(%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) display_poles() := block([rad_given], if glob_type_given_pole = 4 then (rad_given : sqrt(expt(array_given_rad_poles , 2.0) 1, 2 + expt(array_x - array_given_rad_poles , 2.0)), 1 1, 1 omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_poles # glob_large_float then (omniout_float(ALWAYS, 1, 1 "Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4, 1, 1 " "), omniout_str(ALWAYS, "Order of pole (ratio test) Not computed")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if (array_real_poles > 0.0) and (array_real_poles # glob_large_float) 1, 1 1, 1 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles , 1, 1 4, " "), omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles , 1, 2 4, " ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if (array_complex_poles > 0.0) and (array_complex_poles # 1, 1 1, 1 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles , 4, " "), omniout_float(ALWAYS, 1, 1 "Order of pole (six term test) ", 4, array_complex_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO COMPLEX POLE (six term test) for Equation 1")) (%o3) display_poles() := block([rad_given], if glob_type_given_pole = 4 then (rad_given : sqrt(expt(array_given_rad_poles , 2.0) 1, 2 + expt(array_x - array_given_rad_poles , 2.0)), 1 1, 1 omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_poles # glob_large_float then (omniout_float(ALWAYS, 1, 1 "Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4, 1, 1 " "), omniout_str(ALWAYS, "Order of pole (ratio test) Not computed")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if (array_real_poles > 0.0) and (array_real_poles # glob_large_float) 1, 1 1, 1 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles , 1, 1 4, " "), omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles , 1, 2 4, " ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if (array_complex_poles > 0.0) and (array_complex_poles # 1, 1 1, 1 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles , 4, " "), omniout_float(ALWAYS, 1, 1 "Order of pole (six term test) ", 4, array_complex_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO COMPLEX POLE (six term test) for Equation 1")) (%i4) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o4) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i5) 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) (%o5) 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) (%i6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 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, ""), est_tmp : 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 est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%o6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 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, ""), est_tmp : 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 est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%i7) 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)) (%o7) 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)) (%i8) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 3 - 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, " ")))) (%o8) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 3 - 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, " ")))) (%i9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > 1, 1 glob_small_float 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 (%o9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > 1, 1 glob_small_float 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 (%i10) 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, "%")) (%o10) 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, "%")) (%i11) 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_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad], array_pole : glob_large_float, array_pole : glob_large_float, 1 2 tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float, tmp_ratio : glob_large_float, rad_c : glob_large_float, array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0, while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) = 1, n 0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0 1, 1 + n array_y_higher glob_h 1, n tmp_rad else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------, array_y_higher prev_tmp_rad 1, 1 + n if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5) then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0 then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0 then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n), if found_sing = 1 then (if rad_c < array_pole 1 then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms, 1 1, 1 m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0) 1, m or (omniabs(array_y_higher ) = 0.0) 1, m - 1 or (omniabs(array_y_higher ) = 0.0)) do m : m - 1, 1, m - 2 array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, glob_h if omniabs(hdrc) > 0.0 then (rcs : ------, hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) ord_no : -----------------------------------------------------, hdrc array_real_poles : rcs, array_real_poles : ord_no) 1, 1 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float)) 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : 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 0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) 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) = 0.0) rm4 rm3 rm2 or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0 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) # 0.0 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_poles : rad_c, 1, 1 array_complex_poles : ord_no), if array_pole glob_ratio_of_radius < 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_poles()) (%o11) 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_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad], array_pole : glob_large_float, array_pole : glob_large_float, 1 2 tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float, tmp_ratio : glob_large_float, rad_c : glob_large_float, array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0, while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) = 1, n 0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0 1, 1 + n array_y_higher glob_h 1, n tmp_rad else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------, array_y_higher prev_tmp_rad 1, 1 + n if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5) then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0 then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0 then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n), if found_sing = 1 then (if rad_c < array_pole 1 then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms, 1 1, 1 m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0) 1, m or (omniabs(array_y_higher ) = 0.0) 1, m - 1 or (omniabs(array_y_higher ) = 0.0)) do m : m - 1, 1, m - 2 array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, glob_h if omniabs(hdrc) > 0.0 then (rcs : ------, hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) ord_no : -----------------------------------------------------, hdrc array_real_poles : rcs, array_real_poles : ord_no) 1, 1 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float)) 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : 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 0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) 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) = 0.0) rm4 rm3 rm2 or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0 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) # 0.0 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_poles : rad_c, 1, 1 array_complex_poles : ord_no), if array_pole glob_ratio_of_radius < 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_poles()) (%i12) 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 (%o12) 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 (%i13) 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 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_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 2.0 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 3.0 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 4.0 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 5.0 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 order_d + kkk < glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o13) 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 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_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 2.0 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 3.0 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 4.0 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 5.0 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 order_d + kkk < glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i14) log10(x) := --------- log(10.0) log(x) (%o14) log10(x) := --------- log(10.0) (%i15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i16) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o16) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i17) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o17) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i18) 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)) (%o18) 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)) (%i19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i21) 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 (%o21) 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 (%i22) 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 (%o22) 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 (%i23) 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)) (%o23) 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)) (%i24) 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, "~%")) (%o24) 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, "~%")) (%i25) 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~%")) (%o25) 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~%")) (%i26) 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) (%o26) 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) (%i27) 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) (%o27) 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) (%i28) display_pole_debug(typ, m, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_int(ALWAYS, "m", 4, m, 4, " "), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%o28) display_pole_debug(typ, m, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_int(ALWAYS, "m", 4, m, 4, " "), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i33) log_revs(file, revs) := printf(file, revs) (%o33) log_revs(file, revs) := printf(file, revs) (%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i35) 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") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, "")) (%o35) 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") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, "")) (%i36) logstart(file) := printf(file, "") (%o36) logstart(file) := printf(file, "") (%i37) logend(file) := printf(file, "~%") (%o37) logend(file) := printf(file, "~%") (%i38) 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()) (%o38) 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()) (%i39) 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 (%o39) 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 (%i40) 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 (%o40) 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 (%i41) factorial_2(nnn) := nnn! (%o41) factorial_2(nnn) := nnn! (%i42) 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 (%o42) 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 (%i43) 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) (%o43) 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) (%i44) convfp(mmm) := mmm (%o44) convfp(mmm) := mmm (%i45) convfloat(mmm) := mmm (%o45) convfloat(mmm) := mmm (%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i47) Si(x) := 0.0 (%o47) Si(x) := 0.0 (%i48) Ci(x) := 0.0 (%o48) Ci(x) := 0.0 (%i49) ln(x) := log(x) (%o49) ln(x) := log(x) (%i50) arcsin(x) := asin(x) (%o50) arcsin(x) := asin(x) (%i51) arccos(x) := acos(x) (%o51) arccos(x) := acos(x) (%i52) arctan(x) := atan(x) (%o52) arctan(x) := atan(x) (%i53) omniabs(x) := abs(x) (%o53) omniabs(x) := abs(x) (%i54) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o54) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i55) 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) (%o55) 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) (%i56) 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)) (%o56) 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)) (%i57) 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, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, 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_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), 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_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), 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_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, 0.0, float), define_variable(glob_smallish_float, 0.0, 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_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_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:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (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 : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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 + 4), array(array_real_pole, 1 + 4), array(array_complex_pole, 1 + 4), array(array_1st_rel_error, 1 + 2), array(array_last_rel_error, 1 + 2), array(array_type_pole, 1 + 2), array(array_type_real_pole, 1 + 2), array(array_type_complex_pole, 1 + 2), 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 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 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 <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + 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 <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 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_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), 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), found_h : false, glob_h : glob_min_h, if glob_max_h < glob_h then glob_h : glob_max_h, if glob_display_interval < glob_h then glob_h : glob_display_interval, best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, 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, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) 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(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 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, "2013-05-26T02:27:00-05:00"), 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_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, " 189 "), logitem_str(html_log_file, "lin_arcsin diffeq.max"), logitem_str(html_log_file, "lin_arcsin maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o57) 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, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, 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_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), 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_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), 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_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, 0.0, float), define_variable(glob_smallish_float, 0.0, 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_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_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:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (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 : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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 + 4), array(array_real_pole, 1 + 4), array(array_complex_pole, 1 + 4), array(array_1st_rel_error, 1 + 2), array(array_last_rel_error, 1 + 2), array(array_type_pole, 1 + 2), array(array_type_real_pole, 1 + 2), array(array_type_complex_pole, 1 + 2), 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 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 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 <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + 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 <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 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_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), 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), found_h : false, glob_h : glob_min_h, if glob_max_h < glob_h then glob_h : glob_max_h, if glob_display_interval < glob_h then glob_h : glob_display_interval, best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, 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, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) 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(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 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, "2013-05-26T02:27:00-05:00"), 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_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, " 189 "), logitem_str(html_log_file, "lin_arcsin diffeq.max"), logitem_str(html_log_file, "lin_arcsin maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i58) 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_look_poles:true," "glob_max_iter:100," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (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. "" glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.6 "" estimated_steps = 1600000.0000000002 "" step_error = 6.24999999999999900000000000000000E-17 "" est_needed_step_err = 6.24999999999999900000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.85092636216908670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 "" estimated_step_error = 2.85092636216908670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 "" best_h = 2.000000E-6 "" opt_iter = 2 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.913224393310234700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 "" estimated_step_error = 1.913224393310234700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.2839432878991078000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 "" estimated_step_error = 1.2839432878991078000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 8.6163993178245390000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 "" estimated_step_error = 8.6163993178245390000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 "" best_h = 1.600000E-5 "" opt_iter = 5 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.782370073794332000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 "" estimated_step_error = 5.782370073794332000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 "" best_h = 3.200000E-5 "" opt_iter = 6 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.8804860549959880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 "" estimated_step_error = 3.8804860549959880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 "" best_h = 6.400000E-5 "" opt_iter = 7 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.604154385637640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" estimated_step_error = 2.604154385637640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" best_h = 1.280000E-4 "" opt_iter = 8 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.7476241647921564000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 "" estimated_step_error = 1.7476241647921564000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.17281842786677080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 "" estimated_step_error = 1.17281842786677080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.870754639100935000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" estimated_step_error = 7.870754639100935000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" best_h = 1.024000E-3 "" opt_iter = 11 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.2821128156927890000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" estimated_step_error = 5.2821128156927890000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" best_h = 2.048000E-3 "" opt_iter = 12 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.54495220033704430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" estimated_step_error = 3.54495220033704430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" best_h = 4.096000E-3 "" opt_iter = 13 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.3792272311696905000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" estimated_step_error = 2.3792272311696905000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" best_h = 8.192000E-3 "" opt_iter = 14 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.59700812585533370000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" estimated_step_error = 1.59700812585533370000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.07218494690294400000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 1.07218494690294400000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.2013714518787940000000000000000000000000000000000000000000000000000000000000000000E-67 "" estimated_step_error = 7.2013714518787940000000000000000000000000000000000000000000000000000000000000000000E-67 "" best_h = 6.553600E-2 "" opt_iter = 17 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.8409129832298503000000000000000000000000000000000000000000000000000000000E-59 "" estimated_step_error = 4.8409129832298503000000000000000000000000000000000000000000000000000000000E-59 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.25968198404761000000000000000000000000000000000000000000000000000E-51 "" estimated_step_error = 3.25968198404761000000000000000000000000000000000000000000000000000E-51 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" 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 = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.765921825451008 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 12.062193004902966 " " Order of pole (three term test) = 811.9001320718611 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.79 " " y[1] (analytic) = 10.073294711088748 " " y[1] (numeric) = 10.073294711088748 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.761099570483246 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 11.833842725256783 " " Order of pole (three term test) = 797.1864854752303 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.78 " " y[1] (analytic) = 10.074512720530736 " " y[1] (numeric) = 10.074512720530736 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.756019239182988 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 11.6232834863616 " " Order of pole (three term test) = 783.6601211209652 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.77 " " y[1] (analytic) = 10.075740805234805 " " y[1] (numeric) = 10.075740805234805 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.750690967848673 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 11.428658647629458 " " Order of pole (three term test) = 771.1975581773337 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.76 " " y[1] (analytic) = 10.076978966454057 " " y[1] (numeric) = 10.076978966454057 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.745124506817033 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 11.24835648122302 " " Order of pole (three term test) = 759.6915956584359 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.75 " " y[1] (analytic) = 10.078227205452297 " " y[1] (numeric) = 10.078227205452297 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.739329234272754 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 11.080971051054737 " " Order of pole (three term test) = 749.0487118366009 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.74 " " y[1] (analytic) = 10.079485523504044 " " y[1] (numeric) = 10.079485523504045 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.762348718352755300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.733314169632836 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.925270364935285 " " Order of pole (three term test) = 739.1869471577022 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.73 " " y[1] (analytic) = 10.080753921894546 " " y[1] (numeric) = 10.080753921894546 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.727087986512895 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.780170269635732 " " Order of pole (three term test) = 730.0341689324976 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.72 " " y[1] (analytic) = 10.082032401919786 " " y[1] (numeric) = 10.082032401919786 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.72065902528346 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.644712915812816 " " Order of pole (three term test) = 721.5266398219453 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.71 " " y[1] (analytic) = 10.083320964886498 " " y[1] (numeric) = 10.0833209648865 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.761678365278780700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.714035305224224 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.518048885811035 " " Order of pole (three term test) = 713.607829821859 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.7 " " y[1] (analytic) = 10.084619612112185 " " y[1] (numeric) = 10.084619612112185 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.707224536284862 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.399422277394883 " " Order of pole (three term test) = 706.2274247504344 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.69 " " y[1] (analytic) = 10.085928344925117 " " y[1] (numeric) = 10.085928344925117 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.700234130461102 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.288158188215412 " " Order of pole (three term test) = 699.3404943303167 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.6799999999999999 " " y[1] (analytic) = 10.087247164664358 " " y[1] (numeric) = 10.087247164664358 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.693071212794795 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.18365216185409 " " Order of pole (three term test) = 692.9067906708101 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.6699999999999999 " " y[1] (analytic) = 10.088576072679771 " " y[1] (numeric) = 10.088576072679771 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.68574263200709 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 10.085361245761442 " " Order of pole (three term test) = 686.8901539039817 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" 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 = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.67825497077376 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.992796380871242 " " Order of pole (three term test) = 681.2580063461439 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.6499999999999999 " " y[1] (analytic) = 10.091264158992647 " " y[1] (numeric) = 10.091264158992646 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.76029168537549600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.670614555651742 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.905515896989774 " " Order of pole (three term test) = 675.9809201672222 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" 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 = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.662827466666212 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.82311993081293 " " Order of pole (three term test) = 671.0322463926491 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" 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 = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.654899546567178 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.74524561729269 " " Order of pole (three term test) = 666.3877953139823 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.6199999999999999 " " y[1] (analytic) = 10.095371984902286 " " y[1] (numeric) = 10.095371984902284 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75957541936721800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.646836409764775 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.67156293204257 " " Order of pole (three term test) = 662.0255601771912 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.6099999999999999 " " y[1] (analytic) = 10.096761451528309 " " y[1] (numeric) = 10.096761451528309 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.6386434509524 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.601771084095747 " " Order of pole (three term test) = 657.9254774551349 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5999999999999999 " " y[1] (analytic) = 10.098161016183049 " " y[1] (numeric) = 10.098161016183047 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.759089438714145400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.630325853426502 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.535595375740865 " " Order of pole (three term test) = 654.0692181681997 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5899999999999999 " " y[1] (analytic) = 10.099570680303238 " " y[1] (numeric) = 10.099570680303236 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.758843910924454700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.621888597112118 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.472784460243263 " " Order of pole (three term test) = 650.4400056532518 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5799999999999998 " " y[1] (analytic) = 10.100990445336533 " " y[1] (numeric) = 10.100990445336532 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75859669308009900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.613336466302737 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.413107939750553 " " Order of pole (three term test) = 647.0224559450363 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5699999999999998 " " y[1] (analytic) = 10.102420312741522 " " y[1] (numeric) = 10.10242031274152 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75834778638129690000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.604674057123347 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.356354255028464 " " Order of pole (three term test) = 643.8024375554375 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5599999999999998 " " y[1] (analytic) = 10.10386028398774 " " y[1] (numeric) = 10.103860283987737 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.758097192035960000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.595905784725002 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.302328826393449 " " Order of pole (three term test) = 640.7669479493806 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5499999999999998 " " y[1] (analytic) = 10.105310360555679 " " y[1] (numeric) = 10.105310360555677 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75784491125967800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.587035890219454 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.250852411525885 " " Order of pole (three term test) = 637.9040044360075 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5399999999999998 " " y[1] (analytic) = 10.106770543936813 " " y[1] (numeric) = 10.106770543936811 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.757590945275700200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.578068447361877 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.2017596511315 " " Order of pole (three term test) = 635.2025475451527 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5299999999999998 " " y[1] (analytic) = 10.108240835633602 " " y[1] (numeric) = 10.1082408356336 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.757335295314919300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.569007368989993 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.154897777751177 " " Order of pole (three term test) = 632.6523552470483 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5199999999999998 " " y[1] (analytic) = 10.109721237159507 " " y[1] (numeric) = 10.109721237159505 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.757077962615858600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.559856413227209 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.110125466680147 " " Order of pole (three term test) = 630.2439666166332 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.5099999999999998 " " y[1] (analytic) = 10.111211750039011 " " y[1] (numeric) = 10.111211750039008 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.51363789684930100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.550619189457738 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.067311811001879 " " Order of pole (three term test) = 627.9686137462202 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.4999999999999998 " " y[1] (analytic) = 10.112712375807623 " " y[1] (numeric) = 10.112712375807622 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.756558253995023400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.541299164081053 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.026335405297067 " " Order of pole (three term test) = 625.8181608801148 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.48999999999999977 " " y[1] (analytic) = 10.114223116011908 " " y[1] (numeric) = 10.114223116011905 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.512591761176566700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.531899666053148 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.987083524749618 " " Order of pole (three term test) = 623.7850498884898 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.47999999999999976 " " y[1] (analytic) = 10.115743972209481 " " y[1] (numeric) = 10.115743972209481 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.522423892221713 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.949451388195898 " " Order of pole (three term test) = 621.8622513191178 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.46999999999999975 " " y[1] (analytic) = 10.117274945969049 " " y[1] (numeric) = 10.117274945969047 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75576610192647900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.512874912462342 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.913341495211398 " " Order of pole (three term test) = 620.0432203684535 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.45999999999999974 " " y[1] (analytic) = 10.118816038870396 " " y[1] (numeric) = 10.118816038870394 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.755498699231765600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.503255674622375 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.8786630286404 " " Order of pole (three term test) = 618.3218572007463 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.44999999999999973 " " y[1] (analytic) = 10.120367252504419 " " y[1] (numeric) = 10.120367252504417 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.755229622680607200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.49356900927926 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.84533131510573 " " Order of pole (three term test) = 616.692471119106 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.4399999999999997 " " y[1] (analytic) = 10.12192858847314 " " y[1] (numeric) = 10.12192858847314 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.483817634319626 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.813267336987293 " " Order of pole (three term test) = 615.1497481556872 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.4299999999999997 " " y[1] (analytic) = 10.123500048389714 " " y[1] (numeric) = 10.123500048389714 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.474004159345562 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.782397290187442 " " Order of pole (three term test) = 613.6887217033147 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.4199999999999997 " " y[1] (analytic) = 10.125081633878452 " " y[1] (numeric) = 10.12508163387845 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75441236291525080000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.464131089914007 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.752652182708243 " " Order of pole (three term test) = 612.3047458578709 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.4099999999999997 " " y[1] (analytic) = 10.12667334657483 " " y[1] (numeric) = 10.126673346574828 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.75413660400241120000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.454200831615275 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.723967469671187 " " Order of pole (three term test) = 610.993471180999 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.3999999999999997 " " y[1] (analytic) = 10.128275188125508 " " y[1] (numeric) = 10.128275188125508 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.443729929830722 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.696282720950048 " " Order of pole (three term test) = 609.7508226286534 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.3899999999999997 " " y[1] (analytic) = 10.129887160188357 " " y[1] (numeric) = 10.129887160188355 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.753580085651438300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.431577488378636 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.669541318028628 " " Order of pole (three term test) = 608.5729794202629 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.37999999999999967 " " y[1] (analytic) = 10.131509264432447 " " y[1] (numeric) = 10.131509264432445 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.753299328892988500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.419465353996118 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.643690177104238 " " Order of pole (three term test) = 607.4563566505425 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.36999999999999966 " " y[1] (analytic) = 10.133141502538093 " " y[1] (numeric) = 10.133141502538091 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.753016908877980700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.407391802645082 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.61867949579629 " " Order of pole (three term test) = 606.3975884684626 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.35999999999999965 " " y[1] (analytic) = 10.134783876196853 " " y[1] (numeric) = 10.13478387619685 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.752732826964674000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.395355183889016 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.594462521120693 " " Order of pole (three term test) = 605.3935126679191 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.34999999999999964 " " y[1] (analytic) = 10.136436387111551 " " y[1] (numeric) = 10.13643638711155 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.752447084518660700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.38335391774256 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.570995336658749 " " Order of pole (three term test) = 604.4411565524916 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.33999999999999964 " " y[1] (analytic) = 10.138099036996294 " " y[1] (numeric) = 10.138099036996293 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.752159682912850500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.371386491657287 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.548236667069919 " " Order of pole (three term test) = 603.5377239513068 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.3299999999999996 " " y[1] (analytic) = 10.139771827576482 " " y[1] (numeric) = 10.139771827576482 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.359451457637675 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.526147698308026 " " Order of pole (three term test) = 602.680583277034 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.3199999999999996 " " y[1] (analytic) = 10.141454760588838 " " y[1] (numeric) = 10.141454760588836 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.751579907749951600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.347547429481521 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.504691912073332 " " Order of pole (three term test) = 601.867256528521 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.3099999999999996 " " y[1] (analytic) = 10.143147837781404 " " y[1] (numeric) = 10.143147837781404 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.335673080139353 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.483834933189728 " " Order of pole (three term test) = 601.095409151002 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.2999999999999996 " " y[1] (analytic) = 10.144851060913583 " " y[1] (numeric) = 10.144851060913583 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.323827139187424 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.463544388732688 " " Order of pole (three term test) = 600.3628406758656 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.2899999999999996 " " y[1] (analytic) = 10.146564431756136 " " y[1] (numeric) = 10.146564431756136 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.312008390409693 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.443789777858255 " " Order of pole (three term test) = 599.6674760702903 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.2799999999999996 " " y[1] (analytic) = 10.148287952091211 " " y[1] (numeric) = 10.14828795209121 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.750400508722463600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.300215669483519 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.424542351386393 " " Order of pole (three term test) = 599.0073577338666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.2699999999999996 " " y[1] (analytic) = 10.150021623712348 " " y[1] (numeric) = 10.150021623712348 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.28844786176497 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.405775000290848 " " Order of pole (three term test) = 598.3806380859176 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.25999999999999956 " " y[1] (analytic) = 10.151765448424518 " " y[1] (numeric) = 10.151765448424516 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.749800907462778800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.276703900169103 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.387462152331004 " " Order of pole (three term test) = 597.7855726927709 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.24999999999999956 " " y[1] (analytic) = 10.153519428044111 " " y[1] (numeric) = 10.153519428044111 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.264982763141262 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.369579676135473 " " Order of pole (three term test) = 597.2205138891552 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.23999999999999955 " " y[1] (analytic) = 10.155283564398985 " " y[1] (numeric) = 10.155283564398985 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.253283472715253 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.352104792110948 " " Order of pole (three term test) = 596.6839048521178 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.22999999999999954 " " y[1] (analytic) = 10.157057859328459 " " y[1] (numeric) = 10.157057859328459 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.241605092654869 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.335015989625234 " " Order of pole (three term test) = 596.1742740909775 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.21999999999999953 " " y[1] (analytic) = 10.158842314683342 " " y[1] (numeric) = 10.158842314683342 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.2299467266748 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.318292949935191 " " Order of pole (three term test) = 595.6902303180627 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.20999999999999952 " " y[1] (analytic) = 10.160636932325954 " " y[1] (numeric) = 10.160636932325954 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.21830751673787 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.301916474418872 " " Order of pole (three term test) = 595.2304576711485 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.1999999999999995 " " y[1] (analytic) = 10.162441714130136 " " y[1] (numeric) = 10.162441714130136 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.206686641424966 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.285868417672177 " " Order of pole (three term test) = 594.7937112582881 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.1899999999999995 " " y[1] (analytic) = 10.164256661981273 " " y[1] (numeric) = 10.164256661981273 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.195083314374745 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.270131625104684 " " Order of pole (three term test) = 594.3788130009278 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.1799999999999995 " " y[1] (analytic) = 10.166081777776313 " " y[1] (numeric) = 10.166081777776313 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.183496782789945 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.254689874676313 " " Order of pole (three term test) = 593.984647751466 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.16999999999999948 " " y[1] (analytic) = 10.167917063423786 " " y[1] (numeric) = 10.167917063423785 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.74702136958826420000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.171926326007558 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.239527822464549 " " Order of pole (three term test) = 593.6101596647267 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.15999999999999948 " " y[1] (analytic) = 10.169762520843813 " " y[1] (numeric) = 10.169762520843815 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.746704346103906000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.160371254129972 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.224630951769983 " " Order of pole (three term test) = 593.2543488039588 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.14999999999999947 " " y[1] (analytic) = 10.171618151968147 " " y[1] (numeric) = 10.171618151968149 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.746385690910483300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.148830906714595 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.209985525500569 " " Order of pole (three term test) = 592.9162679641811 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.13999999999999946 " " y[1] (analytic) = 10.173483958740167 " " y[1] (numeric) = 10.173483958740169 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.746065405523306600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.137304651519356 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.195578541588056 " " Order of pole (three term test) = 592.5950196964985 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.12999999999999945 " " y[1] (analytic) = 10.175359943114914 " " y[1] (numeric) = 10.175359943114916 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.74574349146460400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.125791883301682 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.181397691221052 " " Order of pole (three term test) = 592.2897535191534 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.11999999999999945 " " y[1] (analytic) = 10.177246107059101 " " y[1] (numeric) = 10.177246107059103 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.74541995026350100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.11429202266871 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.167431319690099 " " Order of pole (three term test) = 591.9996633017355 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -0.10999999999999946 " " y[1] (analytic) = 10.179142452551142 " " y[1] (numeric) = 10.179142452551142 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.102804514976482 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.153668389657511 " " Order of pole (three term test) = 591.7239848101425 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -9.99999999999994700E-2 " " y[1] (analytic) = 10.181048981581155 " " y[1] (numeric) = 10.181048981581156 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7447679925849602000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.09132882927601 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.14009844668643 " " Order of pole (three term test) = 591.4619934013658 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -8.99999999999994700E-2 " " y[1] (analytic) = 10.182965696151006 " " y[1] (numeric) = 10.182965696151006 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.079864457304298 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.12671158686731 " " Order of pole (three term test) = 591.2130018573528 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -7.99999999999994700E-2 " " y[1] (analytic) = 10.184892598274306 " " y[1] (numeric) = 10.184892598274306 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.068410912518276 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.113498426399945 " " Order of pole (three term test) = 590.9763583485724 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -6.99999999999994800E-2 " " y[1] (analytic) = 10.186829689976442 " " y[1] (numeric) = 10.186829689976442 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.056967729169875 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.10045007299842 " " Order of pole (three term test) = 590.7514445185103 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -5.99999999999994800E-2 " " y[1] (analytic) = 10.188776973294598 " " y[1] (numeric) = 10.188776973294598 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.04553446142046 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.087558098995556 " " Order of pole (three term test) = 590.5376736809187 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.999999999999948000E-2 " " y[1] (analytic) = 10.190734450277771 " " y[1] (numeric) = 10.19073445027777 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.743109731754252400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.034110682492992 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.07481451603549 " " Order of pole (three term test) = 590.3344891224692 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -3.999999999999947500E-2 " " y[1] (analytic) = 10.192702122986791 " " y[1] (numeric) = 10.19270212298679 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.742773229283502700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.0226959838602 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.062211751245592 " " Order of pole (three term test) = 590.1413625035755 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -2.99999999999994700E-2 " " y[1] (analytic) = 10.194679993494345 " " y[1] (numeric) = 10.194679993494345 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 9.011289974467322 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.049742624798306 " " Order of pole (three term test) = 589.9577923515325 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -1.99999999999994680E-2 " " y[1] (analytic) = 10.196668063885001 " " y[1] (numeric) = 10.196668063885001 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.99989227998793 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.037400328764322 " " Order of pole (three term test) = 589.7833026393753 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -9.99999999999946900E-3 " " y[1] (analytic) = 10.198666336255217 " " y[1] (numeric) = 10.198666336255217 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.988502542111341 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.025178407183022 " " Order of pole (three term test) = 589.617441445639 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.308253836489030000000000000000E-16 " " y[1] (analytic) = 10.200674812713373 " " y[1] (numeric) = 10.200674812713373 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.977120417860394 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.013070737268238 " " Order of pole (three term test) = 589.4597796895484 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000053000E-2 " " y[1] (analytic) = 10.202693495379789 " " y[1] (numeric) = 10.202693495379789 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.965745578938195 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.001071511676972 " " Order of pole (three term test) = 589.3099099368579 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000005300E-2 " " y[1] (analytic) = 10.204722386386742 " " y[1] (numeric) = 10.20472238638674 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.740720396049125200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.954377711102637 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.9891752217804495 " " Order of pole (three term test) = 589.1674452723671 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.000000000000053000E-2 " " y[1] (analytic) = 10.206761487878488 " " y[1] (numeric) = 10.20676148787849 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.740372635835416600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.943016513567539 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.9773766418696646 " " Order of pole (three term test) = 589.032018234589 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.000000000000053500E-2 " " y[1] (analytic) = 10.208810802011302 " " y[1] (numeric) = 10.2088108020113 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.740023273866804500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.931661698429208 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.96567081424146 " " Order of pole (three term test) = 588.9032798090213 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000005300E-2 " " y[1] (analytic) = 10.210870330953464 " " y[1] (numeric) = 10.21087033095346 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.479344623573099600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.92031299011738 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.954053035111535 " " Order of pole (three term test) = 588.7808984764785 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.00000000000005400E-2 " " y[1] (analytic) = 10.21294007688531 " " y[1] (numeric) = 10.212940076885307 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.47863950248887500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.908970124869562 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.942518841305204 " " Order of pole (three term test) = 588.6645593132442 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000005300E-2 " " y[1] (analytic) = 10.215020041999246 " " y[1] (numeric) = 10.215020041999244 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.73896559389675800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.897632850227584 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.93106399767534 " " Order of pole (three term test) = 588.5539631396546 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000005300E-2 " " y[1] (analytic) = 10.217110228499772 " " y[1] (numeric) = 10.217110228499768 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.47721968281256700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.886300924555703 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.919684485210703 " " Order of pole (three term test) = 588.4488257147424 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000005200E-2 " " y[1] (analytic) = 10.21921063860349 " " y[1] (numeric) = 10.219210638603487 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.476504990884499700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.874974116579061 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.908376489788903 " " Order of pole (three term test) = 588.3488769738717 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000052 " " y[1] (analytic) = 10.22132127453915 " " y[1] (numeric) = 10.221321274539145 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.21368067304099500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.863652204941847 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.8971363915394015 " " Order of pole (three term test) = 588.253860307099 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000051 " " y[1] (analytic) = 10.223442138547647 " " y[1] (numeric) = 10.223442138547645 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.737533029802623400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.85233497778418 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.885960754780031 " " Order of pole (three term test) = 588.1635318758364 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000051 " " y[1] (analytic) = 10.225573232882073 " " y[1] (numeric) = 10.22557323288207 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.47434182699522860000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.84102223233702 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.874846318491946 " " Order of pole (three term test) = 588.0776599654791 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1300000000000005 " " y[1] (analytic) = 10.22771455980771 " " y[1] (numeric) = 10.227714559807707 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.47361442092034200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.829713774534282 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.8637899873081745 " " Order of pole (three term test) = 587.99602437241 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1400000000000005 " " y[1] (analytic) = 10.229866121602074 " " y[1] (numeric) = 10.22986612160207 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.472883844783023500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.818409418641409 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.8527888229781135 " " Order of pole (three term test) = 587.9184158228055 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000052 " " y[1] (analytic) = 10.232027920554925 " " y[1] (numeric) = 10.232027920554923 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.736075050999188000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.807108986899783 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.841840036289300 " " Order of pole (three term test) = 587.8446354220961 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000053 " " y[1] (analytic) = 10.234199958968304 " " y[1] (numeric) = 10.234199958968302 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.735706597997058000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.795812309186207 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.830940979413842 " " Order of pole (three term test) = 587.774494132842 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000054 " " y[1] (analytic) = 10.236382239156544 " " y[1] (numeric) = 10.236382239156542 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.735336565105269600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.784519222686919 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.820089138662087 " " Order of pole (three term test) = 587.7078122799476 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000055 " " y[1] (analytic) = 10.238574763446298 " " y[1] (numeric) = 10.238574763446296 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.734964954050235200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.773229571585402 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.8092821276149955 " " Order of pole (three term test) = 587.6444190812497 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000056 " " y[1] (analytic) = 10.240777534176564 " " y[1] (numeric) = 10.240777534176562 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.734591766564610700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.761943206763512 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.798517680617097 " " Order of pole (three term test) = 587.5841522023244 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000057 " " y[1] (analytic) = 10.242990553698707 " " y[1] (numeric) = 10.242990553698705 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.73421700438727300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.750659985515304 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.7877936466128395 " " Order of pole (three term test) = 587.5268573343856 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000058 " " y[1] (analytic) = 10.245213824376487 " " y[1] (numeric) = 10.245213824376485 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.733840669263296600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.73937977127302 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.777107983301270 " " Order of pole (three term test) = 587.4723877935573 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000058 " " y[1] (analytic) = 10.247447348586077 " " y[1] (numeric) = 10.247447348586075 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.733462762943933400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.728102433344748 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.766458751596491 " " Order of pole (three term test) = 587.4206041407374 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000006 " " y[1] (analytic) = 10.24969112871609 " " y[1] (numeric) = 10.24969112871609 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.716827846663232 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.755844110377049 " " Order of pole (three term test) = 587.3713738209276 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000006 " " y[1] (analytic) = 10.251945167167612 " " y[1] (numeric) = 10.25194516716761 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.732702243754800600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.705555891545345 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.7452623115049555 " " Order of pole (three term test) = 587.3245708207104 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000006 " " y[1] (analytic) = 10.254209466354208 " " y[1] (numeric) = 10.254209466354206 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.732319634418213500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.69428645346185 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.73471169510502 " " Order of pole (three term test) = 587.2800753433155 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000006 " " y[1] (analytic) = 10.256484028701966 " " y[1] (numeric) = 10.256484028701964 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.731935460952559500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.683019422816905 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.724190685086508 " " Order of pole (three term test) = 587.2377735000294 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000063 " " y[1] (analytic) = 10.258768856649509 " " y[1] (numeric) = 10.258768856649507 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.73154972513963500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.67175469473698 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.713697784894057 " " Order of pole (three term test) = 587.1975570170811 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000064 " " y[1] (analytic) = 10.261063952648028 " " y[1] (numeric) = 10.261063952648025 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.46232485753455170000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.66049216886877 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.703231573481181 " " Order of pole (three term test) = 587.1593229576222 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000065 " " y[1] (analytic) = 10.263369319161303 " " y[1] (numeric) = 10.2633693191613 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.46154714725867450000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.64923174918565 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.692790701486182 " " Order of pole (three term test) = 587.1229734573648 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000066 " " y[1] (analytic) = 10.265684958665728 " " y[1] (numeric) = 10.265684958665725 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.46076632305133700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.63797334380245 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.682373887606880 " " Order of pole (three term test) = 587.0884154737151 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000066 " " y[1] (analytic) = 10.268010873650345 " " y[1] (numeric) = 10.268010873650342 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.459982388524183700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.626716864798071 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.671979915159257 " " Order of pole (three term test) = 587.055560547365 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000007 " " y[1] (analytic) = 10.270347066616857 " " y[1] (numeric) = 10.270347066616853 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.45919534730075700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.615462228045681 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.661607628813428 " " Order of pole (three term test) = 587.0243245759294 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000007 " " y[1] (analytic) = 10.272693540079663 " " y[1] (numeric) = 10.27269354007966 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.458405203016452500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.604209353050086 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.6512559314945285 " " Order of pole (three term test) = 586.9946275987768 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000007 " " y[1] (analytic) = 10.275050296565878 " " y[1] (numeric) = 10.275050296565876 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.728805979659236700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.592958162792122 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.640923781443386 " " Order of pole (three term test) = 586.9663935927373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000007 " " y[1] (analytic) = 10.277417338615372 " " y[1] (numeric) = 10.277417338615368 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.456815619865779600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.581708583579609 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.630610189424479 " " Order of pole (three term test) = 586.9395502778161 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000007 " " y[1] (analytic) = 10.279794668780779 " " y[1] (numeric) = 10.279794668780774 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.18402428249357100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.570460544904671 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.620314216078296 " " Order of pole (three term test) = 586.9140289327709 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000007 " " y[1] (analytic) = 10.282182289627533 " " y[1] (numeric) = 10.282182289627528 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.182820502585930000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.559213979307161 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.610034969406924 " " Order of pole (three term test) = 586.8897642197578 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000007 " " y[1] (analytic) = 10.284580203733896 " " y[1] (numeric) = 10.284580203733892 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.454408063744459600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.547968822243874 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.599771602387080 " " Order of pole (three term test) = 586.8666940176815 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000073 " " y[1] (analytic) = 10.286988413690983 " " y[1] (numeric) = 10.28698841369098 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.45359937809610440000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.536725011963386 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.589523310704367 " " Order of pole (three term test) = 586.8447592638286 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000074 " " y[1] (analytic) = 10.28940692210279 " " y[1] (numeric) = 10.289406922102787 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.45278761516261630000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.525482489386151 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.5792893306020055 " " Order of pole (three term test) = 586.8239038033273 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000075 " " y[1] (analytic) = 10.291835731586216 " " y[1] (numeric) = 10.291835731586215 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7259863893362700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.514241197989842 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.569068936840073 " " Order of pole (three term test) = 586.8040742461951 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000076 " " y[1] (analytic) = 10.294274844771103 " " y[1] (numeric) = 10.294274844771099 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.45115487236585140000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.503001083699427 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.558861440754890 " " Order of pole (three term test) = 586.7852198312173 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000077 " " y[1] (analytic) = 10.296724264300245 " " y[1] (numeric) = 10.296724264300241 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.45033389999391200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.49176209478207 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.5486661884189585 " " Order of pole (three term test) = 586.7672922967499 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000008 " " y[1] (analytic) = 10.299183992829436 " " y[1] (numeric) = 10.299183992829432 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.449509865319421000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.480524181746427 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.538482558893068 " " Order of pole (three term test) = 586.7502457578474 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000008 " " y[1] (analytic) = 10.301654033027484 " " y[1] (numeric) = 10.301654033027479 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.173024158174555000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.469287297246327 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.52830996256583 " " Order of pole (three term test) = 586.7340365893934 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000008 " " y[1] (analytic) = 10.30413438757624 " " y[1] (numeric) = 10.304134387576237 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.447852624169993600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.458051395988482 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.518147839577946 " " Order of pole (three term test) = 586.7186233150737 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000008 " " y[1] (analytic) = 10.306625059170642 " " y[1] (numeric) = 10.306625059170639 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.447019425276718300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.446816434644182 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.507995658326239 " " Order of pole (three term test) = 586.7039665018515 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000008 " " y[1] (analytic) = 10.30912605051872 " " y[1] (numeric) = 10.309126050518717 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.44618317924412300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.435582371764783 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.497852914040964 " " Order of pole (three term test) = 586.6900286594715 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000008 " " y[1] (analytic) = 10.311637364341644 " " y[1] (numeric) = 10.31163736434164 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.445343889890883000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.424349167700747 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.4877191274370025 " " Order of pole (three term test) = 586.6767741450949 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000008 " " y[1] (analytic) = 10.314159003373739 " " y[1] (numeric) = 10.314159003373737 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.722250780523364200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.413116784524215 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.477593843431617 " " Order of pole (three term test) = 586.6641690725166 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000008 " " y[1] (analytic) = 10.316690970362526 " " y[1] (numeric) = 10.316690970362524 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.721828098276195500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.401885185954816 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.467476629927196 " " Order of pole (three term test) = 586.6521812258906 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000008 " " y[1] (analytic) = 10.319233268068743 " " y[1] (numeric) = 10.319233268068741 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.721403900129779600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.39065433728873 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.457367076656153 " " Order of pole (three term test) = 586.6407799777669 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000008 " " y[1] (analytic) = 10.321785899266379 " " y[1] (numeric) = 10.321785899266377 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.720978188015414300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.379424205330704 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.447264794080834 " " Order of pole (three term test) = 586.6299362109143 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000008 " " y[1] (analytic) = 10.324348866742701 " " y[1] (numeric) = 10.324348866742698 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.441101927739652600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.368194758329045 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.437169412352010 " " Order of pole (three term test) = 586.6196222442447 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000008 " " y[1] (analytic) = 10.326922173298282 " " y[1] (numeric) = 10.32692217329828 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.720122229635149500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.356965965913345 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.427080580319111 " " Order of pole (three term test) = 586.6098117623316 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000008 " " y[1] (analytic) = 10.32950582174704 " " y[1] (numeric) = 10.329505821747038 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.719691987258896200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.345737799034907 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.416997964587363 " " Order of pole (three term test) = 586.6004797481552 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000008 " " y[1] (analytic) = 10.332099814916257 " " y[1] (numeric) = 10.332099814916255 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.71926023869393680000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.33451022990971 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.40692124862699 " " Order of pole (three term test) = 586.5916024195343 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000008 " " y[1] (analytic) = 10.334704155646616 " " y[1] (numeric) = 10.334704155646612 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.43765397179694800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.32328323196381 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.396850131922195 " " Order of pole (three term test) = 586.5831571682735 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000009 " " y[1] (analytic) = 10.337318846792225 " " y[1] (numeric) = 10.337318846792225 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.31205677978108 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.386784329167584 " " Order of pole (three term test) = 586.5751225026778 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000009 " " y[1] (analytic) = 10.339943891220667 " " y[1] (numeric) = 10.339943891220667 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.30083084905322 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.376723569499714 " " Order of pole (three term test) = 586.5674779924638 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000009 " " y[1] (analytic) = 10.342579291813003 " " y[1] (numeric) = 10.342579291813001 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.717518221790556600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.289605416531865 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.366667595772881 " " Order of pole (three term test) = 586.5602042168318 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000009 " " y[1] (analytic) = 10.345225051463819 " " y[1] (numeric) = 10.345225051463817 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.71707897176089090000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.27838045998277 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.356616163866774 " " Order of pole (three term test) = 586.5532827147206 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000009 " " y[1] (analytic) = 10.34788117308126 " " y[1] (numeric) = 10.347881173081257 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.43327645474171900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.267155958141984 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.346569042030999 " " Order of pole (three term test) = 586.5466959376707 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000009 " " y[1] (analytic) = 10.350547659587054 " " y[1] (numeric) = 10.350547659587049 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.148587971830430000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.25593189067384 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.336526010261803 " " Order of pole (three term test) = 586.5404272049461 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000009 " " y[1] (analytic) = 10.353224513916542 " " y[1] (numeric) = 10.353224513916539 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.43150452694716830000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.244708238130826 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.326486859711130 " " Order of pole (three term test) = 586.5344606609362 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000009 " " y[1] (analytic) = 10.355911739018726 " " y[1] (numeric) = 10.35591173901872 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.14592114388347200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.233484981915103 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.3164513921233025 " " Order of pole (three term test) = 586.5287812344832 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000009 " " y[1] (analytic) = 10.358609337856276 " " y[1] (numeric) = 10.35860933785627 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.14458103823385200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.222262104241748 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.306419419302036 " " Order of pole (three term test) = 586.5233746003707 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000009 " " y[1] (analytic) = 10.361317313405584 " " y[1] (numeric) = 10.361317313405578 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.14323647950241100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.211039588103505 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.296390762602774 " " Order of pole (three term test) = 586.5182271425817 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.690000000000001 " " y[1] (analytic) = 10.364035668656788 " " y[1] (numeric) = 10.364035668656783 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.14188747373484900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.199817417237144 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.286365252451905 " " Order of pole (three term test) = 586.5133259194738 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.700000000000001 " " y[1] (analytic) = 10.3667644066138 " " y[1] (numeric) = 10.366764406613797 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.42702268466131700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.188595576091126 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.276342727888388 " " Order of pole (three term test) = 586.5086586305167 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.710000000000001 " " y[1] (analytic) = 10.369503530294352 " " y[1] (numeric) = 10.369503530294347 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.139176145349631000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.177374049794823 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.266323036129582 " " Order of pole (three term test) = 586.5042135847616 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.720000000000001 " " y[1] (analytic) = 10.37225304273001 " " y[1] (numeric) = 10.372253042730007 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.42520922326574440000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.166152824128927 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.256306032158545 " " Order of pole (three term test) = 586.4999796708278 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.730000000000001 " " y[1] (analytic) = 10.375012946966232 " " y[1] (numeric) = 10.375012946966226 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.13644710174461100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.15493188549721 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.246291578332471 " " Order of pole (three term test) = 586.4959463283931 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.740000000000001 " " y[1] (analytic) = 10.377783246062373 " " y[1] (numeric) = 10.377783246062368 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.13507595200810600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.143711220899457 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.236279544009456 " " Order of pole (three term test) = 586.4921035209738 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.750000000000001 " " y[1] (analytic) = 10.380563943091746 " " y[1] (numeric) = 10.38056394309174 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.13370039182432100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.132490817905595 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.226269805195935 " " Order of pole (three term test) = 586.4884417101977 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.760000000000001 " " y[1] (analytic) = 10.383355041141636 " " y[1] (numeric) = 10.38335504114163 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.13232042734313300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.121270664630927 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.21626224421029 " " Order of pole (three term test) = 586.4849518312109 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.770000000000001 " " y[1] (analytic) = 10.386156543313344 " " y[1] (numeric) = 10.386156543313339 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.13093606472899900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.110050749712418 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.206256749363574 " " Order of pole (three term test) = 586.4816252693084 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.780000000000001 " " y[1] (analytic) = 10.38896845272222 " " y[1] (numeric) = 10.388968452722215 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.129547310160880000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.098831062286012 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.196253214657351 " " Order of pole (three term test) = 586.4784538378018 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.790000000000001 " " y[1] (analytic) = 10.391790772497696 " " y[1] (numeric) = 10.391790772497691 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 5.12815416983216900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 8.08761159196494 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.186251539495611 " " Order of pole (three term test) = 586.475429756875 " " "NO COMPLEX POLE (six term test) for Equation 1" "Finished!" "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;" Iterations = 160 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 2 Minutes 20 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 5 Seconds "Time to Timeout "= 0 Years 0 Days 0 Hours 0 Minutes 39 Seconds Percent Done = 100.62500000000007 "%" (%o58) true (%o58) diffeq.max