(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, array_tmp1 1 temp2], array_tmp1 : array_m1 array_const_3D0 , array_tmp2 : -----------, 1 1 1 1 array_x 1 array_tmp2 array_tmp3 1 1 array_tmp3 : -----------, array_tmp4 : -----------, 1 array_x 1 array_x 1 1 array_tmp4 1 array_tmp5 : -----------, array_tmp6 : array_tmp5 + array_const_0D0 , 1 array_x 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_m1 array_const_3D0 , 2 2 1 array_tmp1 - array_tmp2 array_x 2 1 2 array_tmp2 : ----------------------------------, 2 array_x 1 array_tmp2 - array_tmp3 array_x 2 1 2 array_tmp3 : ----------------------------------, 2 array_x 1 array_tmp3 - array_tmp4 array_x 2 1 2 array_tmp4 : ----------------------------------, 2 array_x 1 array_tmp4 - array_tmp5 array_x 2 1 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 2 array_x 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_3D0 , 3 3 1 array_tmp1 - array_tmp2 array_x 3 2 2 array_tmp2 : ----------------------------------, 3 array_x 1 array_tmp2 - array_tmp3 array_x 3 2 2 array_tmp3 : ----------------------------------, 3 array_x 1 array_tmp3 - array_tmp4 array_x 3 2 2 array_tmp4 : ----------------------------------, 3 array_x 1 array_tmp4 - array_tmp5 array_x 3 2 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 3 array_x 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1 : array_m1 array_const_3D0 , 4 4 1 array_tmp1 - array_tmp2 array_x 4 3 2 array_tmp2 : ----------------------------------, 4 array_x 1 array_tmp2 - array_tmp3 array_x 4 3 2 array_tmp3 : ----------------------------------, 4 array_x 1 array_tmp3 - array_tmp4 array_x 4 3 2 array_tmp4 : ----------------------------------, 4 array_x 1 array_tmp4 - array_tmp5 array_x 4 3 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 4 array_x 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1 : array_m1 array_const_3D0 , 5 5 1 array_tmp1 - array_tmp2 array_x 5 4 2 array_tmp2 : ----------------------------------, 5 array_x 1 array_tmp2 - array_tmp3 array_x 5 4 2 array_tmp3 : ----------------------------------, 5 array_x 1 array_tmp3 - array_tmp4 array_x 5 4 2 array_tmp4 : ----------------------------------, 5 array_x 1 array_tmp4 - array_tmp5 array_x 5 4 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 5 array_x 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_3D0 , kkk kkk 1 - ats(kkk, array_x, array_tmp2, 2) array_tmp2 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp3, 2) array_tmp3 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp4, 2) array_tmp4 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp5, 2) array_tmp5 : ----------------------------------, kkk array_x 1 array_tmp6 : array_tmp5 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp6 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, array_tmp1 1 temp2], array_tmp1 : array_m1 array_const_3D0 , array_tmp2 : -----------, 1 1 1 1 array_x 1 array_tmp2 array_tmp3 1 1 array_tmp3 : -----------, array_tmp4 : -----------, 1 array_x 1 array_x 1 1 array_tmp4 1 array_tmp5 : -----------, array_tmp6 : array_tmp5 + array_const_0D0 , 1 array_x 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_m1 array_const_3D0 , 2 2 1 array_tmp1 - array_tmp2 array_x 2 1 2 array_tmp2 : ----------------------------------, 2 array_x 1 array_tmp2 - array_tmp3 array_x 2 1 2 array_tmp3 : ----------------------------------, 2 array_x 1 array_tmp3 - array_tmp4 array_x 2 1 2 array_tmp4 : ----------------------------------, 2 array_x 1 array_tmp4 - array_tmp5 array_x 2 1 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 2 array_x 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_3D0 , 3 3 1 array_tmp1 - array_tmp2 array_x 3 2 2 array_tmp2 : ----------------------------------, 3 array_x 1 array_tmp2 - array_tmp3 array_x 3 2 2 array_tmp3 : ----------------------------------, 3 array_x 1 array_tmp3 - array_tmp4 array_x 3 2 2 array_tmp4 : ----------------------------------, 3 array_x 1 array_tmp4 - array_tmp5 array_x 3 2 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 3 array_x 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1 : array_m1 array_const_3D0 , 4 4 1 array_tmp1 - array_tmp2 array_x 4 3 2 array_tmp2 : ----------------------------------, 4 array_x 1 array_tmp2 - array_tmp3 array_x 4 3 2 array_tmp3 : ----------------------------------, 4 array_x 1 array_tmp3 - array_tmp4 array_x 4 3 2 array_tmp4 : ----------------------------------, 4 array_x 1 array_tmp4 - array_tmp5 array_x 4 3 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 4 array_x 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1 : array_m1 array_const_3D0 , 5 5 1 array_tmp1 - array_tmp2 array_x 5 4 2 array_tmp2 : ----------------------------------, 5 array_x 1 array_tmp2 - array_tmp3 array_x 5 4 2 array_tmp3 : ----------------------------------, 5 array_x 1 array_tmp3 - array_tmp4 array_x 5 4 2 array_tmp4 : ----------------------------------, 5 array_x 1 array_tmp4 - array_tmp5 array_x 5 4 2 array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 , 5 array_x 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_3D0 , kkk kkk 1 - ats(kkk, array_x, array_tmp2, 2) array_tmp2 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp3, 2) array_tmp3 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp4, 2) array_tmp4 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp5, 2) array_tmp5 : ----------------------------------, kkk array_x 1 array_tmp6 : array_tmp5 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp6 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) 1.0 --- x --- x (%i55) exact_soln_y(x) := block(---) x 1.0 --- x --- x (%o55) exact_soln_y(x) := block(---) x (%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing5postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"), 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:-1.0,"), omniout_str(ALWAYS, "x_end:-0.7,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.00001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0/x/x/x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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_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_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_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, 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 : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:59:56-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing5"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "sing5 diffeq.max"), logitem_str(html_log_file, "sing5 maxima results" ), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing5postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"), 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:-1.0,"), omniout_str(ALWAYS, "x_end:-0.7,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.00001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0/x/x/x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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_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_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_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, 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 : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:59:56-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing5"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "sing5 diffeq.max"), logitem_str(html_log_file, "sing5 maxima results" ), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/sing5postode.ode#################" "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-1.0," "x_end:-0.7," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.00001," "glob_look_poles:true," "glob_max_iter:100," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0/x/x/x) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 0.30000000000000004 "" estimated_steps = 300.00000000000006 "" step_error = 3.3333333333333330000000000000E-13 "" est_needed_step_err = 3.3333333333333330000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 4.0404069204059845000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" max_value3 = 4.0404069204059845000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" value3 = 4.0404069204059845000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -1. " " y[1] (analytic) = -1. " " y[1] (numeric) = -1. " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1. " " y[1] (analytic) = -1. " " y[1] (numeric) = -1. " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 1.0000000000000027 " " Order of pole = 6.75015598972095200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.999 " " y[1] (analytic) = -1.003006010015021 " " y[1] (numeric) = -1.003006010015021 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.998 " " y[1] (analytic) = -1.0060240802406737 " " y[1] (numeric) = -1.006024080240674 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20715000054383400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9980000000000024 " " Order of pole = 6.03961325396085200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.997 " " y[1] (analytic) = -1.0090542712201236 " " y[1] (numeric) = -1.0090542712201236 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9970000000000011 " " Order of pole = 2.84217094304040100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.996 " " y[1] (analytic) = -1.0120966438616192 " " y[1] (numeric) = -1.0120966438616195 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.193907135961126500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9960000000000049 " " Order of pole = 1.24344978758017530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.995 " " y[1] (analytic) = -1.0151512594410652 " " y[1] (numeric) = -1.0151512594410654 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.187305614409496300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9950000000000012 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.994 " " y[1] (analytic) = -1.0182181796046124 " " y[1] (numeric) = -1.0182181796046126 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.1807173489207800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9940000000000003 " " Order of pole = 7.105427357601002000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.993 " " y[1] (analytic) = -1.021297466371271 " " y[1] (numeric) = -1.021297466371271 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.993000000000006 " " Order of pole = 1.56319401867222040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.992 " " y[1] (analytic) = -1.0243891821355442 " " y[1] (numeric) = -1.0243891821355442 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.8779087045642053 " " Order of pole = 2.157385381451604200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.991 " " y[1] (analytic) = -1.0274933896700835 " " y[1] (numeric) = -1.0274933896700833 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.161031955605352600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.99 " " y[1] (analytic) = -1.0306101521283648 " " y[1] (numeric) = -1.0306101521283644 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.30899316228305800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.989 " " y[1] (analytic) = -1.0337395330473862 " " y[1] (numeric) = -1.0337395330473858 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.295948792254477600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9890000000000021 " " Order of pole = 5.329070518200751000000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.988 " " y[1] (analytic) = -1.036881596350389 " " y[1] (numeric) = -1.0368815963503888 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.141465387239805000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9880000000000042 " " Order of pole = 1.10134124042815530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.987 " " y[1] (analytic) = -1.0400364063496002 " " y[1] (numeric) = -1.0400364063495995 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.4049086234696500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9870000000000044 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.986 " " y[1] (analytic) = -1.0432040277489936 " " y[1] (numeric) = -1.0432040277489931 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.256973689109599400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.985 " " y[1] (analytic) = -1.046384525647081 " " y[1] (numeric) = -1.0463845256470805 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.24403456822375350000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9850000000000065 " " Order of pole = 1.66977542903623540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.984 " " y[1] (analytic) = -1.0495779655397188 " " y[1] (numeric) = -1.0495779655397184 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.23112169301020900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9840000000000048 " " Order of pole = 1.24344978758017530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.983 " " y[1] (analytic) = -1.0527844133229418 " " y[1] (numeric) = -1.0527844133229411 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.3273525552354200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.982 " " y[1] (analytic) = -1.056003935295817 " " y[1] (numeric) = -1.0560039352958166 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.20537457301861700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.981 " " y[1] (analytic) = -1.0592365981633254 " " y[1] (numeric) = -1.0592365981633247 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.28881041242479500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9810000000000019 " " Order of pole = 4.61852778244065100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.98 " " y[1] (analytic) = -1.062482469039261 " " y[1] (numeric) = -1.06248246903926 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.35946423194400200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.980000000000005 " " Order of pole = 1.27897692436818030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.979 " " y[1] (analytic) = -1.0657416154491584 " " y[1] (numeric) = -1.0657416154491577 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.25042510415951800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9790000000000052 " " Order of pole = 1.35003119794419040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.978 " " y[1] (analytic) = -1.0690141053332438 " " y[1] (numeric) = -1.0690141053332431 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.23129116306131500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9780000000000001 " " Order of pole = 7.105427357601002000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.977 " " y[1] (analytic) = -1.0723000070494075 " " y[1] (numeric) = -1.0723000070494069 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.21219631069536000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9770000000000072 " " Order of pole = 1.88293824976426550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.976 " " y[1] (analytic) = -1.0755993893762033 " " y[1] (numeric) = -1.0755993893762026 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.1931405070936310000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.975 " " y[1] (analytic) = -1.078912321515872 " " y[1] (numeric) = -1.0789123215158711 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.23216494971745500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9750000000000042 " " Order of pole = 1.10134124042815530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.974 " " y[1] (analytic) = -1.0822388730973884 " " y[1] (numeric) = -1.0822388730973878 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.1551458863107200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9740000000000086 " " Order of pole = 2.23820961764431560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.973 " " y[1] (analytic) = -1.0855791141795361 " " y[1] (numeric) = -1.0855791141795357 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.090804659462321500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9730000000000051 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.972 " " y[1] (analytic) = -1.088933115254005 " " y[1] (numeric) = -1.0889331152540045 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.07820465397890130000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.971 " " y[1] (analytic) = -1.0923009472485155 " " y[1] (numeric) = -1.0923009472485148 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.09844582166729700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9710000000000045 " " Order of pole = 1.17239551400416530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.97 " " y[1] (analytic) = -1.0956826815299676 " " y[1] (numeric) = -1.095682681529967 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.07962347132229300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9700000000000034 " " Order of pole = 8.88178419700125200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.969 " " y[1] (analytic) = -1.0990783899076189 " " y[1] (numeric) = -1.099078389907618 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.08111985328707500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.968 " " y[1] (analytic) = -1.1024881446362844 " " y[1] (numeric) = -1.1024881446362833 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.00701583960471880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.967 " " y[1] (analytic) = -1.1059120184195663 " " y[1] (numeric) = -1.1059120184195654 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.03118516579104400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9670000000000117 " " Order of pole = 3.1263880373444410000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.966 " " y[1] (analytic) = -1.1093500844131106 " " y[1] (numeric) = -1.1093500844131094 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.00078689335703060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9660000000000069 " " Order of pole = 1.81188397618825550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.965 " " y[1] (analytic) = -1.1128024162278867 " " y[1] (numeric) = -1.1128024162278853 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.19721849101139780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.964 " " y[1] (analytic) = -1.1162690879334993 " " y[1] (numeric) = -1.116269087933498 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.19350042382393410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9640000000000034 " " Order of pole = 8.52651282912120200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.963 " " y[1] (analytic) = -1.1197501740615254 " " y[1] (numeric) = -1.1197501740615243 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.91491718727033300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9630000000000053 " " Order of pole = 1.42108547152020040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.962 " " y[1] (analytic) = -1.1232457496088792 " " y[1] (numeric) = -1.1232457496088781 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.88406165802757400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.961 " " y[1] (analytic) = -1.1267558900412045 " " y[1] (numeric) = -1.1267558900412034 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.85327021085779900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.961000000000006 " " Order of pole = 1.56319401867222040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.96 " " y[1] (analytic) = -1.1302806712962965 " " y[1] (numeric) = -1.1302806712962954 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.82254277914762400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.713732016703418 " " Order of pole = 1.905320345940708600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.959 " " y[1] (analytic) = -1.1338201697875523 " " y[1] (numeric) = -1.1338201697875514 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.83350343702693400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9590000000000076 " " Order of pole = 1.98951966012828050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.958 " " y[1] (analytic) = -1.1373744624074493 " " y[1] (numeric) = -1.1373744624074484 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.80902375652203700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9580000000000076 " " Order of pole = 2.06057393370429050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.957 " " y[1] (analytic) = -1.1409436265310529 " " y[1] (numeric) = -1.1409436265310517 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.73074391064088100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.7173575970119936 " " Order of pole = 2.246558494789496800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.956 " " y[1] (analytic) = -1.1445277400195533 " " y[1] (numeric) = -1.1445277400195524 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.76021749970823400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9560000000000007 " " Order of pole = 1.776356839400250500000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.955 " " y[1] (analytic) = -1.1481268812238343 " " y[1] (numeric) = -1.1481268812238334 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.73589081681791400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9550000000000073 " " Order of pole = 1.91846538655227050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.954 " " y[1] (analytic) = -1.1517411289880684 " " y[1] (numeric) = -1.1517411289880675 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.71161502655104400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.953 " " y[1] (analytic) = -1.1553705626533444 " " y[1] (numeric) = -1.1553705626533433 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.60923759452114500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9530000000000043 " " Order of pole = 1.17239551400416530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.952 " " y[1] (analytic) = -1.159015262061325 " " y[1] (numeric) = -1.1590152620613239 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.57901988840603500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.951 " " y[1] (analytic) = -1.1626753075579357 " " y[1] (numeric) = -1.1626753075579348 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.63909247858407400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.951000000000006 " " Order of pole = 1.59872115546022540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.95 " " y[1] (analytic) = -1.1663507799970843 " " y[1] (numeric) = -1.1663507799970834 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.61501972590394900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.950000000000004 " " Order of pole = 1.06581410364015030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.949 " " y[1] (analytic) = -1.170041760744411 " " y[1] (numeric) = -1.17004176074441 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.59099759939374400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9490000000000085 " " Order of pole = 2.30926389122032560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.948 " " y[1] (analytic) = -1.1737483316810713 " " y[1] (numeric) = -1.1737483316810706 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.675269534322069000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9480000000000085 " " Order of pole = 2.27373675443232060000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.947 " " y[1] (analytic) = -1.177470575207552 " " y[1] (numeric) = -1.1774705752075512 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.54310501172028500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.5653393181719961 " " Order of pole = 1.284661266254261000000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.946 " " y[1] (analytic) = -1.1812085742475156 " " y[1] (numeric) = -1.181208574247515 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.63942583298171500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.945 " " y[1] (analytic) = -1.1849624122516822 " " y[1] (numeric) = -1.184962412251681 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.36926786154756800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.6284605934032496 " " Order of pole = 1.168842800325364800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.944 " " y[1] (analytic) = -1.1887321732017395 " " y[1] (numeric) = -1.1887321732017384 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.33955561777110900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9440000000000025 " " Order of pole = 6.75015598972095200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.943 " " y[1] (analytic) = -1.1925179416142908 " " y[1] (numeric) = -1.1925179416142897 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.30990625702676500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9430000000000032 " " Order of pole = 8.88178419700125200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.942 " " y[1] (analytic) = -1.1963198025448327 " " y[1] (numeric) = -1.1963198025448316 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.28031971270115600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9420000000000003 " " Order of pole = 7.105427357601002000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.941 " " y[1] (analytic) = -1.2001378415917687 " " y[1] (numeric) = -1.2001378415917676 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.25079591818089600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.94 " " y[1] (analytic) = -1.2039721449004557 " " y[1] (numeric) = -1.2039721449004548 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.37706784548208700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9400000000000048 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.939 " " y[1] (analytic) = -1.207822799167287 " " y[1] (numeric) = -1.207822799167286 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.35354904968232900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9390000000000042 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.938 " " y[1] (analytic) = -1.2116898916438077 " " y[1] (numeric) = -1.2116898916438066 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.16260036731841800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9380000000000008 " " Order of pole = 2.131628207280300600000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9369999999999999 " " y[1] (analytic) = -1.215573510140867 " " y[1] (numeric) = -1.2155735101408658 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.1333269058857500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9370000000000047 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9359999999999999 " " y[1] (analytic) = -1.2194737430328053 " " y[1] (numeric) = -1.2194737430328042 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.10411586119153000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9360000000000034 " " Order of pole = 8.88178419700125200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9349999999999999 " " y[1] (analytic) = -1.2233906792616778 " " y[1] (numeric) = -1.2233906792616767 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.07496716662237100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9350000000000042 " " Order of pole = 1.17239551400416530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9339999999999999 " " y[1] (analytic) = -1.2273244083415136 " " y[1] (numeric) = -1.2273244083415122 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.08550569066778710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.5177136997230768 " " Order of pole = 1.374012015276093700000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9329999999999999 " " y[1] (analytic) = -1.231275020362611 " " y[1] (numeric) = -1.2312750203626097 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.08202278736868590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9330000000000023 " " Order of pole = 6.39488462184090200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9319999999999999 " " y[1] (analytic) = -1.2352426059958719 " " y[1] (numeric) = -1.2352426059958705 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.07854734210377470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9309999999999999 " " y[1] (analytic) = -1.2392272564971698 " " y[1] (numeric) = -1.2392272564971687 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.95899455732873700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.22336111321316826 " " Order of pole = 2.9682922786378185000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9299999999999999 " " y[1] (analytic) = -1.2432290637117602 " " y[1] (numeric) = -1.243229063711759 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.07161879370210020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9300000000000086 " " Order of pole = 2.38031816479633560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9289999999999999 " " y[1] (analytic) = -1.247248120078723 " " y[1] (numeric) = -1.247248120078722 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.90138062148437700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9290000000000008 " " Order of pole = 2.131628207280300600000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9279999999999999 " " y[1] (analytic) = -1.2512845186354509 " " y[1] (numeric) = -1.2512845186354493 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.24217331176623660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.2742587221253 " " Order of pole = 4.352074256530613600000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9269999999999999 " " y[1] (analytic) = -1.2553383530221671 " " y[1] (numeric) = -1.2553383530221656 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.23816199093518240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.927 " " Order of pole = 3.552713678800501000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9259999999999999 " " y[1] (analytic) = -1.259409717486492 " " y[1] (numeric) = -1.2594097174864907 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.05785084159037960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9260000000000005 " " Order of pole = 1.421085471520200400000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9249999999999999 " " y[1] (analytic) = -1.2634987068880423 " " y[1] (numeric) = -1.263498706888041 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.05442737874383840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9250000000000035 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9239999999999999 " " y[1] (analytic) = -1.2676054167030726 " " y[1] (numeric) = -1.267605416703071 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.22617986164641440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9229999999999999 " " y[1] (analytic) = -1.2717299430291567 " " y[1] (numeric) = -1.271729943029155 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.22220306519871240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9230000000000028 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9219999999999999 " " y[1] (analytic) = -1.275872382589911 " " y[1] (numeric) = -1.2758723825899094 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.21823487653216480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.6404061466367182 " " Order of pole = 9.166001291305292000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9209999999999999 " " y[1] (analytic) = -1.2800328327397572 " " y[1] (numeric) = -1.2800328327397557 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.21427528632089820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9210000000000055 " " Order of pole = 1.52766688188421540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9199999999999999 " " y[1] (analytic) = -1.2842113914687272 " " y[1] (numeric) = -1.2842113914687254 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.38322775455890200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9189999999999999 " " y[1] (analytic) = -1.288408157407309 " " y[1] (numeric) = -1.2884081574073072 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.37872213024081650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9190000000000007 " " Order of pole = 1.776356839400250500000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9179999999999999 " " y[1] (analytic) = -1.292623229831337 " " y[1] (numeric) = -1.2926232298313354 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.2024480131600510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9180000000000023 " " Order of pole = 6.39488462184090200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9169999999999999 " " y[1] (analytic) = -1.2968567086669234 " " y[1] (numeric) = -1.2968567086669216 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.36974025544134260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9170000000000089 " " Order of pole = 2.52242671194835570000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9159999999999999 " " y[1] (analytic) = -1.301108694495432 " " y[1] (numeric) = -1.3011086944954302 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.36526398364367170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9160000000000066 " " Order of pole = 1.84741111297626050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9149999999999999 " " y[1] (analytic) = -1.3053792885584978 " " y[1] (numeric) = -1.3053792885584958 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.53089715904108860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9150000000000066 " " Order of pole = 1.84741111297626050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9139999999999999 " " y[1] (analytic) = -1.309668592763088 " " y[1] (numeric) = -1.3096685927630862 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.35634071796175680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9129999999999999 " " y[1] (analytic) = -1.3139767096866104 " " y[1] (numeric) = -1.3139767096866086 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.35189370276123070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9130000000000066 " " Order of pole = 1.81188397618825550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9119999999999999 " " y[1] (analytic) = -1.3183037425820634 " " y[1] (numeric) = -1.3183037425820614 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.51588847074890450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.8890324279211224 " " Order of pole = 8.705924869900628000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9109999999999999 " " y[1] (analytic) = -1.3226497953832332 " " y[1] (numeric) = -1.3226497953832312 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.51090746114412800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9110000000000048 " " Order of pole = 1.35003119794419040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9099999999999999 " " y[1] (analytic) = -1.3270149727099374 " " y[1] (numeric) = -1.3270149727099354 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.50593737480164660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9100000000000004 " " Order of pole = 1.421085471520200400000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9089999999999999 " " y[1] (analytic) = -1.3313993798733124 " " y[1] (numeric) = -1.3313993798733104 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.50097819973105060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9079999999999999 " " y[1] (analytic) = -1.3358031228811493 " " y[1] (numeric) = -1.3358031228811473 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.49602992394193250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9080000000000016 " " Order of pole = 4.26325641456060100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9069999999999999 " " y[1] (analytic) = -1.3402263084432773 " " y[1] (numeric) = -1.3402263084432753 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.4910925354438830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.907000000000001 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9059999999999999 " " y[1] (analytic) = -1.3446690439769928 " " y[1] (numeric) = -1.3446690439769904 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.8164251383012692000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9049999999999999 " " y[1] (analytic) = -1.349131437612537 " " y[1] (numeric) = -1.3491314376125345 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.81041712177254450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.905000000000004 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9039999999999999 " " y[1] (analytic) = -1.3536135981986246 " " y[1] (numeric) = -1.353613598198622 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.96846076505607840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9040000000000015 " " Order of pole = 3.90798504668055100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9029999999999999 " " y[1] (analytic) = -1.3581156353080173 " " y[1] (numeric) = -1.3581156353080148 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.7984408622329082000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.27163830700354874 " " Order of pole = 1.50954804212233280000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9019999999999999 " " y[1] (analytic) = -1.3626376592431517 " " y[1] (numeric) = -1.3626376592431488 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.11837669716885450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9020000000000018 " " Order of pole = 4.97379915032070130000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9009999999999999 " " y[1] (analytic) = -1.367179781041811 " " y[1] (numeric) = -1.367179781041808 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.11133890659631560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.762594405895857 " " Order of pole = 3.514699642437335600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8999999999999999 " " y[1] (analytic) = -1.3717421124828535 " " y[1] (numeric) = -1.3717421124828508 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.94244620388417360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9000000000000027 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8989999999999999 " " y[1] (analytic) = -1.3763247660919893 " " y[1] (numeric) = -1.3763247660919864 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.09731012268399240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8990000000000082 " " Order of pole = 2.34479102800833060000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8979999999999999 " " y[1] (analytic) = -1.3809278551476063 " " y[1] (numeric) = -1.3809278551476034 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.090319094705250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8980000000000048 " " Order of pole = 1.38555833473219540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8969999999999999 " " y[1] (analytic) = -1.3855514936866526 " " y[1] (numeric) = -1.3855514936866498 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.08334361961881510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8970000000000025 " " Order of pole = 7.10542735760100200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8959999999999999 " " y[1] (analytic) = -1.3901957965105687 " " y[1] (numeric) = -1.390195796510566 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.91666185855865480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8960000000000032 " " Order of pole = 8.88178419700125200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8949999999999999 " " y[1] (analytic) = -1.3948608791912742 " " y[1] (numeric) = -1.394860879191271 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.22862689414071640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8950000000000066 " " Order of pole = 1.88293824976426550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8939999999999999 " " y[1] (analytic) = -1.3995468580772046 " " y[1] (numeric) = -1.3995468580772017 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.06251033851856340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8929999999999999 " " y[1] (analytic) = -1.4042538502994093 " " y[1] (numeric) = -1.4042538502994062 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.2137197404070710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8930000000000057 " " Order of pole = 1.63424829224823040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8919999999999999 " " y[1] (analytic) = -1.408981973777696 " " y[1] (numeric) = -1.4089819737776932 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.04869893138948040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8909999999999999 " " y[1] (analytic) = -1.413731347226838 " " y[1] (numeric) = -1.413731347226835 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.19887921071304420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8910000000000068 " " Order of pole = 1.95399252334027550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8899999999999999 " " y[1] (analytic) = -1.4185020901628302 " " y[1] (numeric) = -1.4185020901628271 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.1914838832515210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8900000000000067 " " Order of pole = 1.95399252334027550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8889999999999999 " " y[1] (analytic) = -1.423294322909208 " " y[1] (numeric) = -1.423294322909205 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.18410515584466170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.7303624429616864 " " Order of pole = 2.87290191636202500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8879999999999999 " " y[1] (analytic) = -1.428108166603419 " " y[1] (numeric) = -1.4281081666034159 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.17674300984071980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8880000000000009 " " Order of pole = 2.84217094304040100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8869999999999999 " " y[1] (analytic) = -1.4329437432032528 " " y[1] (numeric) = -1.4329437432032495 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.32435438562994450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8870000000000028 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8859999999999999 " " y[1] (analytic) = -1.4378011754933304 " " y[1] (numeric) = -1.437801175493327 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.31650184367992920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8849999999999999 " " y[1] (analytic) = -1.442680587091652 " " y[1] (numeric) = -1.4426805870916486 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.3086670075667110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8850000000000131 " " Order of pole = 3.7658764995285310000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8839999999999999 " " y[1] (analytic) = -1.4475821024562023 " " y[1] (numeric) = -1.4475821024561988 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.45423984779335900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8840000000000059 " " Order of pole = 1.66977542903623540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8829999999999999 " " y[1] (analytic) = -1.4525058468916177 " " y[1] (numeric) = -1.4525058468916143 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.2930503729146060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8830000000000086 " " Order of pole = 2.48689957516035070000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8819999999999999 " " y[1] (analytic) = -1.4574519465559141 " " y[1] (numeric) = -1.4574519465559104 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.58997100566204950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8820000000000036 " " Order of pole = 1.03028696685214530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8809999999999999 " " y[1] (analytic) = -1.4624205284672733 " " y[1] (numeric) = -1.4624205284672696 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.5811715647083827000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.4107985716468478 " " Order of pole = 2.291500322826323000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8799999999999999 " " y[1] (analytic) = -1.4674117205108945 " " y[1] (numeric) = -1.467411720510891 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.42107489611953440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8800000000000024 " " Order of pole = 7.10542735760100200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8789999999999999 " " y[1] (analytic) = -1.4724256514459073 " " y[1] (numeric) = -1.4724256514459035 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.56363252026936440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8790000000000093 " " Order of pole = 2.70006239588838070000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8779999999999999 " " y[1] (analytic) = -1.477462450912345 " " y[1] (numeric) = -1.477462450912341 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.70518068745673000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8780000000000036 " " Order of pole = 1.10134124042815530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8769999999999999 " " y[1] (analytic) = -1.4825222494381851 " " y[1] (numeric) = -1.4825222494381813 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.5461731081310990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.877 " " Order of pole = 3.552713678800501000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8759999999999999 " " y[1] (analytic) = -1.4876051784464532 " " y[1] (numeric) = -1.4876051784464495 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.5374732075533750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8760000000000001 " " Order of pole = 7.105427357601002000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8749999999999999 " " y[1] (analytic) = -1.4927113702623913 " " y[1] (numeric) = -1.4927113702623873 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.67754568517020060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8750000000000102 " " Order of pole = 2.9842794901924210000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8739999999999999 " " y[1] (analytic) = -1.4978409581206908 " " y[1] (numeric) = -1.4978409581206868 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.66837601614611200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8740000000000054 " " Order of pole = 1.63424829224823040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8729999999999999 " " y[1] (analytic) = -1.5029940761727956 " " y[1] (numeric) = -1.5029940761727913 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.8069621567095010000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8719999999999999 " " y[1] (analytic) = -1.5081708594942669 " " y[1] (numeric) = -1.5081708594942627 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.79732728358794540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8720000000000079 " " Order of pole = 2.34479102800833060000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8709999999999999 " " y[1] (analytic) = -1.5133714440922208 " " y[1] (numeric) = -1.5133714440922166 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.78771448347647670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8710000000000038 " " Order of pole = 1.10134124042815530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8699999999999999 " " y[1] (analytic) = -1.5185959669128315 " " y[1] (numeric) = -1.5185959669128275 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.63190669258506150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8700000000000027 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8689999999999999 " " y[1] (analytic) = -1.5238445658489046 " " y[1] (numeric) = -1.5238445658489004 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.7685550010314570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8690000000000044 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8679999999999999 " " y[1] (analytic) = -1.5291173797475186 " " y[1] (numeric) = -1.5291173797475144 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.75900826807173760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.868000000000009 " " Order of pole = 2.66453525910037570000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8669999999999999 " " y[1] (analytic) = -1.5344145484177403 " " y[1] (numeric) = -1.5344145484177363 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.6047738486134614000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8670000000000084 " " Order of pole = 2.52242671194835570000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8659999999999999 " " y[1] (analytic) = -1.539736212638409 " " y[1] (numeric) = -1.5397362126384049 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.73998069211245250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.866000000000007 " " Order of pole = 2.06057393370429050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8649999999999999 " " y[1] (analytic) = -1.5450825141659932 " " y[1] (numeric) = -1.5450825141659887 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.87421031419654470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8650000000000031 " " Order of pole = 8.88178419700125200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8639999999999999 " " y[1] (analytic) = -1.5504535957425198 " " y[1] (numeric) = -1.5504535957425152 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 3.0074661481194180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8629999999999999 " " y[1] (analytic) = -1.5558496011035787 " " y[1] (numeric) = -1.555849601103574 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.99703563899633540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8630000000000035 " " Order of pole = 1.06581410364015030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8619999999999999 " " y[1] (analytic) = -1.5612706749863998 " " y[1] (numeric) = -1.5612706749863954 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.8444088329138130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8620000000000052 " " Order of pole = 1.59872115546022540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8609999999999999 " " y[1] (analytic) = -1.5667169631380067 " " y[1] (numeric) = -1.5667169631380022 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.83452097793457260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8610000000000045 " " Order of pole = 1.35003119794419040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8599999999999999 " " y[1] (analytic) = -1.5721886123234439 " " y[1] (numeric) = -1.5721886123234394 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.8246560646039130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8600000000000027 " " Order of pole = 7.81597009336110200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8589999999999999 " " y[1] (analytic) = -1.5776857703340836 " " y[1] (numeric) = -1.5776857703340792 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.8148140662764820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8590000000000049 " " Order of pole = 1.45661260830820540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8579999999999999 " " y[1] (analytic) = -1.5832085859960092 " " y[1] (numeric) = -1.5832085859960043 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.0854944519376190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8569999999999999 " " y[1] (analytic) = -1.5887572091784743 " " y[1] (numeric) = -1.5887572091784694 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.0747185788548830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8570000000000004 " " Order of pole = 1.421085471520200400000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8559999999999999 " " y[1] (analytic) = -1.5943317908024461 " " y[1] (numeric) = -1.5943317908024413 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.0639678243460350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8560000000000024 " " Order of pole = 7.46069872548105200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8549999999999999 " " y[1] (analytic) = -1.5999324828492243 " " y[1] (numeric) = -1.5999324828492196 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.9144584245965877000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8550000000000066 " " Order of pole = 1.98951966012828050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8539999999999999 " " y[1] (analytic) = -1.6055594383691438 " " y[1] (numeric) = -1.605559438369139 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.042541553810450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8540000000000016 " " Order of pole = 4.97379915032070130000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8529999999999999 " " y[1] (analytic) = -1.6112128114903561 " " y[1] (numeric) = -1.611212811490351 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.16967806912593460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.853000000000001 " " Order of pole = 3.55271367880050100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8519999999999999 " " y[1] (analytic) = -1.616892757427696 " " y[1] (numeric) = -1.6168927574276908 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.15854337884502230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8520000000000053 " " Order of pole = 1.63424829224823040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8509999999999999 " " y[1] (analytic) = -1.6225994324916304 " " y[1] (numeric) = -1.6225994324916255 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.0105898045640330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8510000000000005 " " Order of pole = 1.776356839400250500000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8499999999999999 " " y[1] (analytic) = -1.6283329940972937 " " y[1] (numeric) = -1.6283329940972886 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.136352288990450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.850000000000001 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8489999999999999 " " y[1] (analytic) = -1.6340936007736029 " " y[1] (numeric) = -1.6340936007735978 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.1252958281324783000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.849000000000004 " " Order of pole = 1.27897692436818030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8479999999999999 " " y[1] (analytic) = -1.6398814121724654 " " y[1] (numeric) = -1.63988141217246 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.2496682251803560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8480000000000052 " " Order of pole = 1.56319401867222040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8469999999999999 " " y[1] (analytic) = -1.645696589078069 " " y[1] (numeric) = -1.645696589078064 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.1032609213443846000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8470000000000043 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8459999999999999 " " y[1] (analytic) = -1.6515392934162634 " " y[1] (numeric) = -1.6515392934162583 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.09228241412995300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8460000000000087 " " Order of pole = 2.66453525910037570000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8449999999999999 " " y[1] (analytic) = -1.6574096882640281 " " y[1] (numeric) = -1.6574096882640224 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.48324241672415050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8439999999999999 " " y[1] (analytic) = -1.6633079378590292 " " y[1] (numeric) = -1.6633079378590236 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.3373947161408050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8440000000000061 " " Order of pole = 1.84741111297626050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8429999999999999 " " y[1] (analytic) = -1.6692342076092725 " " y[1] (numeric) = -1.6692342076092672 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.19252414904269600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8430000000000052 " " Order of pole = 1.66977542903623540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8419999999999999 " " y[1] (analytic) = -1.6751886641028426 " " y[1] (numeric) = -1.675188664102837 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.313725338571769700000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8420000000000071 " " Order of pole = 2.20268248085631060000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8409999999999999 " " y[1] (analytic) = -1.681171475117736 " " y[1] (numeric) = -1.6811714751177302 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.434010042102640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8410000000000056 " " Order of pole = 1.77635683940025050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8399999999999999 " " y[1] (analytic) = -1.68718280963179 " " y[1] (numeric) = -1.6871828096317845 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.29016813793714200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8400000000000005 " " Order of pole = 2.486899575160350700000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8389999999999999 " " y[1] (analytic) = -1.693222837832706 " " y[1] (numeric) = -1.6932228378327006 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.27843152070350500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8390000000000055 " " Order of pole = 1.70530256582424040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8379999999999999 " " y[1] (analytic) = -1.6992917311281663 " " y[1] (numeric) = -1.6992917311281608 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.26672284778339700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8380000000000021 " " Order of pole = 6.75015598972095200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8369999999999999 " " y[1] (analytic) = -1.70538966215605 " " y[1] (numeric) = -1.7053896621560443 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.38524376930493360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8370000000000026 " " Order of pole = 8.52651282912120200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8359999999999999 " " y[1] (analytic) = -1.7115168047947453 " " y[1] (numeric) = -1.7115168047947396 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.37312476972328860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8349999999999999 " " y[1] (analytic) = -1.7176733341735626 " " y[1] (numeric) = -1.7176733341735568 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.36103472831083940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.5888924531332838 " " Order of pole = 4.305888978706207000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8339999999999999 " " y[1] (analytic) = -1.7238594266832459 " " y[1] (numeric) = -1.7238594266832399 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.47778028775280600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8329999999999999 " " y[1] (analytic) = -1.7300752599865847 " " y[1] (numeric) = -1.7300752599865787 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.46528528072376050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8330000000000074 " " Order of pole = 2.30926389122032560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8319999999999999 " " y[1] (analytic) = -1.7363210130291316 " " y[1] (numeric) = -1.7363210130291253 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.5807024687528590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8320000000000054 " " Order of pole = 1.66977542903623540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8309999999999998 " " y[1] (analytic) = -1.7425968660500182 " " y[1] (numeric) = -1.7425968660500117 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.69522846521696870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8310000000000017 " " Order of pole = 5.68434188608080100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8299999999999998 " " y[1] (analytic) = -1.7489030005928792 " " y[1] (numeric) = -1.7489030005928727 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.68190433697179500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8300000000000055 " " Order of pole = 1.74082970261224550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8289999999999998 " " y[1] (analytic) = -1.7552395995168808 " " y[1] (numeric) = -1.7552395995168748 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.4156045332078816000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8290000000000041 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8279999999999998 " " y[1] (analytic) = -1.761606847007857 " " y[1] (numeric) = -1.7616068470078505 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.65535224489121700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8280000000000011 " " Order of pole = 3.90798504668055100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8269999999999998 " " y[1] (analytic) = -1.7680049285895483 " " y[1] (numeric) = -1.7680049285895418 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.64212420378428940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8270000000000017 " " Order of pole = 5.68434188608080100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8259999999999998 " " y[1] (analytic) = -1.7744340311349585 " " y[1] (numeric) = -1.7744340311349522 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.5037926622294420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8249999999999998 " " y[1] (analytic) = -1.780894342877815 " " y[1] (numeric) = -1.7808943428778086 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.6157639382583523000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8250000000000065 " " Order of pole = 2.06057393370429050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8239999999999998 " " y[1] (analytic) = -1.7873860534241406 " " y[1] (numeric) = -1.7873860534241344 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.47840295944479100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8240000000000027 " " Order of pole = 9.23705556488130200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8229999999999998 " " y[1] (analytic) = -1.7939093537639434 " " y[1] (numeric) = -1.7939093537639366 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.8370850445890140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.823000000000005 " " Order of pole = 1.59872115546022540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8219999999999998 " " y[1] (analytic) = -1.8004644362830122 " " y[1] (numeric) = -1.8004644362830056 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 3.69978879533050360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8220000000000081 " " Order of pole = 2.52242671194835570000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8209999999999998 " " y[1] (analytic) = -1.8070514947748366 " " y[1] (numeric) = -1.80705149477483 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 3.68630233671396250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8210000000000053 " " Order of pole = 1.70530256582424040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8199999999999998 " " y[1] (analytic) = -1.813670724452635 " " y[1] (numeric) = -1.8136707244526284 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 3.6728486918491380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8200000000000063 " " Order of pole = 1.98951966012828050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8189999999999998 " " y[1] (analytic) = -1.8203223219615061 " " y[1] (numeric) = -1.8203223219614992 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.7814087481269330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8190000000000076 " " Order of pole = 2.38031816479633560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8179999999999998 " " y[1] (analytic) = -1.8270064853906944 " " y[1] (numeric) = -1.8270064853906878 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 3.646039683502520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8180000000000055 " " Order of pole = 1.77635683940025050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8169999999999998 " " y[1] (analytic) = -1.8337234142859824 " " y[1] (numeric) = -1.8337234142859755 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.75377371475415830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8170000000000036 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8159999999999998 " " y[1] (analytic) = -1.8404733096621975 " " y[1] (numeric) = -1.8404733096621904 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.860652213916180300000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8160000000000053 " " Order of pole = 1.63424829224823040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8149999999999998 " " y[1] (analytic) = -1.8472563740158463 " " y[1] (numeric) = -1.8472563740158394 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.7262736507503980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8150000000000047 " " Order of pole = 1.52766688188421540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8139999999999998 " " y[1] (analytic) = -1.8540728113378728 " " y[1] (numeric) = -1.854072811337866 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.7125741290111570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.3228188955313651 " " Order of pole = 7.709388682997087000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8129999999999998 " " y[1] (analytic) = -1.86092282712654 " " y[1] (numeric) = -1.8609228271265328 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.81822784589757940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8130000000000042 " " Order of pole = 1.35003119794419040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8119999999999998 " " y[1] (analytic) = -1.8678066284004402 " " y[1] (numeric) = -1.867806628400433 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.80415576728409870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8120000000000033 " " Order of pole = 1.06581410364015030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8109999999999998 " " y[1] (analytic) = -1.874724423711635 " " y[1] (numeric) = -1.8747244237116276 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 3.9085595033849760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8110000000000028 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8099999999999998 " " y[1] (analytic) = -1.8816764231589216 " " y[1] (numeric) = -1.8816764231589145 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.7761154203508324000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8100000000000042 " " Order of pole = 1.35003119794419040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8089999999999998 " " y[1] (analytic) = -1.8886628384012363 " " y[1] (numeric) = -1.8886628384012285 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.11484835427522100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8079999999999998 " " y[1] (analytic) = -1.8956838826711817 " " y[1] (numeric) = -1.8956838826711742 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.9824765281082336000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8080000000000016 " " Order of pole = 5.68434188608080100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8069999999999998 " " y[1] (analytic) = -1.9027397707887002 " " y[1] (numeric) = -1.9027397707886924 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.0844057036526460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8070000000000027 " " Order of pole = 8.88178419700125200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8059999999999998 " " y[1] (analytic) = -1.9098307191748711 " " y[1] (numeric) = -1.9098307191748636 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.95297682231898540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8060000000000037 " " Order of pole = 1.24344978758017530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8049999999999998 " " y[1] (analytic) = -1.916956945865856 " " y[1] (numeric) = -1.9169569458658482 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.0541135726268585000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8050000000000088 " " Order of pole = 2.84217094304040100000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8039999999999998 " " y[1] (analytic) = -1.9241186705269733 " " y[1] (numeric) = -1.9241186705269655 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.0390238353893410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8029999999999998 " " y[1] (analytic) = -1.931316114466921 " " y[1] (numeric) = -1.9313161144669133 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.02397158816291960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8030000000000013 " " Order of pole = 4.61852778244065100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8019999999999998 " " y[1] (analytic) = -1.938549500652137 " " y[1] (numeric) = -1.9385495006521292 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.00895678431822700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8020000000000032 " " Order of pole = 1.06581410364015030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8009999999999998 " " y[1] (analytic) = -1.9458190537213043 " " y[1] (numeric) = -1.9458190537212963 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.1080930737180640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.8010000000000025 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7999999999999998 " " y[1] (analytic) = -1.9531250000000013 " " y[1] (numeric) = -1.9531249999999933 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.0927261579781743000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7989999999999998 " " y[1] (analytic) = -1.9604675675154999 " " y[1] (numeric) = -1.960467567515492 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.0773976115460160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7990000000000007 " " Order of pole = 2.84217094304040100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7979999999999998 " " y[1] (analytic) = -1.9678469860117107 " " y[1] (numeric) = -1.9678469860117025 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 4.1749437027505080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.798 " " Order of pole = 7.105427357601002000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7969999999999998 " " y[1] (analytic) = -1.9752634869642787 " " y[1] (numeric) = -1.9752634869642705 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 4.1592680857238630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7970000000000024 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7959999999999998 " " y[1] (analytic) = -1.982717303595832 " " y[1] (numeric) = -1.9827173035958239 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 4.1436317559373460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7949999999999998 " " y[1] (analytic) = -1.9902086708913838 " " y[1] (numeric) = -1.990208670891375 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.35117167296716570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7950000000000002 " " Order of pole = 1.065814103640150300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7939999999999998 " " y[1] (analytic) = -1.997737825613887 " " y[1] (numeric) = -1.9977378256138782 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.3347728020393067000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7940000000000058 " " Order of pole = 1.91846538655227050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7929999999999998 " " y[1] (analytic) = -2.0053050063199507 " " y[1] (numeric) = -2.0053050063199422 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.2076865915952030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7930000000000038 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7919999999999998 " " y[1] (analytic) = -2.0129104533757136 " " y[1] (numeric) = -2.0129104533757047 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.4124089981778490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7909999999999998 " " y[1] (analytic) = -2.0205544089728744 " " y[1] (numeric) = -2.020554408972866 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.17593060086929040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7899999999999998 " " y[1] (analytic) = -2.0282371171448927 " " y[1] (numeric) = -2.028237117144884 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.37906599870529700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7900000000000088 " " Order of pole = 2.9132252166164110000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7889999999999998 " " y[1] (analytic) = -2.035958823783345 " " y[1] (numeric) = -2.035958823783336 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.3624576751000150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.34645931818391934 " " Order of pole = 4.9613646524448995000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7879999999999998 " " y[1] (analytic) = -2.0437197766544566 " " y[1] (numeric) = -2.0437197766544473 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.5631859677541764000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7880000000000063 " " Order of pole = 2.06057393370429050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7869999999999998 " " y[1] (analytic) = -2.051520225415792 " " y[1] (numeric) = -2.051520225415783 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.329367113697910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7870000000000018 " " Order of pole = 6.39488462184090200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7859999999999998 " " y[1] (analytic) = -2.0593604216331247 " " y[1] (numeric) = -2.0593604216331154 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.5285290077856610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7849999999999998 " " y[1] (analytic) = -2.0672406187974723 " " y[1] (numeric) = -2.0672406187974626 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.7260887425792890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7850000000000001 " " Order of pole = 1.065814103640150300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7839999999999998 " " y[1] (analytic) = -2.075161072342308 " " y[1] (numeric) = -2.0751610723422984 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.7080502554308584000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7829999999999998 " " y[1] (analytic) = -2.0831220396609496 " " y[1] (numeric) = -2.08312203966094 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.6900577261865770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.783000000000009 " " Order of pole = 2.9842794901924210000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7819999999999998 " " y[1] (analytic) = -2.0911237801241245 " " y[1] (numeric) = -2.0911237801241143 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.884479782418789700000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7820000000000036 " " Order of pole = 1.20792265079217030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7809999999999998 " " y[1] (analytic) = -2.099166555097715 " " y[1] (numeric) = -2.099166555097705 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.8657653208827834000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.5682823935983922 " " Order of pole = 2.47464271296848900000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7799999999999998 " " y[1] (analytic) = -2.107250627960689 " " y[1] (numeric) = -2.1072506279606786 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.8470987223936357000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7789999999999998 " " y[1] (analytic) = -2.115376264123208 " " y[1] (numeric) = -2.115376264123198 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.8284799256670360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7790000000000038 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7779999999999998 " " y[1] (analytic) = -2.123543731044932 " " y[1] (numeric) = -2.1235437310449212 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.0190353420020950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7780000000000091 " " Order of pole = 3.0908609005564360000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7769999999999998 " " y[1] (analytic) = -2.1317532982535012 " " y[1] (numeric) = -2.1317532982534906 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 4.9997066007279006000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7770000000000001 " " Order of pole = 1.065814103640150300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7759999999999998 " " y[1] (analytic) = -2.1400052373632192 " " y[1] (numeric) = -2.1400052373632086 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 4.9804275477072190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7760000000000028 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7749999999999998 " " y[1] (analytic) = -2.1482998220939225 " " y[1] (numeric) = -2.148299822093912 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 4.9611981189912024000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7750000000000047 " " Order of pole = 1.59872115546022540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7739999999999998 " " y[1] (analytic) = -2.1566373282900475 " " y[1] (numeric) = -2.1566373282900364 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.1479356777406290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7740000000000056 " " Order of pole = 1.91846538655227050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7729999999999998 " " y[1] (analytic) = -2.165018033939894 " " y[1] (numeric) = -2.165018033939883 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.1280082069560210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7730000000000021 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7719999999999998 " " y[1] (analytic) = -2.1734422191950924 " " y[1] (numeric) = -2.173442219195081 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.3124575174479060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7720000000000015 " " Order of pole = 5.329070518200751000000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7709999999999998 " " y[1] (analytic) = -2.181910166390267 " " y[1] (numeric) = -2.1819101663902556 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.2918399822132720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7710000000000028 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7699999999999998 " " y[1] (analytic) = -2.190422160062911 " " y[1] (numeric) = -2.190422160062899 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.4740172394929190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7700000000000039 " " Order of pole = 1.35003119794419040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7689999999999998 " " y[1] (analytic) = -2.1989784869734588 " " y[1] (numeric) = -2.1989784869734468 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.4527175854524000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7690000000000008 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7679999999999998 " " y[1] (analytic) = -2.2075794361255805 " " y[1] (numeric) = -2.2075794361255685 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.4314732551574660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7680000000000028 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7669999999999998 " " y[1] (analytic) = -2.2162252987866764 " " y[1] (numeric) = -2.2162252987866644 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.4102841766656650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7670000000000008 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7659999999999998 " " y[1] (analytic) = -2.2249163685085924 " " y[1] (numeric) = -2.2249163685085804 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.3891502780345450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7660000000000124 " " Order of pole = 4.1922021409845910000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7649999999999998 " " y[1] (analytic) = -2.233652941148552 " " y[1] (numeric) = -2.2336529411485397 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.5668889498150460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7639999999999998 " " y[1] (analytic) = -2.2424353148903036 " " y[1] (numeric) = -2.242435314890291 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.5450865374950760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7629999999999998 " " y[1] (analytic) = -2.2512637902654955 " " y[1] (numeric) = -2.251263790265483 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.5233411249133670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7630000000000022 " " Order of pole = 8.52651282912120200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7619999999999998 " " y[1] (analytic) = -2.2601386701752717 " " y[1] (numeric) = -2.2601386701752593 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.5016526374629350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.762000000000004 " " Order of pole = 1.42108547152020040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7609999999999998 " " y[1] (analytic) = -2.269060259912096 " " y[1] (numeric) = -2.2690602599120835 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.480021000536790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7610000000000058 " " Order of pole = 1.95399252334027550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7599999999999998 " " y[1] (analytic) = -2.2780288671818067 " " y[1] (numeric) = -2.2780288671817943 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.4584461395279460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7600000000000057 " " Order of pole = 1.98951966012828050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7589999999999998 " " y[1] (analytic) = -2.2870448021259033 " " y[1] (numeric) = -2.287044802125891 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.4369279798294160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7590000000000058 " " Order of pole = 1.98951966012828050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7579999999999998 " " y[1] (analytic) = -2.296108377344069 " " y[1] (numeric) = -2.2961083773440567 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.4154664468342120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.6236251256069161 " " Order of pole = 1.00754959930782200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7569999999999998 " " y[1] (analytic) = -2.3052199079169324 " " y[1] (numeric) = -2.3052199079169196 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 5.5867065182901810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7570000000000013 " " Order of pole = 5.329070518200751000000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7559999999999998 " " y[1] (analytic) = -2.3143797114290683 " " y[1] (numeric) = -2.3143797114290554 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 5.5645955683303270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.7158325710956847 " " Order of pole = 6.226130722097878000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7549999999999998 " " y[1] (analytic) = -2.3235881079922445 " " y[1] (numeric) = -2.323588107992232 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.3514208619986870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7539999999999998 " " y[1] (analytic) = -2.3328454202689164 " " y[1] (numeric) = -2.3328454202689035 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 5.5205488429521620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7540000000000061 " " Order of pole = 2.09610107049229550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7529999999999998 " " y[1] (analytic) = -2.342151973495967 " " y[1] (numeric) = -2.3421519734959535 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 5.6882202548180720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7530000000000007 " " Order of pole = 2.486899575160350700000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7519999999999998 " " y[1] (analytic) = -2.3515080955087044 " " y[1] (numeric) = -2.351508095508691 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 5.6655881053302380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7520000000000029 " " Order of pole = 1.03028696685214530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7509999999999998 " " y[1] (analytic) = -2.3609141167651146 " " y[1] (numeric) = -2.3609141167651018 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 5.4549155321659230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7510000000000028 " " Order of pole = 9.94759830064140300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7499999999999998 " " y[1] (analytic) = -2.3703703703703725 " " y[1] (numeric) = -2.370370370370359 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 5.620504062164849000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7489999999999998 " " y[1] (analytic) = -2.3798771921016115 " " y[1] (numeric) = -2.3798771921015978 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 5.7846537422356850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7490000000000027 " " Order of pole = 9.94759830064140300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7479999999999998 " " y[1] (analytic) = -2.3894349204329663 " " y[1] (numeric) = -2.3894349204329526 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 5.7615151547452060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7480000000000009 " " Order of pole = 3.55271367880050100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7469999999999998 " " y[1] (analytic) = -2.399043896560878 " " y[1] (numeric) = -2.3990438965608636 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 5.9235492670950340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.2971440269220865 " " Order of pole = 1.123190429552778400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7459999999999998 " " y[1] (analytic) = -2.4087044644296713 " " y[1] (numeric) = -2.4087044644296567 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.0841602369521230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.5959966442859942 " " Order of pole = 5.0892623448817180000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7449999999999998 " " y[1] (analytic) = -2.4184169707574115 " " y[1] (numeric) = -2.418416970757397 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.05972588774150100000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7439999999999998 " " y[1] (analytic) = -2.4281817650620328 " " y[1] (numeric) = -2.4281817650620185 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 5.8524674386717330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7440000000000045 " " Order of pole = 1.59872115546022540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7429999999999998 " " y[1] (analytic) = -2.437999199687757 " " y[1] (numeric) = -2.4379991996877424 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.0110536241886280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7419999999999998 " " y[1] (analytic) = -2.447869629831786 " " y[1] (numeric) = -2.4478696298317715 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 5.986815533987050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7420000000000023 " " Order of pole = 9.23705556488130200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7409999999999998 " " y[1] (analytic) = -2.457793413571295 " " y[1] (numeric) = -2.4577934135712804 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 5.9626426875958260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7399999999999998 " " y[1] (analytic) = -2.46777091189071 " " y[1] (numeric) = -2.4677709118906948 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 6.1184906030575750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.74 " " Order of pole = 1.065814103640150300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7389999999999998 " " y[1] (analytic) = -2.477802488709282 " " y[1] (numeric) = -2.477802488709267 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 6.0937194161780840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7390000000000035 " " Order of pole = 1.27897692436818030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7379999999999998 " " y[1] (analytic) = -2.4878885109089657 " " y[1] (numeric) = -2.48788851090895 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.2475156248353810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7369999999999998 " " y[1] (analytic) = -2.498029348362593 " " y[1] (numeric) = -2.4980293483625773 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.2221536167861240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7370000000000033 " " Order of pole = 1.24344978758017530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7359999999999998 " " y[1] (analytic) = -2.5082253739623597 " " y[1] (numeric) = -2.508225373962344 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.1968603404238750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7360000000000043 " " Order of pole = 1.52766688188421540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7349999999999998 " " y[1] (analytic) = -2.5184769636486206 " " y[1] (numeric) = -2.518476963648605 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.1716357024899030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7350000000000074 " " Order of pole = 2.66453525910037570000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7339999999999998 " " y[1] (analytic) = -2.5287844964389983 " " y[1] (numeric) = -2.5287844964389827 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.1464796097254690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.508423211073131 " " Order of pole = 1.044853092935227300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7329999999999998 " " y[1] (analytic) = -2.53914835445781 " " y[1] (numeric) = -2.539148354457794 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 6.296288882268180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7330000000000026 " " Order of pole = 1.03028696685214530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7319999999999998 " " y[1] (analytic) = -2.549568922965818 " " y[1] (numeric) = -2.5495689229658014 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 6.4447368401943030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7320000000000103 " " Order of pole = 3.6592950891645160000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7309999999999998 " " y[1] (analytic) = -2.560046590390303 " " y[1] (numeric) = -2.5600465903902863 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 6.5918292415645330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.7310000000000074 " " Order of pole = 2.70006239588838070000000000000E-13 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;" Iterations = 270 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 0 Minutes 19 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 0 Minutes 19 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 3 Minutes 20 Seconds "Time to Timeout " Unknown Percent Done = 90.3333333333334 "%" (%o57) true (%o57) diffeq.max