = 2.3037127760971998000000000000E-15 " " relative error = 1.0419990065235868000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1452366872933597 " " Order of pole = 3.5240001911682306 " " x[1] = -1.8760000000000137 " " y[1] (analytic) = 0.2212694849908458 " " y[1] (numeric) = 0.22126948499084811 " " absolute error = 2.3037127760971998000000000000E-15 " " relative error = 1.0411344231187177000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.144326909150688 " " Order of pole = 3.523752059639328 " " x[1] = -1.8750000000000138 " " y[1] (analytic) = 0.22145328719722931 " " y[1] (numeric) = 0.22145328719723165 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 1.0528036775703362000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.143417519198647 " " Order of pole = 3.523508070631113 " " x[1] = -1.8740000000000139 " " y[1] (analytic) = 0.22163729676967817 " " y[1] (numeric) = 0.22163729676968053 " " absolute error = 2.3592239273284576000000000000000E-15 " " relative error = 1.0644525816339134000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.142508520218603 " " Order of pole = 3.5232682627293563 " " x[1] = -1.873000000000014 " " y[1] (analytic) = 0.2218215139806311 " " y[1] (numeric) = 0.22182151398063343 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 1.0510560088938922000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1415999149642593 " " Order of pole = 3.5230326741508975 " " x[1] = -1.872000000000014 " " y[1] (analytic) = 0.22200593910288025 " " y[1] (numeric) = 0.22200593910288266 " " absolute error = 2.4147350785597155000000000000000E-15 " " relative error = 1.0876894052103254000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1406917061627855 " " Order of pole = 3.522801342759575 " " x[1] = -1.8710000000000142 " " y[1] (analytic) = 0.22219057240957193 " " y[1] (numeric) = 0.22219057240957432 " " absolute error = 2.3869795029440866000000000000000E-15 " " relative error = 1.0742937817109903000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1397838965146 " " Order of pole = 3.5225743060627117 " " x[1] = -1.8700000000000143 " " y[1] (analytic) = 0.22237541417420625 " " y[1] (numeric) = 0.22237541417420867 " " absolute error = 2.4147350785597155000000000000000E-15 " " relative error = 1.0858822174775314000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.138876488691556 " " Order of pole = 3.5223516011848055 " " x[1] = -1.8690000000000144 " " y[1] (analytic) = 0.2225604646706379 " " y[1] (numeric) = 0.22256046467064033 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.0974503750205276000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1379694853374125 " " Order of pole = 3.522133264873947 " " x[1] = -1.8680000000000145 " " y[1] (analytic) = 0.22274572417307606 " " y[1] (numeric) = 0.22274572417307856 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 1.1214589257235867000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1370628890688272 " " Order of pole = 3.5219193335156334 " " x[1] = -1.8670000000000146 " " y[1] (analytic) = 0.22293119295608496 " " y[1] (numeric) = 0.22293119295608746 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 1.1205259220492673000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.136156702472521 " " Order of pole = 3.521709843091852 " " x[1] = -1.8660000000000148 " " y[1] (analytic) = 0.2231168712945838 " " y[1] (numeric) = 0.22311687129458632 " " absolute error = 2.525757381022231000000000000000E-15 " " relative error = 1.1320333448417016000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.135250928106886 " " Order of pole = 3.5215048292036037 " " x[1] = -1.8650000000000149 " " y[1] (analytic) = 0.2233027594638473 " " y[1] (numeric) = 0.22330275946384984 " " absolute error = 2.525757381022231000000000000000E-15 " " relative error = 1.1310909847628421000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.134345568500475 " " Order of pole = 3.521304327049066 " " x[1] = -1.864000000000015 " " y[1] (analytic) = 0.22348885773950578 " " y[1] (numeric) = 0.2234888577395083 " " absolute error = 2.525757381022231000000000000000E-15 " " relative error = 1.1301491298354588000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1334406261526806 " " Order of pole = 3.521108371432746 " " x[1] = -1.863000000000015 " " y[1] (analytic) = 0.22367516639754537 " " y[1] (numeric) = 0.22367516639754792 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 1.141616656763503000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.132536103532432 " " Order of pole = 3.520916996746461 " " x[1] = -1.8620000000000152 " " y[1] (analytic) = 0.22386168571430848 " " y[1] (numeric) = 0.22386168571431106 " " absolute error = 2.581268532253489000000000000000E-15 " " relative error = 1.15306401093919000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1316320030786553 " " Order of pole = 3.5207302369755773 " " x[1] = -1.8610000000000153 " " y[1] (analytic) = 0.2240484159664938 " " y[1] (numeric) = 0.22404841596649647 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.1892676177183302000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1307283271992166 " " Order of pole = 3.5205481256833373 " " x[1] = -1.8600000000000154 " " y[1] (analytic) = 0.22423535743115688 " " y[1] (numeric) = 0.22423535743115952 " " absolute error = 2.6367796834847470000000000000000E-15 " " relative error = 1.1758982676468728000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1298250782711494 " " Order of pole = 3.5203706960137815 " " x[1] = -1.8590000000000155 " " y[1] (analytic) = 0.2244225103857098 " " y[1] (numeric) = 0.2244225103857125 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 1.2120203118915088000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.128922258640695 " " Order of pole = 3.520197980691762 " " x[1] = -1.8580000000000156 " " y[1] (analytic) = 0.2246098751079221 " " y[1] (numeric) = 0.22460987510792482 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 1.2110092706407885000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.128019870620933 " " Order of pole = 3.5200300119886556 " " x[1] = -1.8570000000000157 " " y[1] (analytic) = 0.22479745187592054 " " y[1] (numeric) = 0.22479745187592326 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 1.2099987733993504000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.127117916494753 " " Order of pole = 3.5198668217644276 " " x[1] = -1.8560000000000159 " " y[1] (analytic) = 0.22498524096818948 " " y[1] (numeric) = 0.22498524096819225 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 1.2336620613950965000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.126216398510871 " " Order of pole = 3.5197084414100352 " " x[1] = -1.855000000000016 " " y[1] (analytic) = 0.22517324266357128 " " y[1] (numeric) = 0.22517324266357405 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 1.2326320519840005000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.125315318887219 " " Order of pole = 3.519554901895585 " " x[1] = -1.854000000000016 " " y[1] (analytic) = 0.22536145724126624 " " y[1] (numeric) = 0.22536145724126902 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 1.2316025976844168000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.124414679807058 " " Order of pole = 3.5194062337141077 " " x[1] = -1.8530000000000162 " " y[1] (analytic) = 0.2255498849808331 " " y[1] (numeric) = 0.2255498849808359 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 1.242879435481309000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.123514483421177 " " Order of pole = 3.5192624669125543 " " x[1] = -1.8520000000000163 " " y[1] (analytic) = 0.22573852616218912 " " y[1] (numeric) = 0.22573852616219195 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.2541362615081825000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1226147318469506 " " Order of pole = 3.5191236310778002 " " x[1] = -1.8510000000000164 " " y[1] (analytic) = 0.22592738106561047 " " y[1] (numeric) = 0.22592738106561333 " " absolute error = 2.858824288409778000000000000000E-15 " " relative error = 1.2653730924183826000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.121715427166423 " " Order of pole = 3.5189897553086524 " " x[1] = -1.8500000000000165 " " y[1] (analytic) = 0.2261164499717323 " " y[1] (numeric) = 0.22611644997173516 " " absolute error = 2.858824288409778000000000000000E-15 " " relative error = 1.264315041549241800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1208165714290783 " " Order of pole = 3.5188608682550218 " " x[1] = -1.8490000000000166 " " y[1] (analytic) = 0.22630573316154903 " " y[1] (numeric) = 0.22630573316155192 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.2755221989735510000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1199181666490565 " " Order of pole = 3.5187369980775074 " " x[1] = -1.8480000000000167 " " y[1] (analytic) = 0.22649523091641466 " " y[1] (numeric) = 0.22649523091641754 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.274455030397821000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.119020214804562 " " Order of pole = 3.5186181724383054 " " x[1] = -1.8470000000000169 " " y[1] (analytic) = 0.22668494351804286 " " y[1] (numeric) = 0.22668494351804577 " " absolute error = 2.914335439641036000000000000000E-15 " " relative error = 1.2856325587451603000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.118122717840136 " " Order of pole = 3.5185044185333005 " " x[1] = -1.846000000000017 " " y[1] (analytic) = 0.22687487124850733 " " y[1] (numeric) = 0.22687487124851027 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.296790164140323200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1172256776633587 " " Order of pole = 3.5183957630441363 " " x[1] = -1.845000000000017 " " y[1] (analytic) = 0.22706501439024204 " " y[1] (numeric) = 0.22706501439024498 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.295704238346592000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 2.1163290961468055 " " Order of pole = 3.518292232165795 " " x[1] = -1.8440000000000172 " " y[1] (analytic) = 0.22725537322604128 " " y[1] (numeric) = 0.22725537322604425 " " absolute error = 2.9698465908722940000000000000000E-15 " " relative error = 1.3068322868292814000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);" Iterations = 156 "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 54 Minutes 45 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 54 Minutes 3 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 57 Minutes 5 Seconds "Time to Timeout " Unknown Percent Done = 5.233333333332757 "%" (%o54) true (%o54) diffeq.max