(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : arcsin(array_tmp2 ), array_tmp3_a1 : cos(array_tmp3 ), 1 1 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 array_tmp3 : --------------, array_tmp3_a1 : - array_tmp2 array_tmp3 , 2 array_tmp3_a1 2 1 2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary array_y_higher : temporary, temporary : ---------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 - att(2, array_tmp3_a1, array_tmp3, 2) array_tmp3 : --------------------------------------, 3 array_tmp3_a1 1 array_tmp3 array_tmp2 1 2 2 array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 , 3 2 3 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 - att(3, array_tmp3_a1, array_tmp3, 2) array_tmp3 : --------------------------------------, 4 array_tmp3_a1 1 array_tmp3 array_tmp2 2 3 2 array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 , 4 3 4 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 - att(4, array_tmp3_a1, array_tmp3, 2) array_tmp3 : --------------------------------------, 5 array_tmp3_a1 1 array_tmp3 array_tmp2 3 4 2 array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 , 5 4 5 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk - att(kkk - 1, array_tmp3_a1, array_tmp3, 2) --------------------------------------------, array_tmp3_a1 1 array_tmp3 array_tmp2 (kkk - 2) kkk - 1 2 array_tmp3_a1 : - --------------------------------------- kkk kkk - 1 - array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1, kkk 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : arcsin(array_tmp2 ), array_tmp3_a1 : cos(array_tmp3 ), 1 1 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 array_tmp3 : --------------, array_tmp3_a1 : - array_tmp2 array_tmp3 , 2 array_tmp3_a1 2 1 2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary array_y_higher : temporary, temporary : ---------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 - att(2, array_tmp3_a1, array_tmp3, 2) array_tmp3 : --------------------------------------, 3 array_tmp3_a1 1 array_tmp3 array_tmp2 1 2 2 array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 , 3 2 3 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 - att(3, array_tmp3_a1, array_tmp3, 2) array_tmp3 : --------------------------------------, 4 array_tmp3_a1 1 array_tmp3 array_tmp2 2 3 2 array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 , 4 3 4 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 - att(4, array_tmp3_a1, array_tmp3, 2) array_tmp3 : --------------------------------------, 5 array_tmp3_a1 1 array_tmp3 array_tmp2 3 4 2 array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 , 5 4 5 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk - att(kkk - 1, array_tmp3_a1, array_tmp3, 2) --------------------------------------------, array_tmp3_a1 1 array_tmp3 array_tmp2 (kkk - 2) kkk - 1 2 array_tmp3_a1 : - --------------------------------------- kkk kkk - 1 - array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1, kkk 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) omniabs(x) := abs(x) (%o49) omniabs(x) := abs(x) y (%i50) expt(x, y) := x y (%o50) expt(x, y) := x (%i51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i52) exact_soln_y(x) := block(10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2)) + 10.0 (0.2 + 0.1 x) arcsin(0.2 + 0.1 x)) (%o52) exact_soln_y(x) := block(10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2)) + 10.0 (0.2 + 0.1 x) arcsin(0.2 + 0.1 x)) (%i53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/lin_arcsinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-0.8,"), omniout_str(ALWAYS, "x_end:0.8,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (10.\ 0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 -"), omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "), 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, max_terms : 30, Digits : 32, 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_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, 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 : - 0.8, x_end : 0.8, 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_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-14T22:58:28-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_arcsin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "lin_arcsin diffeq.max"), logitem_str(html_log_file, "lin_arcsin maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/lin_arcsinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-0.8,"), omniout_str(ALWAYS, "x_end:0.8,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (10.\ 0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 -"), omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "), 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, max_terms : 30, Digits : 32, 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_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, 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 : - 0.8, x_end : 0.8, 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_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-14T22:58:28-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_arcsin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "lin_arcsin diffeq.max"), logitem_str(html_log_file, "lin_arcsin maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i54) main() "##############ECHO OF PROBLEM#################" "##############temp/lin_arcsinpostode.ode#################" "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "max_terms:30," "Digits:32," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-0.8," "x_end:0.8," "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," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (10.0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 -" "expt((0.1 * x + 0.2) , 2 ))) " "));" "" "/* 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 = 1.6 "" estimated_steps = 1600. "" step_error = 6.2500000000000000E-14 "" est_needed_step_err = 6.2500000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.927332782487510000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" max_value3 = 1.927332782487510000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" value3 = 1.927332782487510000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -0.8 " " y[1] (analytic) = 10.072086775666431 " " y[1] (numeric) = 10.072086775666431 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.255215200502686 " " Order of pole = 10.623650523505582 " " x[1] = -0.799 " " y[1] (analytic) = 10.072207115912965 " " y[1] (numeric) = 10.072207115912965 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.229841430327255 " " Order of pole = 10.552869778015953 " " x[1] = -0.798 " " y[1] (analytic) = 10.072327556888597 " " y[1] (numeric) = 10.072327556888597 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.204684132210465 " " Order of pole = 10.48271186315457 " " x[1] = -0.797 " " y[1] (analytic) = 10.072448098594556 " " y[1] (numeric) = 10.072448098594554 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763580037357662400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.17974074807891 " " Order of pole = 10.41316944041452 " " x[1] = -0.796 " " y[1] (analytic) = 10.072568741032068 " " y[1] (numeric) = 10.072568741032066 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763558914384971000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.155008759371183 " " Order of pole = 10.344235284597225 " " x[1] = -0.795 " " y[1] (analytic) = 10.072689484202364 " " y[1] (numeric) = 10.072689484202364 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.130485686279824 " " Order of pole = 10.275902281638857 " " x[1] = -0.794 " " y[1] (analytic) = 10.072810328106677 " " y[1] (numeric) = 10.072810328106677 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.106169087009073 " " Order of pole = 10.208163426481612 " " x[1] = -0.793 " " y[1] (analytic) = 10.072931272746237 " " y[1] (numeric) = 10.072931272746237 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.082056557046553 " " Order of pole = 10.141011820985021 " " x[1] = -0.792 " " y[1] (analytic) = 10.07305231812228 " " y[1] (numeric) = 10.07305231812228 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.058145728452415 " " Order of pole = 10.07444067188709 " " x[1] = -0.791 " " y[1] (analytic) = 10.073173464236037 " " y[1] (numeric) = 10.073173464236037 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.034434269172031 " " Order of pole = 10.008443288833796 " " x[1] = -0.79 " " y[1] (analytic) = 10.073294711088748 " " y[1] (numeric) = 10.073294711088746 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763431816846205700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 12.010919882350448 " " Order of pole = 9.94301308241242 " " x[1] = -0.789 " " y[1] (analytic) = 10.073416058681646 " " y[1] (numeric) = 10.073416058681643 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52682114796463660000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.98760030567517 " " Order of pole = 9.87814356226717 " " x[1] = -0.788 " " y[1] (analytic) = 10.073537507015969 " " y[1] (numeric) = 10.073537507015965 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.526778627990538300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.964473310728655 " " Order of pole = 9.81382833524227 " " x[1] = -0.787 " " y[1] (analytic) = 10.073659056092955 " " y[1] (numeric) = 10.073659056092952 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.526736073772197600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.94153670235269 " " Order of pole = 9.750061103558828 " " x[1] = -0.786 " " y[1] (analytic) = 10.073780705913848 " " y[1] (numeric) = 10.073780705913842 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.290040227967542000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.918788318030025 " " Order of pole = 9.686835663041599 " " x[1] = -0.785 " " y[1] (analytic) = 10.073902456479882 " " y[1] (numeric) = 10.073902456479878 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52665086261111540000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.896226027282506 " " Order of pole = 9.624145901393156 " " x[1] = -0.784 " " y[1] (analytic) = 10.074024307792303 " " y[1] (numeric) = 10.074024307792302 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763304102836272300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.873847731075331 " " Order of pole = 9.561985796485104 " " x[1] = -0.783 " " y[1] (analytic) = 10.074146259852357 " " y[1] (numeric) = 10.074146259852354 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52656551449806730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.851651361241318 " " Order of pole = 9.500349414707067 " " x[1] = -0.782 " " y[1] (analytic) = 10.074268312661282 " " y[1] (numeric) = 10.07426831266128 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763261394544887700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.829634879913026 " " Order of pole = 9.439230909338214 " " x[1] = -0.781 " " y[1] (analytic) = 10.074390466220326 " " y[1] (numeric) = 10.074390466220324 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763240014724878600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.807796278972214 " " Order of pole = 9.378624518968408 " " x[1] = -0.78 " " y[1] (analytic) = 10.074512720530736 " " y[1] (numeric) = 10.074512720530732 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.526437235580104400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.78613357950511 " " Order of pole = 9.318524565935874 " " x[1] = -0.779 " " y[1] (analytic) = 10.074635075593758 " " y[1] (numeric) = 10.074635075593752 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28959161122436800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.764644831276037 " " Order of pole = 9.258925454817891 " " x[1] = -0.778 " " y[1] (analytic) = 10.074757531410636 " " y[1] (numeric) = 10.074757531410633 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.526351545160274500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.743328112206433 " " Order of pole = 9.199821670936402 " " x[1] = -0.777 " " y[1] (analytic) = 10.074880087982628 " " y[1] (numeric) = 10.074880087982624 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52630864861428700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.722181527869843 " " Order of pole = 9.14120777891003 " " x[1] = -0.776 " " y[1] (analytic) = 10.075002745310979 " " y[1] (numeric) = 10.075002745310975 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52626571784704900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.701203210996132 " " Order of pole = 9.083078421232202 " " x[1] = -0.775 " " y[1] (analytic) = 10.07512550339694 " " y[1] (numeric) = 10.075125503396938 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763111376430330500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.680391320986601 " " Order of pole = 9.025428316880621 " " x[1] = -0.774 " " y[1] (analytic) = 10.075248362241767 " " y[1] (numeric) = 10.075248362241766 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.763089876828611300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.659744043435387 " " Order of pole = 8.968252259944435 " " x[1] = -0.773 " " y[1] (analytic) = 10.075371321846712 " " y[1] (numeric) = 10.07537132184671 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76306836011941900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.63925958967038 " " Order of pole = 8.911545118308183 " " x[1] = -0.772 " " y[1] (analytic) = 10.07549438221303 " " y[1] (numeric) = 10.075494382213027 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52609365260761100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.618936196293285 " " Order of pole = 8.855301832332373 " " x[1] = -0.771 " " y[1] (analytic) = 10.075617543341975 " " y[1] (numeric) = 10.075617543341972 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.526050550765649000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.598772124738593 " " Order of pole = 8.799517413588987 " " x[1] = -0.77 " " y[1] (analytic) = 10.075740805234805 " " y[1] (numeric) = 10.075740805234801 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.5260074147150594000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.578765660833488 " " Order of pole = 8.744186943599125 " " x[1] = -0.769 " " y[1] (analytic) = 10.075864167892778 " " y[1] (numeric) = 10.075864167892775 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52596424445795200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.558915114376045 " " Order of pole = 8.689305572623695 " " x[1] = -0.768 " " y[1] (analytic) = 10.075987631317151 " " y[1] (numeric) = 10.07598763131715 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.762960519998218500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.539218818709918 " " Order of pole = 8.634868518443156 " " x[1] = -0.767 " " y[1] (analytic) = 10.07611119550919 " " y[1] (numeric) = 10.076111195509187 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52587780133262700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.51967513032443 " " Order of pole = 8.58087106521139 " " x[1] = -0.766 " " y[1] (analytic) = 10.07623486047015 " " y[1] (numeric) = 10.076234860470146 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.525834528468636500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.50028242844767 " " Order of pole = 8.527308562288262 " " x[1] = -0.765 " " y[1] (analytic) = 10.076358626201296 " " y[1] (numeric) = 10.076358626201293 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.525791221406582000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.481039114656962 " " Order of pole = 8.474176423122763 " " x[1] = -0.764 " " y[1] (analytic) = 10.07648249270389 " " y[1] (numeric) = 10.076482492703887 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52574788014857900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.4619436124915 " " Order of pole = 8.42147012414189 " " x[1] = -0.763 " " y[1] (analytic) = 10.076606459979196 " " y[1] (numeric) = 10.076606459979194 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.762852252348374200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.442994367080876 " " Order of pole = 8.369185203685696 " " x[1] = -0.762 " " y[1] (analytic) = 10.076730528028483 " " y[1] (numeric) = 10.07673052802848 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.525661095053209700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.424189844773146 " " Order of pole = 8.317317260940456 " " x[1] = -0.761 " " y[1] (analytic) = 10.076854696853013 " " y[1] (numeric) = 10.07685469685301 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.525617651220085400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.40552853277404 " " Order of pole = 8.265861954903968 " " x[1] = -0.76 " " y[1] (analytic) = 10.076978966454057 " " y[1] (numeric) = 10.076978966454053 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.525574173199500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.387008938795091 " " Order of pole = 8.214815003376607 " " x[1] = -0.759 " " y[1] (analytic) = 10.07710333683288 " " y[1] (numeric) = 10.077103336832877 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52553066099357700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.368629590704948 " " Order of pole = 8.16417218196127 " " x[1] = -0.758 " " y[1] (analytic) = 10.077227807990756 " " y[1] (numeric) = 10.077227807990752 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52548711460444530000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.350389036191547 " " Order of pole = 8.113929323094602 " " x[1] = -0.757 " " y[1] (analytic) = 10.077352379928952 " " y[1] (numeric) = 10.077352379928948 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52544353403423270000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.332285842428726 " " Order of pole = 8.064082315090907 " " x[1] = -0.756 " " y[1] (analytic) = 10.07747705264874 " " y[1] (numeric) = 10.077477052648737 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52539991928506940000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.314318595750024 " " Order of pole = 8.014627101206692 " " x[1] = -0.755 " " y[1] (analytic) = 10.077601826151396 " " y[1] (numeric) = 10.077601826151392 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52535627035908700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.296485901330007 " " Order of pole = 7.965559678726777 " " x[1] = -0.754 " " y[1] (analytic) = 10.077726700438193 " " y[1] (numeric) = 10.077726700438188 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28796888088762700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.278786382871926 " " Order of pole = 7.916876098068705 " " x[1] = -0.753 " " y[1] (analytic) = 10.077851675510404 " " y[1] (numeric) = 10.077851675510399 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28790330497779900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.261218682297633 " " Order of pole = 7.868572461893187 " " x[1] = -0.752 " " y[1] (analytic) = 10.077976751369308 " " y[1] (numeric) = 10.0779767513693 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.0504502370831300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.243781459450675 " " Order of pole = 7.820644924252967 " " x[1] = -0.751 " " y[1] (analytic) = 10.078101928016178 " " y[1] (numeric) = 10.078101928016173 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28777199939448500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.226473391799109 " " Order of pole = 7.773089689740367 " " x[1] = -0.75 " " y[1] (analytic) = 10.078227205452297 " " y[1] (numeric) = 10.078227205452292 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28770626972741500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.209293174148794 " " Order of pole = 7.725903012665313 " " x[1] = -0.749 " " y[1] (analytic) = 10.078352583678942 " " y[1] (numeric) = 10.078352583678937 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.287640488814352000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.19223951835686 " " Order of pole = 7.679081196233312 " " x[1] = -0.748 " " y[1] (analytic) = 10.078478062697393 " " y[1] (numeric) = 10.078478062697387 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28757465665851200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.175311153056425 " " Order of pole = 7.6326205917562575 " " x[1] = -0.747 " " y[1] (analytic) = 10.07860364250893 " " y[1] (numeric) = 10.078603642508927 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52500584884207400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.158506823383174 " " Order of pole = 7.586517597868216 " " x[1] = -0.746 " " y[1] (analytic) = 10.07872932311484 " " y[1] (numeric) = 10.078729323114837 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.524961892420910300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.14182529070896 " " Order of pole = 7.540768659761532 " " x[1] = -0.745 " " y[1] (analytic) = 10.078855104516405 " " y[1] (numeric) = 10.078855104516402 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.524917901844333000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.125265332380508 " " Order of pole = 7.495370268437554 " " x[1] = -0.744 " " y[1] (analytic) = 10.078980986714908 " " y[1] (numeric) = 10.078980986714905 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.5248738771144900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.108825741459613 " " Order of pole = 7.450318959961322 " " x[1] = -0.743 " " y[1] (analytic) = 10.079106969711637 " " y[1] (numeric) = 10.079106969711633 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52482981823353300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.092505326475653 " " Order of pole = 7.405611314752270 " " x[1] = -0.742 " " y[1] (analytic) = 10.079233053507878 " " y[1] (numeric) = 10.079233053507872 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28717858780542200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.07630291117468 " " Order of pole = 7.361243956864236 " " x[1] = -0.741 " " y[1] (analytic) = 10.079359238104916 " " y[1] (numeric) = 10.079359238104912 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52474159802688900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.06021733428001 " " Order of pole = 7.317213553299283 " " x[1] = -0.74 " " y[1] (analytic) = 10.079485523504044 " " y[1] (numeric) = 10.07948552350404 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52469743670551060000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.044247449251575 " " Order of pole = 7.273516813317265 " " x[1] = -0.739 " " y[1] (analytic) = 10.07961190970655 " " y[1] (numeric) = 10.079611909706546 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52465324124163800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.028392124056621 " " Order of pole = 7.23015048777863 " " x[1] = -0.738 " " y[1] (analytic) = 10.079738396713728 " " y[1] (numeric) = 10.079738396713722 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28691351745614300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 11.012650240937084 " " Order of pole = 7.18711136847687 " " x[1] = -0.737 " " y[1] (analytic) = 10.079864984526866 " " y[1] (numeric) = 10.07986498452686 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28684712184256500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.99702069618751 " " Order of pole = 7.1443962875020475 " " x[1] = -0.736 " " y[1] (analytic) = 10.07999167314726 " " y[1] (numeric) = 10.079991673147255 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.286780675024967000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.981502399933678 " " Order of pole = 7.102002116605690 " " x[1] = -0.735 " " y[1] (analytic) = 10.080118462576204 " " y[1] (numeric) = 10.080118462576198 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.286714177006593000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.966094275918568 " " Order of pole = 7.059925766587291 " " x[1] = -0.734 " " y[1] (analytic) = 10.080245352814993 " " y[1] (numeric) = 10.080245352814988 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.2866476277906900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.950795261287265 " " Order of pole = 7.018164186677119 " " x[1] = -0.733 " " y[1] (analytic) = 10.080372343864923 " " y[1] (numeric) = 10.080372343864918 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28658102738051100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.935604306380434 " " Order of pole = 6.976714363944204 " " x[1] = -0.732 " " y[1] (analytic) = 10.080499435727292 " " y[1] (numeric) = 10.080499435727287 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28651437577930600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.920520374532298 " " Order of pole = 6.9355733227171115 " " x[1] = -0.731 " " y[1] (analytic) = 10.080626628403401 " " y[1] (numeric) = 10.080626628403394 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.0485968973204400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.905542441865204 " " Order of pole = 6.894738123994400 " " x[1] = -0.73 " " y[1] (analytic) = 10.080753921894546 " " y[1] (numeric) = 10.080753921894539 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04850789202245500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.890669497098218 " " Order of pole = 6.854205864896215 " " x[1] = -0.729 " " y[1] (analytic) = 10.080881316202031 " " y[1] (numeric) = 10.080881316202023 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 8.81052352310349500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.875900541349644 " " Order of pole = 6.8139736780975895 " " x[1] = -0.728 " " y[1] (analytic) = 10.081008811327154 " " y[1] (numeric) = 10.081008811327147 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04832967670581800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.861234587951929 " " Order of pole = 6.7740387312980275 " " x[1] = -0.727 " " y[1] (analytic) = 10.081136407271222 " " y[1] (numeric) = 10.081136407271215 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04824046669586800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.846670662259715 " " Order of pole = 6.734398226670514 " " x[1] = -0.726 " " y[1] (analytic) = 10.081264104035537 " " y[1] (numeric) = 10.08126410403553 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04815118845730300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.83220780147459 " " Order of pole = 6.6950494003597 " " x[1] = -0.725 " " y[1] (analytic) = 10.081391901621405 " " y[1] (numeric) = 10.081391901621398 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04806184199448200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.817845054458852 " " Order of pole = 6.65598952194712 " " x[1] = -0.724 " " y[1] (analytic) = 10.08151980003013 " " y[1] (numeric) = 10.081519800030124 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.285979320483828000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.803581481563988 " " Order of pole = 6.617215893959823 " " x[1] = -0.723 " " y[1] (analytic) = 10.081647799263022 " " y[1] (numeric) = 10.081647799263017 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28591220831014500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.789416154455369 " " Order of pole = 6.578725851367388 " " x[1] = -0.722 " " y[1] (analytic) = 10.08177589932139 " " y[1] (numeric) = 10.081775899321384 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28584504497809100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.77534815594284 " " Order of pole = 6.540516761096178 " " x[1] = -0.721 " " y[1] (analytic) = 10.08190410020654 " " y[1] (numeric) = 10.081904100206534 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28577783049094800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.761376579816343 " " Order of pole = 6.502586021558152 " " x[1] = -0.72 " " y[1] (analytic) = 10.082032401919786 " " y[1] (numeric) = 10.08203240191978 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04761408646932200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.747500530678025 " " Order of pole = 6.464931062169036 " " x[1] = -0.719 " " y[1] (analytic) = 10.082160804462436 " " y[1] (numeric) = 10.08216080446243 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04752433075267800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.733719123784473 " " Order of pole = 6.427549342896214 " " x[1] = -0.718 " " y[1] (analytic) = 10.082289307835804 " " y[1] (numeric) = 10.082289307835799 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28557588013178400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.720031484888938 " " Order of pole = 6.390438353806282 " " x[1] = -0.717 " " y[1] (analytic) = 10.082417912041207 " " y[1] (numeric) = 10.082417912041201 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.285508461057106000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.706436750084388 " " Order of pole = 6.353595614614797 " " x[1] = -0.716 " " y[1] (analytic) = 10.082546617079954 " " y[1] (numeric) = 10.08254661707995 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52362732722917600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.692934065651096 " " Order of pole = 6.317018674249233 " " x[1] = -0.715 " " y[1] (analytic) = 10.082675422953365 " " y[1] (numeric) = 10.082675422953361 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52358231299670100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.679522587909025 " " Order of pole = 6.280705110425856 " " x[1] = -0.714 " " y[1] (analytic) = 10.082804329662757 " " y[1] (numeric) = 10.082804329662753 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52353726467617530000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.666201483069703 " " Order of pole = 6.244652529224865 " " x[1] = -0.713 " " y[1] (analytic) = 10.082933337209447 " " y[1] (numeric) = 10.082933337209443 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52349218226979800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.65296992709079 " " Order of pole = 6.2088585646733065 " " x[1] = -0.712 " " y[1] (analytic) = 10.083062445594752 " " y[1] (numeric) = 10.083062445594749 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52344706577976900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.63982710553556 " " Order of pole = 6.173320878342146 " " x[1] = -0.711 " " y[1] (analytic) = 10.083191654819997 " " y[1] (numeric) = 10.083191654819991 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28510287281243300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.626772213431607 " " Order of pole = 6.138037158940982 " " x[1] = -0.71 " " y[1] (analytic) = 10.083320964886498 " " y[1] (numeric) = 10.083320964886493 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28503509583634200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.61380445513684 " " Order of pole = 6.10300512193411 " " x[1] = -0.709 " " y[1] (analytic) = 10.08345037579558 " " y[1] (numeric) = 10.083450375795575 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28496726774468800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.600923044202357 " " Order of pole = 6.068222509146963 " " x[1] = -0.708 " " y[1] (analytic) = 10.083579887548568 " " y[1] (numeric) = 10.083579887548563 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.284899388540778000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.588127203239742 " " Order of pole = 6.033687088385620 " " x[1] = -0.707 " " y[1] (analytic) = 10.083709500146783 " " y[1] (numeric) = 10.083709500146778 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28483145822792500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.575416163794277 " " Order of pole = 5.999396653073510 " " x[1] = -0.706 " " y[1] (analytic) = 10.083839213591554 " " y[1] (numeric) = 10.083839213591547 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04635130241259200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.56278916621227 " " Order of pole = 5.965349021870452 " " x[1] = -0.705 " " y[1] (analytic) = 10.083969027884205 " " y[1] (numeric) = 10.083969027884198 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04626059238486800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.550245459519449 " " Order of pole = 5.931542038324444 " " x[1] = -0.704 " " y[1] (analytic) = 10.084098943026065 " " y[1] (numeric) = 10.084098943026058 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04616981422515200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.53778430129691 " " Order of pole = 5.897973570515731 " " x[1] = -0.703 " " y[1] (analytic) = 10.084228959018462 " " y[1] (numeric) = 10.084228959018455 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04607896793787200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.525404957557397 " " Order of pole = 5.864641510701930 " " x[1] = -0.702 " " y[1] (analytic) = 10.084359075862727 " " y[1] (numeric) = 10.08435907586272 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04598805352746300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.51310670262823 " " Order of pole = 5.831543774982425 " " x[1] = -0.701 " " y[1] (analytic) = 10.08448929356019 " " y[1] (numeric) = 10.084489293560184 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04589707099835600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.50088881903464 " " Order of pole = 5.798678302963985 " " x[1] = -0.7 " " y[1] (analytic) = 10.084619612112185 " " y[1] (numeric) = 10.084619612112178 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04580602035498900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.488750597380461 " " Order of pole = 5.766043057418141 " " x[1] = -0.699 " " y[1] (analytic) = 10.08475003152004 " " y[1] (numeric) = 10.084750031520034 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28428617620135400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.476691336240503 " " Order of pole = 5.733636023973215 " " x[1] = -0.698 " " y[1] (analytic) = 10.084880551785096 " " y[1] (numeric) = 10.084880551785089 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04562371474324700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.46471034204509 " " Order of pole = 5.701455210782804 " " x[1] = -0.697 " " y[1] (analytic) = 10.085011172908684 " " y[1] (numeric) = 10.085011172908677 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04553245978375900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.452806928970478 " " Order of pole = 5.669498648211473 " " x[1] = -0.696 " " y[1] (analytic) = 10.085141894892141 " " y[1] (numeric) = 10.085141894892136 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28408085254584800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.440980418834238 " " Order of pole = 5.637764388535164 " " x[1] = -0.695 " " y[1] (analytic) = 10.085272717736807 " " y[1] (numeric) = 10.0852727177368 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04534974557981100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.429230140985535 " " Order of pole = 5.606250505626193 " " x[1] = -0.694 " " y[1] (analytic) = 10.085403641444016 " " y[1] (numeric) = 10.085403641444008 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.0452582863442600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.417555432204802 " " Order of pole = 5.574955094665864 " " x[1] = -0.693 " " y[1] (analytic) = 10.08553466601511 " " y[1] (numeric) = 10.085534666015104 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04516675902560100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.405955636596369 " " Order of pole = 5.543876271836147 " " x[1] = -0.692 " " y[1] (analytic) = 10.085665791451431 " " y[1] (numeric) = 10.085665791451424 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04507516362829800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.394430105493726 " " Order of pole = 5.513012174048615 " " x[1] = -0.691 " " y[1] (analytic) = 10.085797017754318 " " y[1] (numeric) = 10.085797017754311 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.04498350015681800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.382978197355706 " " Order of pole = 5.482360958646279 " " x[1] = -0.69 " " y[1] (analytic) = 10.085928344925117 " " y[1] (numeric) = 10.08592834492511 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 7.0448917686156300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.371599277670905 " " Order of pole = 5.451920803129667 " " x[1] = -0.689 " " y[1] (analytic) = 10.086059772965168 " " y[1] (numeric) = 10.086059772965163 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28359997675690500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.360292718860938 " " Order of pole = 5.421689904879347 " " x[1] = -0.688 " " y[1] (analytic) = 10.08619130187582 " " y[1] (numeric) = 10.086191301875814 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.283531076006517000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.349057900187496 " " Order of pole = 5.391666480889533 " " x[1] = -0.6869999999999999 " " y[1] (analytic) = 10.086322931658415 " " y[1] (numeric) = 10.086322931658412 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52230808280927840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.337894207659359 " " Order of pole = 5.36184876750146 " " x[1] = -0.6859999999999999 " " y[1] (analytic) = 10.086454662314306 " " y[1] (numeric) = 10.086454662314301 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28339312138246700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.326801033939786 " " Order of pole = 5.33223502013767 " " x[1] = -0.6849999999999999 " " y[1] (analytic) = 10.086586493844836 " " y[1] (numeric) = 10.08658649384483 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.283324067515530000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.315777778257791 " " Order of pole = 5.302823513047652 " " x[1] = -0.6839999999999999 " " y[1] (analytic) = 10.086718426251355 " " y[1] (numeric) = 10.08671842625135 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28325496261647500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.304823846319751 " " Order of pole = 5.27361253905444 " " x[1] = -0.6829999999999999 " " y[1] (analytic) = 10.086850459535215 " " y[1] (numeric) = 10.08685045953521 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28318580668866700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.293938650222804 " " Order of pole = 5.244600409306305 " " x[1] = -0.6819999999999999 " " y[1] (analytic) = 10.086982593697767 " " y[1] (numeric) = 10.086982593697762 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28311659973547900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.283121608368647 " " Order of pole = 5.21578545302944 " " x[1] = -0.6809999999999999 " " y[1] (analytic) = 10.087114828740363 " " y[1] (numeric) = 10.087114828740358 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.283047341760283000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.272372145380059 " " Order of pole = 5.187166017288739 " " x[1] = -0.6799999999999999 " " y[1] (analytic) = 10.087247164664358 " " y[1] (numeric) = 10.087247164664353 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.28297803276645600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.261689692018379 " " Order of pole = 5.158740466751183 " " x[1] = -0.6789999999999999 " " y[1] (analytic) = 10.087379601471104 " " y[1] (numeric) = 10.0873796014711 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52193911517158230000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.251073685099774 " " Order of pole = 5.130507183445399 " " x[1] = -0.6779999999999999 " " y[1] (analytic) = 10.08751213916196 " " y[1] (numeric) = 10.087512139161957 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.521892841157611700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.240523567418942 " " Order of pole = 5.1024645665434605 " " x[1] = -0.6769999999999999 " " y[1] (analytic) = 10.087644777738282 " " y[1] (numeric) = 10.087644777738278 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52184653313797900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.230038787667073 " " Order of pole = 5.074611032125170 " " x[1] = -0.6759999999999999 " " y[1] (analytic) = 10.087777517201427 " " y[1] (numeric) = 10.087777517201424 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52180019111494270000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.219618800356063 " " Order of pole = 5.046945012961007 " " x[1] = -0.6749999999999999 " " y[1] (analytic) = 10.087910357552754 " " y[1] (numeric) = 10.087910357552751 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.521753815090760000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.209263065739835 " " Order of pole = 5.019464958286253 " " x[1] = -0.6739999999999999 " " y[1] (analytic) = 10.088043298793623 " " y[1] (numeric) = 10.088043298793622 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76085370253384600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.198971049742916 " " Order of pole = 4.992169333596635 " " x[1] = -0.6729999999999999 " " y[1] (analytic) = 10.088176340925399 " " y[1] (numeric) = 10.088176340925395 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52166096104799700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.188742223883457 " " Order of pole = 4.965056620427259 " " x[1] = -0.6719999999999999 " " y[1] (analytic) = 10.08830948394944 " " y[1] (numeric) = 10.088309483949436 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52161448303394100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.178576065200449 " " Order of pole = 4.9381253161438785 " " x[1] = -0.6709999999999999 " " y[1] (analytic) = 10.088442727867108 " " y[1] (numeric) = 10.088442727867106 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76078398551389400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.168472056182404 " " Order of pole = 4.911373933738464 " " x[1] = -0.6699999999999999 " " y[1] (analytic) = 10.088576072679771 " " y[1] (numeric) = 10.08857607267977 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76076071251590100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.158429684698689 " " Order of pole = 4.884801001632564 " " x[1] = -0.6689999999999999 " " y[1] (analytic) = 10.088709518388795 " " y[1] (numeric) = 10.088709518388793 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76073742252412600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.148448443926927 " " Order of pole = 4.858405063468712 " " x[1] = -0.6679999999999999 " " y[1] (analytic) = 10.088843064995544 " " y[1] (numeric) = 10.088843064995542 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760714115539703800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.138527832287572 " " Order of pole = 4.8321846779232445 " " x[1] = -0.6669999999999999 " " y[1] (analytic) = 10.088976712501388 " " y[1] (numeric) = 10.088976712501385 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.521381583127538600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.128667353373242 " " Order of pole = 4.806138418503252 " " x[1] = -0.6659999999999999 " " y[1] (analytic) = 10.089110460907692 " " y[1] (numeric) = 10.08911046090769 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760667450597459300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.118866515886005 " " Order of pole = 4.780264873367152 " " x[1] = -0.6649999999999999 " " y[1] (analytic) = 10.08924431021583 " " y[1] (numeric) = 10.089244310215829 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7606440926419100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.109124833568687 " " Order of pole = 4.7545626451274074 " " x[1] = -0.6639999999999999 " " y[1] (analytic) = 10.089378260427173 " " y[1] (numeric) = 10.089378260427171 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760620717698259400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.099441825143252 " " Order of pole = 4.729030350674062 " " x[1] = -0.6629999999999999 " " y[1] (analytic) = 10.089512311543091 " " y[1] (numeric) = 10.08951231154309 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760597325767645800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.089817014245913 " " Order of pole = 4.703666620988553 " " x[1] = -0.6619999999999999 " " y[1] (analytic) = 10.089646463564957 " " y[1] (numeric) = 10.089646463564955 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760573916851208800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.080249929365108 " " Order of pole = 4.678470100965917 " " x[1] = -0.6609999999999999 " " y[1] (analytic) = 10.089780716494145 " " y[1] (numeric) = 10.089780716494145 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.070740103781551 " " Order of pole = 4.653439449243027 " " x[1] = -0.6599999999999999 " " y[1] (analytic) = 10.089915070332035 " " y[1] (numeric) = 10.089915070332033 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760527048065425300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.061287075505081 " " Order of pole = 4.628573338017212 " " x[1] = -0.6589999999999999 " " y[1] (analytic) = 10.090049525079996 " " y[1] (numeric) = 10.090049525079994 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760503588198361300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.051890387216392 " " Order of pole = 4.603870452879338 " " x[1] = -0.6579999999999999 " " y[1] (analytic) = 10.090184080739409 " " y[1] (numeric) = 10.090184080739409 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.042549586210498 " " Order of pole = 4.579329492651980 " " x[1] = -0.6569999999999999 " " y[1] (analytic) = 10.090318737311653 " " y[1] (numeric) = 10.090318737311653 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.033264224334266 " " Order of pole = 4.554949169209700 " " x[1] = -0.6559999999999999 " " y[1] (analytic) = 10.090453494798108 " " y[1] (numeric) = 10.090453494798108 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.024033857934755 " " Order of pole = 4.530728207331588 " " x[1] = -0.6549999999999999 " " y[1] (analytic) = 10.090588353200154 " " y[1] (numeric) = 10.090588353200154 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.01485804779945 " " Order of pole = 4.506665344529427 " " x[1] = -0.6539999999999999 " " y[1] (analytic) = 10.090723312519174 " " y[1] (numeric) = 10.090723312519172 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76038603416703800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 10.00573635910203 " " Order of pole = 4.482759330892307 " " x[1] = -0.6529999999999999 " " y[1] (analytic) = 10.090858372756546 " " y[1] (numeric) = 10.090858372756546 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.996668361349307 " " Order of pole = 4.459008928934697 " " x[1] = -0.6519999999999999 " " y[1] (analytic) = 10.090993533913661 " " y[1] (numeric) = 10.09099353391366 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760338893717746400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.98765362832584 " " Order of pole = 4.435412913437332 " " x[1] = -0.6509999999999999 " " y[1] (analytic) = 10.091128795991898 " " y[1] (numeric) = 10.091128795991898 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.978691738042377 " " Order of pole = 4.411970071299624 " " x[1] = -0.6499999999999999 " " y[1] (analytic) = 10.091264158992647 " " y[1] (numeric) = 10.091264158992647 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.96978227268325 " " Order of pole = 4.388679201388658 " " x[1] = -0.6489999999999999 " " y[1] (analytic) = 10.091399622917294 " " y[1] (numeric) = 10.091399622917294 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.960924818555142 " " Order of pole = 4.3655391143924085 " " x[1] = -0.6479999999999999 " " y[1] (analytic) = 10.091535187767226 " " y[1] (numeric) = 10.091535187767226 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.952118966037006 " " Order of pole = 4.342548632676063 " " x[1] = -0.6469999999999999 " " y[1] (analytic) = 10.091670853543835 " " y[1] (numeric) = 10.091670853543835 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.943364309530203 " " Order of pole = 4.3197065901391625 " " x[1] = -0.6459999999999999 " " y[1] (analytic) = 10.09180662024851 " " y[1] (numeric) = 10.09180662024851 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.934660447410062 " " Order of pole = 4.29701183207672 " " x[1] = -0.6449999999999999 " " y[1] (analytic) = 10.091942487882644 " " y[1] (numeric) = 10.091942487882642 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76017336754853200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.926006981975855 " " Order of pole = 4.274463215035550 " " x[1] = -0.6439999999999999 " " y[1] (analytic) = 10.092078456447627 " " y[1] (numeric) = 10.092078456447625 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7601496530829800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.917403519404838 " " Order of pole = 4.252059606682778 " " x[1] = -0.6429999999999999 " " y[1] (analytic) = 10.092214525944854 " " y[1] (numeric) = 10.092214525944852 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760125921653398800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.908849669706287 " " Order of pole = 4.229799885674083 " " x[1] = -0.6419999999999999 " " y[1] (analytic) = 10.09235069637572 " " y[1] (numeric) = 10.092350696375718 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760102173260943700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.900345046671452 " " Order of pole = 4.207682941509773 " " x[1] = -0.6409999999999999 " " y[1] (analytic) = 10.092486967741623 " " y[1] (numeric) = 10.09248696774162 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.52015681581354100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.891889267832273 " " Order of pole = 4.185707674416928 " " x[1] = -0.6399999999999999 " " y[1] (analytic) = 10.092623340043954 " " y[1] (numeric) = 10.092623340043952 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76005462559203600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.883481954414838 " " Order of pole = 4.163872995215787 " " x[1] = -0.6389999999999999 " " y[1] (analytic) = 10.092759813284117 " " y[1] (numeric) = 10.092759813284115 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.760030826317896800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.875122731293585 " " Order of pole = 4.1421778251881705 " " x[1] = -0.6379999999999999 " " y[1] (analytic) = 10.092896387463508 " " y[1] (numeric) = 10.092896387463506 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76000701008551100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.866811226950851 " " Order of pole = 4.120621095961958 " " x[1] = -0.6369999999999999 " " y[1] (analytic) = 10.09303306258353 " " y[1] (numeric) = 10.093033062583528 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.759983176896037500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.8585470734314 " " Order of pole = 4.099201749380384 " " x[1] = -0.6359999999999999 " " y[1] (analytic) = 10.09316983864558 " " y[1] (numeric) = 10.09316983864558 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.850329906301399 " " Order of pole = 4.077918737384586 " " x[1] = -0.6349999999999999 " " y[1] (analytic) = 10.093306715651064 " " y[1] (numeric) = 10.093306715651064 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.84215936460583 " " Order of pole = 4.056771021891343 " " x[1] = -0.6339999999999999 " " y[1] (analytic) = 10.093443693601387 " " y[1] (numeric) = 10.093443693601385 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.759911575596691500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.834035090827866 " " Order of pole = 4.0357575746767544 " " x[1] = -0.6329999999999999 " " y[1] (analytic) = 10.093580772497951 " " y[1] (numeric) = 10.093580772497948 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.51977534918094100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.825956730847842 " " Order of pole = 4.0148773772584825 " " x[1] = -0.6319999999999999 " " y[1] (analytic) = 10.093717952342159 " " y[1] (numeric) = 10.093717952342157 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.759863756632968300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.817923933905274 " " Order of pole = 3.9941294207871323 " " x[1] = -0.6309999999999999 " " y[1] (analytic) = 10.093855233135422 " " y[1] (numeric) = 10.09385523313542 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.759839821725347500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "Real estimate of pole used" Radius of convergence = 9.809936352555656 " " Order of pole = 3.9735127059219373 " " x[1] = -0.6299999999999999 " " y[1] (analytic) = 10.093992614879147 " " y[1] (numeric) = 10.093992614879145 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75981586986877200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;" Iterations = 170 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 25 Minutes 17 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 25 Minutes 0 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 28 Minutes 2 Seconds "Time to Timeout " Unknown Percent Done = 10.687500000000009 "%" (%o54) true (%o54) diffeq.max