(%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 : sin(array_tmp1 ), array_tmp2_g : cos(array_tmp1 ), 1 1 1 1 array_tmp3 : array_const_0D2 array_x , array_tmp4 : sin(array_tmp3 ), 1 1 1 1 1 array_tmp4_g : cos(array_tmp3 ), array_tmp5 : 1 1 1 expt(array_tmp2 , array_tmp4 ), array_tmp5_a1 : ln(array_tmp2 ), 1 1 1 1 array_tmp6 : array_tmp5 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , 2 1 2 array_tmp2_g array_tmp1 1 2 array_tmp2 : -------------------------, 2 1 - array_tmp2 array_tmp1 1 2 array_tmp2_g : -------------------------, 2 1 array_tmp3 : array_const_0D2 array_x , 2 1 2 array_tmp4_g array_tmp3 1 2 array_tmp4 : -------------------------, 2 1 - array_tmp4 array_tmp3 1 2 array_tmp4_g : -------------------------, 2 1 array_tmp2 - att(1, array_tmp2, array_tmp5_a1, 2) 2 array_tmp5_a1 : --------------------------------------------------, 2 array_tmp2 1 ats(2, array_tmp2, array_tmp5_a1, 1) 1 array_tmp5_a2 : --------------------------------------, 1 glob_h ats(1, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 2 1 array_tmp6 : array_tmp5 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp6 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 array_tmp2_g array_tmp1 2 2 array_tmp2 : -------------------------, 3 2 - array_tmp2 array_tmp1 2 2 array_tmp2_g : -------------------------, 3 2 array_tmp4_g array_tmp3 2 2 array_tmp4 : -------------------------, 3 2 - array_tmp4 array_tmp3 2 2 array_tmp4_g : -------------------------, 3 2 array_tmp2 - att(2, array_tmp2, array_tmp5_a1, 2) 3 array_tmp5_a1 : --------------------------------------------------, 3 array_tmp2 1 ats(3, array_tmp2, array_tmp5_a1, 1) 2 array_tmp5_a2 : --------------------------------------, 2 glob_h ats(2, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 3 2 array_tmp6 : array_tmp5 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp6 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 array_tmp2_g array_tmp1 3 2 array_tmp2 : -------------------------, 4 3 - array_tmp2 array_tmp1 3 2 array_tmp2_g : -------------------------, 4 3 array_tmp4_g array_tmp3 3 2 array_tmp4 : -------------------------, 4 3 - array_tmp4 array_tmp3 3 2 array_tmp4_g : -------------------------, 4 3 array_tmp2 - att(3, array_tmp2, array_tmp5_a1, 2) 4 array_tmp5_a1 : --------------------------------------------------, 4 array_tmp2 1 ats(4, array_tmp2, array_tmp5_a1, 1) 3 array_tmp5_a2 : --------------------------------------, 3 glob_h ats(3, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 4 3 array_tmp6 : array_tmp5 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp6 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 array_tmp2_g array_tmp1 4 2 array_tmp2 : -------------------------, 5 4 - array_tmp2 array_tmp1 4 2 array_tmp2_g : -------------------------, 5 4 array_tmp4_g array_tmp3 4 2 array_tmp4 : -------------------------, 5 4 - array_tmp4 array_tmp3 4 2 array_tmp4_g : -------------------------, 5 4 array_tmp2 - att(4, array_tmp2, array_tmp5_a1, 2) 5 array_tmp5_a1 : --------------------------------------------------, 5 array_tmp2 1 ats(5, array_tmp2, array_tmp5_a1, 1) 4 array_tmp5_a2 : --------------------------------------, 4 glob_h ats(4, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 5 4 array_tmp6 : array_tmp5 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp6 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_tmp2 : kkk array_tmp2_g array_tmp1 kkk - 1 2 -------------------------------, array_tmp2_g : kkk - 1 kkk - array_tmp2 array_tmp1 kkk - 1 2 -------------------------------, array_tmp4 : kkk - 1 kkk array_tmp4_g array_tmp3 kkk - 1 2 -------------------------------, array_tmp4_g : kkk - 1 kkk - array_tmp4 array_tmp3 kkk - 1 2 -------------------------------, array_tmp5_a1 : kkk - 1 kkk array_tmp2 - att(kkk - 1, array_tmp2, array_tmp5_a1, 2) kkk ----------------------------------------------------------, array_tmp2 1 ats(kkk, array_tmp2, array_tmp5_a1, 1) (kkk - 1) array_tmp5_a2 : ------------------------------------------------, kkk - 1 glob_h ats(kkk - 1, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------------, kkk kkk - 1 array_tmp6 : array_tmp5 , order_d : 1, kkk kkk if order_d + kkk < glob_max_terms then (if not subscript(array_y_set_initial, 1, order_d + kkk) then (temporary : array_tmp6 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : sin(array_tmp1 ), array_tmp2_g : cos(array_tmp1 ), 1 1 1 1 array_tmp3 : array_const_0D2 array_x , array_tmp4 : sin(array_tmp3 ), 1 1 1 1 1 array_tmp4_g : cos(array_tmp3 ), array_tmp5 : 1 1 1 expt(array_tmp2 , array_tmp4 ), array_tmp5_a1 : ln(array_tmp2 ), 1 1 1 1 array_tmp6 : array_tmp5 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , 2 1 2 array_tmp2_g array_tmp1 1 2 array_tmp2 : -------------------------, 2 1 - array_tmp2 array_tmp1 1 2 array_tmp2_g : -------------------------, 2 1 array_tmp3 : array_const_0D2 array_x , 2 1 2 array_tmp4_g array_tmp3 1 2 array_tmp4 : -------------------------, 2 1 - array_tmp4 array_tmp3 1 2 array_tmp4_g : -------------------------, 2 1 array_tmp2 - att(1, array_tmp2, array_tmp5_a1, 2) 2 array_tmp5_a1 : --------------------------------------------------, 2 array_tmp2 1 ats(2, array_tmp2, array_tmp5_a1, 1) 1 array_tmp5_a2 : --------------------------------------, 1 glob_h ats(1, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 2 1 array_tmp6 : array_tmp5 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp6 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 array_tmp2_g array_tmp1 2 2 array_tmp2 : -------------------------, 3 2 - array_tmp2 array_tmp1 2 2 array_tmp2_g : -------------------------, 3 2 array_tmp4_g array_tmp3 2 2 array_tmp4 : -------------------------, 3 2 - array_tmp4 array_tmp3 2 2 array_tmp4_g : -------------------------, 3 2 array_tmp2 - att(2, array_tmp2, array_tmp5_a1, 2) 3 array_tmp5_a1 : --------------------------------------------------, 3 array_tmp2 1 ats(3, array_tmp2, array_tmp5_a1, 1) 2 array_tmp5_a2 : --------------------------------------, 2 glob_h ats(2, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 3 2 array_tmp6 : array_tmp5 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp6 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 array_tmp2_g array_tmp1 3 2 array_tmp2 : -------------------------, 4 3 - array_tmp2 array_tmp1 3 2 array_tmp2_g : -------------------------, 4 3 array_tmp4_g array_tmp3 3 2 array_tmp4 : -------------------------, 4 3 - array_tmp4 array_tmp3 3 2 array_tmp4_g : -------------------------, 4 3 array_tmp2 - att(3, array_tmp2, array_tmp5_a1, 2) 4 array_tmp5_a1 : --------------------------------------------------, 4 array_tmp2 1 ats(4, array_tmp2, array_tmp5_a1, 1) 3 array_tmp5_a2 : --------------------------------------, 3 glob_h ats(3, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 4 3 array_tmp6 : array_tmp5 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp6 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 array_tmp2_g array_tmp1 4 2 array_tmp2 : -------------------------, 5 4 - array_tmp2 array_tmp1 4 2 array_tmp2_g : -------------------------, 5 4 array_tmp4_g array_tmp3 4 2 array_tmp4 : -------------------------, 5 4 - array_tmp4 array_tmp3 4 2 array_tmp4_g : -------------------------, 5 4 array_tmp2 - att(4, array_tmp2, array_tmp5_a1, 2) 5 array_tmp5_a1 : --------------------------------------------------, 5 array_tmp2 1 ats(5, array_tmp2, array_tmp5_a1, 1) 4 array_tmp5_a2 : --------------------------------------, 4 glob_h ats(4, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 5 4 array_tmp6 : array_tmp5 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp6 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_tmp2 : kkk array_tmp2_g array_tmp1 kkk - 1 2 -------------------------------, array_tmp2_g : kkk - 1 kkk - array_tmp2 array_tmp1 kkk - 1 2 -------------------------------, array_tmp4 : kkk - 1 kkk array_tmp4_g array_tmp3 kkk - 1 2 -------------------------------, array_tmp4_g : kkk - 1 kkk - array_tmp4 array_tmp3 kkk - 1 2 -------------------------------, array_tmp5_a1 : kkk - 1 kkk array_tmp2 - att(kkk - 1, array_tmp2, array_tmp5_a1, 2) kkk ----------------------------------------------------------, array_tmp2 1 ats(kkk, array_tmp2, array_tmp5_a1, 1) (kkk - 1) array_tmp5_a2 : ------------------------------------------------, kkk - 1 glob_h ats(kkk - 1, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------------, kkk kkk - 1 array_tmp6 : array_tmp5 , order_d : 1, kkk kkk if order_d + kkk < glob_max_terms then (if not subscript(array_y_set_initial, 1, order_d + kkk) then (temporary : array_tmp6 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%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(0.0) (%o56) exact_soln_y(x) := block(0.0) (%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/expt_sin_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), 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:1000000,"), 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, " (0.0) "), 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, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + 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_g, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5_c1, 1 + max_terms), array(array_tmp5_a1, 1 + max_terms), array(array_tmp5_a2, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 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_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 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_g : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term array(array_tmp5_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term), term array(array_tmp5_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_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), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, 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 ) = expt(sin(0.1 * x) , sin(0.2 * x));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-05-26T02:12:09-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_sin_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_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, "expt_sin_sin diffeq.max"), logitem_str(html_log_file, "expt_sin_sin 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/expt_sin_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), 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:1000000,"), 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, " (0.0) "), 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, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + 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_g, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5_c1, 1 + max_terms), array(array_tmp5_a1, 1 + max_terms), array(array_tmp5_a2, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 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_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 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_g : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term array(array_tmp5_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term), term array(array_tmp5_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_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), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, 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 ) = expt(sin(0.1 * x) , sin(0.2 * x));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-05-26T02:12:09-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_sin_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_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, "expt_sin_sin diffeq.max"), logitem_str(html_log_file, "expt_sin_sin 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/expt_sin_sinpostode.ode#################" "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "/* 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(" " (0.0) " "));" "/* 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 = 4.9 "" estimated_steps = 4900000.000000001 "" step_error = 2.04081632653061200000000000000000E-17 "" est_needed_step_err = 2.04081632653061200000000000000000E-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 = 6.158066706119337000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-138 "" estimated_step_error = 6.158066706119337000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-138 "" 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 = 4.13259024771666150000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 "" estimated_step_error = 4.13259024771666150000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 "" 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 = 2.77330972278200100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-122 "" estimated_step_error = 2.77330972278200100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-122 "" 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 = 1.861103571429221000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" estimated_step_error = 1.861103571429221000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" 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 = 1.24892106950604010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" estimated_step_error = 1.24892106950604010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" 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 = 8.380771622328244000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-99 "" estimated_step_error = 8.380771622328244000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-99 "" 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 = 5.6234411354117730000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-91 "" estimated_step_error = 5.6234411354117730000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-91 "" 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 = 3.77275485996358900000000000000000000000000000000000000000000000000000000000000000000000000000000000E-83 "" estimated_step_error = 3.77275485996358900000000000000000000000000000000000000000000000000000000000000000000000000000000000E-83 "" 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 = 2.5304145384643545000000000000000000000000000000000000000000000000000000000000000000000000000E-75 "" estimated_step_error = 2.5304145384643545000000000000000000000000000000000000000000000000000000000000000000000000000E-75 "" 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 = 1.69620519205534750000000000000000000000000000000000000000000000000000000000000000000E-67 "" estimated_step_error = 1.69620519205534750000000000000000000000000000000000000000000000000000000000000000000E-67 "" 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 = 1.135726209525316400000000000000000000000000000000000000000000000000000000000E-59 "" estimated_step_error = 1.135726209525316400000000000000000000000000000000000000000000000000000000000E-59 "" 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 = 7.5873694205637410000000000000000000000000000000000000000000000000000E-52 "" estimated_step_error = 7.5873694205637410000000000000000000000000000000000000000000000000000E-52 "" 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 = 5.04632114398428600000000000000000000000000000000000000000000E-44 "" estimated_step_error = 5.04632114398428600000000000000000000000000000000000000000000E-44 "" 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 = 3.327212595559371000000000000000000000000000000000000E-36 "" estimated_step_error = 3.327212595559371000000000000000000000000000000000000E-36 "" 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 = 2.1578615880663662000000000000000000000000000E-28 "" estimated_step_error = 2.1578615880663662000000000000000000000000000E-28 "" 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 = 1.359863871404512200000000000000000000E-20 "" estimated_step_error = 1.359863871404512200000000000000000000E-20 "" 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 = 8.2742829905347240000000000000E-13 "" estimated_step_error = 8.2742829905347240000000000000E-13 "" best_h = 3.276800E-2 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.0 " " absolute error = 0.0 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.11503396423404122 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 9.103889960356604000E-3 " " absolute error = 9.103889960356604000E-3 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.1265404017155627 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.81436824830770120E-2 " " absolute error = 1.81436824830770120E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.13804732616484777 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 2.71214308966240770E-2 " " absolute error = 2.71214308966240770E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.14955472701260386 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 3.60390223522624600E-2 " " absolute error = 3.60390223522624600E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.1610625945230743 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 4.48982021548457340E-2 " " absolute error = 4.48982021548457340E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.17257091966932722 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 5.37005930467322100E-2 " " absolute error = 5.37005930467322100E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.18407969403455426 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 6.24477107607942300E-2 " " absolute error = 6.24477107607942300E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.19558890973260887 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 7.11409767540201900E-2 " " absolute error = 7.11409767540201900E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.20709855934308463 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 7.97817287696724900E-2 " " absolute error = 7.97817287696724900E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.21860863585760196 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 8.83712296991079600E-2 " " absolute error = 8.83712296991079600E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.2301191326348582 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 9.69106750925982500E-2 " " absolute error = 9.69106750925982500E-2 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.2416300433626327 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.10540119958273614 " " absolute error = 0.10540119958273614 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.2531413620253883 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.11384388242241292 " " absolute error = 0.11384388242241292 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.26465308287640543 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.12223975229430539 " " absolute error = 0.12223975229430539 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.27616520041368475 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.13058979151534245 " " absolute error = 0.13058979151534245 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.2876777093589057 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.13889493973439263 " " absolute error = 0.13889493973439263 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.2991906046390004 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.14715609720214926 " " absolute error = 0.14715609720214926 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.3107038813699065 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.15537412767730044 " " absolute error = 0.15537412767730044 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.3222175348421486 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.16354986102144042 " " absolute error = 0.16354986102144042 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.3337315605080302 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.1716840955259996 " " absolute error = 0.1716840955259996 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.3452459539701632 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.17977760000716086 " " absolute error = 0.17977760000716086 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.3567607109711823 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.18783111569885816 " " absolute error = 0.18783111569885816 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.36827582738445547 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.1958453579692001 " " absolute error = 0.1958453579692001 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.37979129920570937 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.20382101788178328 " " absolute error = 0.20382101788178328 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.3913071225454282 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.21175876362017745 " " absolute error = 0.21175876362017745 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.4028232936219131 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.2196592417912324 " " absolute error = 0.2196592417912324 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.41433980875497856 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.2275230786206687 " " absolute error = 0.2275230786206687 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.42585666436017844 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.2353508810525855 " " absolute error = 0.2353508810525855 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.43737385694349795 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.24314323776297975 " " absolute error = 0.24314323776297975 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.44889138309646665 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.25090072009607284 " " absolute error = 0.25090072009607284 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.46040923949168355 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.25862388293113725 " " absolute error = 0.25862388293113725 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.47192742287867084 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.2663132654865758 " " absolute error = 0.2663132654865758 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.4834459300800139 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.2739693920672004 " " absolute error = 0.2739693920672004 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.4949647579878335 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.2815927727599659 " " absolute error = 0.2815927727599659 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.5064839035604328 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.2891839040828167 " " absolute error = 0.2891839040828167 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.518003363819268 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.29674326959078584 " " absolute error = 0.29674326959078584 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.5295231358460489 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3042713404430388 " " absolute error = 0.3042713404430388 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.5410432167800694 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3117685759341592 " " absolute error = 0.3117685759341592 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.5525636038157106 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.31923542399263377 " " absolute error = 0.31923542399263377 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.5640842942000852 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3266723216491904 " " absolute error = 0.3266723216491904 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.5756052852308473 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.33407969547738053 " " absolute error = 0.33407969547738053 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.5871265742541176 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3414579620085623 " " absolute error = 0.3414579620085623 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.598648158662564 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3488075281232351 " " absolute error = 0.3488075281232351 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.6101700358935509 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.80001449404137400E-2 " " Order of pole (six term test) = -1.0731235032024227 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3561287914204921 " " absolute error = 0.3561287914204921 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.621692203427424 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.78352431030394300E-2 " " Order of pole (six term test) = -1.0732876483847988 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.36342214056719585 " " absolute error = 0.36342214056719585 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.6332146587858946 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.11095432933079667 " " Order of pole (six term test) = -1.0734380375923624 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.37068795562833584 " " absolute error = 0.37068795562833584 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.6447373995305157 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.1309718584522961 " " Order of pole (six term test) = -1.0735752650739219 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3779266083798974 " " absolute error = 0.3779266083798974 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.6562604232611833 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.14915703280287063 " " Order of pole (six term test) = -1.0736995561847031 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3851384626054563 " " absolute error = 0.3851384626054563 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.667783727614831 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.16611880149401131 " " Order of pole (six term test) = -1.0738114643205652 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3923238743776088 " " absolute error = 0.3923238743776088 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.6793073102640783 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.18220884117448752 " " Order of pole (six term test) = -1.0739113079595946 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.3994831923252529 " " absolute error = 0.3994831923252529 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.6908311689160186 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.19764558168255122 " " Order of pole (six term test) = -1.0739995673899099 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.40661675788765395 " " absolute error = 0.40661675788765395 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.702355301311037 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.2125790017750666 " " Order of pole (six term test) = -1.074076556056811 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.4137249055561504 " " absolute error = 0.4137249055561504 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7138797052217235 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.22711597250848442 " " Order of pole (six term test) = -1.0741425487974805 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.42080796310428803 " " absolute error = 0.42080796310428803 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7254043784517922 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.24133113416375604 " " Order of pole (six term test) = -1.0741980436875114 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.4278662518071084 " " absolute error = 0.4278662518071084 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7369293188350713 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.2552862326360217 " " Order of pole (six term test) = -1.07424320282324 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.4349000866502607 " " absolute error = 0.4349000866502607 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7484545242345672 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.2690249649799101 " " Order of pole (six term test) = -1.0742784495285402 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.4419097765295563 " " absolute error = 0.4419097765295563 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7599799925415434 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.2825846282688807 " " Order of pole (six term test) = -1.0743040157276322 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.4488956244415378 " " absolute error = 0.4488956244415378 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7715057216746398 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.29599221800982384 " " Order of pole (six term test) = -1.0743203210219345 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.45585792766559186 " " absolute error = 0.45585792766559186 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7830317095790373 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.3092732550228232 " " Order of pole (six term test) = -1.0743275336917257 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.46279697793809776 " " absolute error = 0.46279697793809776 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7945579542257108 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.3224463205101643 " " Order of pole (six term test) = -1.0743259890919994 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.4697130616190674 " " absolute error = 0.4697130616190674 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8060844536106089 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.3355279018223874 " " Order of pole (six term test) = -1.0743159394752926 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.47660645985169986 " " absolute error = 0.47660645985169986 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8176112057539479 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.3485323592355792 " " Order of pole (six term test) = -1.0742975962092878 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.48347744871524545 " " absolute error = 0.48347744871524545 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8291382086995395 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.36147064629805764 " " Order of pole (six term test) = -1.0742712515626067 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.4903262993715458 " " absolute error = 0.4903262993715458 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8406654605141142 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.37435259956933337 " " Order of pole (six term test) = -1.0742371515960496 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.49715327820559213 " " absolute error = 0.49715327820559213 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8521929592866724 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.38718692569378854 " " Order of pole (six term test) = -1.0741955163492403 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5039586469604211 " " absolute error = 0.5039586469604211 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8637207031278944 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.3999807230172291 " " Order of pole (six term test) = -1.074146590056655 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5107426628666465 " " absolute error = 0.5107426628666465 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8752486901695233 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.41274096058687937 " " Order of pole (six term test) = -1.0740905490453265 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5175055787669053 " " absolute error = 0.5175055787669053 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8867769185638372 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.4254723635821177 " " Order of pole (six term test) = -1.0740276666144535 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5242476432354792 " " absolute error = 0.5242476432354792 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8983053864830911 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.4381803435825325 " " Order of pole (six term test) = -1.07395810916824 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5309691006933359 " " absolute error = 0.5309691006933359 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9098340921189877 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.4508697855938107 " " Order of pole (six term test) = -1.0738820305592398 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5376701915188188 " " absolute error = 0.5376701915188188 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9213630336822284 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.46354281028846905 " " Order of pole (six term test) = -1.073799748700317 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5443511521542008 " " absolute error = 0.5443511521542008 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9328922094019579 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.47620411709873983 " " Order of pole (six term test) = -1.0737113484767082 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5510122152083032 " " absolute error = 0.5510122152083032 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9444216175253608 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.4888563167878689 " " Order of pole (six term test) = -1.0736170382647376 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5576536095553698 " " absolute error = 0.5576536095553698 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9559512563172013 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5015016385727661 " " Order of pole (six term test) = -1.073517025866126 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5642755604303737 " " absolute error = 0.5642755604303737 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9674811240593839 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5141430558942701 " " Order of pole (six term test) = -1.0734114339279959 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5708782895209261 " " absolute error = 0.5708782895209261 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9790112190505535 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5267820806434216 " " Order of pole (six term test) = -1.073300474045622 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5774620150559433 " " absolute error = 0.5774620150559433 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9905415396056976 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5394213236989662 " " Order of pole (six term test) = -1.073184249754 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5840269518912223 " " absolute error = 0.5840269518912223 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0020720840557475 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5520615537626921 " " Order of pole (six term test) = -1.073062989480512 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5905733115920653 " " absolute error = 0.5905733115920653 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0136028507472374 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5647046270018976 " " Order of pole (six term test) = -1.0729368180628942 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.5971013025130842 " " absolute error = 0.5971013025130842 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0251338380419175 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5773523996727599 " " Order of pole (six term test) = -1.0728058433946188 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6036111298753133 " " absolute error = 0.6036111298753133 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0366650443164314 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5900049539898388 " " Order of pole (six term test) = -1.0726702998206505 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6101029958407453 " " absolute error = 0.6101029958407453 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.048196467961953 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6026644196424646 " " Order of pole (six term test) = -1.0725302444808982 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.616577099584405 " " absolute error = 0.616577099584405 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0597281073839293 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6153308165765143 " " Order of pole (six term test) = -1.0723858907972392 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.623033637364065 " " absolute error = 0.623033637364065 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0712599610016666 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6280055980028295 " " Order of pole (six term test) = -1.0722373258010869 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6294728025877052 " " absolute error = 0.6294728025877052 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.08279202724812 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6406897119193841 " " Order of pole (six term test) = -1.072084666144356 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6358947858788095 " " absolute error = 0.6358947858788095 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0943243045695943 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6533831911286881 " " Order of pole (six term test) = -1.0719280929443737 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6422997751395915 " " absolute error = 0.6422997751395915 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1058567914253707 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6660873627435677 " " Order of pole (six term test) = -1.0717676730209735 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6486879556122324 " " absolute error = 0.6486879556122324 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1173894862875742 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6788023855655463 " " Order of pole (six term test) = -1.0716035600580387 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6550595099382154 " " absolute error = 0.6550595099382154 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.128922387640794 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6915284813769819 " " Order of pole (six term test) = -1.071435894347923 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6614146182158303 " " absolute error = 0.6614146182158303 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1404554939818916 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7042669953082625 " " Order of pole (six term test) = -1.071264718206125 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6677534580559231 " " absolute error = 0.6677534580559231 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1519888038197081 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7170172701403114 " " Order of pole (six term test) = -1.0710902288086448 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.674076204635961 " " absolute error = 0.674076204635961 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1635223156748788 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7297803970505535 " " Order of pole (six term test) = -1.070912475951797 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6803830307524762 " " absolute error = 0.6803830307524762 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1750560280795266 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7425565693493902 " " Order of pole (six term test) = -1.0707315759543974 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6866741068719552 " " absolute error = 0.6866741068719552 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1865899395771322 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7553457042387186 " " Order of pole (six term test) = -1.0705476623407133 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6929496011802294 " " absolute error = 0.6929496011802294 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1981240487222307 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7681482530861573 " " Order of pole (six term test) = -1.0703608198082932 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.6992096796304279 " " absolute error = 0.6992096796304279 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.209658354080205 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7809651417560877 " " Order of pole (six term test) = -1.070171089271975 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7054545059895438 " " absolute error = 0.7054545059895438 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2211928542271584 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7937953477929243 " " Order of pole (six term test) = -1.0699786660626476 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7116842418836681 " " absolute error = 0.7116842418836681 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2327275477496222 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.806639511686558 " " Order of pole (six term test) = -1.0697836055189587 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7178990468419387 " " absolute error = 0.7178990468419387 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2442624332444026 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8194977507146008 " " Order of pole (six term test) = -1.0695860018232874 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7240990783392545 " " absolute error = 0.7240990783392545 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2557975093184013 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8323705780969703 " " Order of pole (six term test) = -1.0693859124198948 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7302844918377954 " " absolute error = 0.7302844918377954 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2673327745883822 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8452580102969524 " " Order of pole (six term test) = -1.0691834319682183 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7364554408273961 " " absolute error = 0.7364554408273961 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.278868227680891 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8581592545975737 " " Order of pole (six term test) = -1.0689787176918806 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7426120768648107 " " absolute error = 0.7426120768648107 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2904038672319282 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8710751032638048 " " Order of pole (six term test) = -1.0687717938938803 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7487545496119097 " " absolute error = 0.7487545496119097 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.301939691886952 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8840061581139727 " " Order of pole (six term test) = -1.0685626978918776 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7548830068728468 " " absolute error = 0.7548830068728468 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3134757003005781 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8969511583464904 " " Order of pole (six term test) = -1.0683516144940715 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7609975946302302 " " absolute error = 0.7609975946302302 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3250118911365039 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9099114232482666 " " Order of pole (six term test) = -1.0681385178222929 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.767098457080334 " " absolute error = 0.767098457080334 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3365482630672925 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9228856688745216 " " Order of pole (six term test) = -1.0679235884634757 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7731857366673822 " " absolute error = 0.7731857366673822 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3480848147742923 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9358747138056946 " " Order of pole (six term test) = -1.0677068359614843 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7792595741169372 " " absolute error = 0.7792595741169372 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.359621544947386 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.948878874659694 " " Order of pole (six term test) = -1.0674883063215077 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7853201084684223 " " absolute error = 0.7853201084684223 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3711584522849554 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.961897319996227 " " Order of pole (six term test) = -1.0672681373209976 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7913674771068069 " " absolute error = 0.7913674771068069 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3826955354936925 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9749305262882366 " " Order of pole (six term test) = -1.0670463580781195 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.7974018157934848 " " absolute error = 0.7974018157934848 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3942327932884286 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9879779022109112 " " Order of pole (six term test) = -1.0668230821509859 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8034232586963679 " " absolute error = 0.8034232586963679 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4057702243920718 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0010403990780656 " " Order of pole (six term test) = -1.0665982966251786 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.809431938419225 " " absolute error = 0.809431938419225 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4173078275354334 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0141171450934552 " " Order of pole (six term test) = -1.0663721334360599 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8154279860302873 " " absolute error = 0.8154279860302873 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4288456014570832 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0272080167423823 " " Order of pole (six term test) = -1.0661446617173596 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8214115310901461 " " absolute error = 0.8214115310901461 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4403835449033007 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0403136025323936 " " Order of pole (six term test) = -1.0659158930127965 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8273827016789633 " " absolute error = 0.8273827016789633 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4519216566278814 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0534334347427823 " " Order of pole (six term test) = -1.0656859208248814 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8333416244230194 " " absolute error = 0.8333416244230194 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.463459935392015 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.066567726475664 " " Order of pole (six term test) = -1.0654547828123935 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.839288424520616 " " absolute error = 0.839288424520616 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.47499837996426 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0797161962756385 " " Order of pole (six term test) = -1.065222554614115 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8452232257673565 " " absolute error = 0.8452232257673565 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4865369891203477 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0928787409805794 " " Order of pole (six term test) = -1.0649892959274219 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8511461505808222 " " absolute error = 0.8511461505808222 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4980757616430915 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.106055350027897 " " Order of pole (six term test) = -1.0647550576479627 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8570573200246626 " " absolute error = 0.8570573200246626 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.509614696322286 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1192456376315405 " " Order of pole (six term test) = -1.064519918221789 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8629568538321185 " " absolute error = 0.8629568538321185 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5211537919546085 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.132450216095868 " " Order of pole (six term test) = -1.0642838777550985 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8688448704289943 " " absolute error = 0.8688448704289943 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5326930473435494 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1456683598411184 " " Order of pole (six term test) = -1.064047038688658 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8747214869560965 " " absolute error = 0.8747214869560965 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5442324612992215 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.158900203450491 " " Order of pole (six term test) = -1.0638094354267658 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8805868192911548 " " absolute error = 0.8805868192911548 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5557720326383437 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1721459368516072 " " Order of pole (six term test) = -1.063571096711959 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8864409820702391 " " absolute error = 0.8864409820702391 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5673117601841164 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.185405001972379 " " Order of pole (six term test) = -1.0633321077858735 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8922840887086906 " " absolute error = 0.8922840887086906 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5788516427661659 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1986776949986486 " " Order of pole (six term test) = -1.0630924879317671 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.8981162514215774 " " absolute error = 0.8981162514215774 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5903916792203812 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2119634875705583 " " Order of pole (six term test) = -1.0628523173324442 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9039375812436917 " " absolute error = 0.9039375812436917 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6019318683888815 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2252630573152845 " " Order of pole (six term test) = -1.0626115835338545 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9097481880491 " " absolute error = 0.9097481880491 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6134722091199165 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.238575037365756 " " Order of pole (six term test) = -1.0623704283880198 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9155481805702587 " " absolute error = 0.9155481805702587 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6250127002677848 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2519005232579512 " " Order of pole (six term test) = -1.0621288062600645 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9213376664167097 " " absolute error = 0.9213376664167097 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6365533406927482 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2652393479797626 " " Order of pole (six term test) = -1.0618867658097368 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9271167520933651 " " absolute error = 0.9271167520933651 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.648094129260928 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2785909750939568 " " Order of pole (six term test) = -1.0616443831798712 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9328855430183945 " " absolute error = 0.9328855430183945 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6596350648443063 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2919547026859248 " " Order of pole (six term test) = -1.0614017452935247 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9386441435407255 " " absolute error = 0.9386441435407255 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6711761463204964 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.305331819190008 " " Order of pole (six term test) = -1.0611587888538025 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9443926569571666 " " absolute error = 0.9443926569571666 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.682717372572864 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.318720878186178 " " Order of pole (six term test) = -1.0609156550956804 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9501311855291664 " " absolute error = 0.9501311855291664 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6942587424902493 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.332123135939225 " " Order of pole (six term test) = -1.0606722819457737 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.955859830499215 " " absolute error = 0.955859830499215 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7058002549670865 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3455373559284758 " " Order of pole (six term test) = -1.0604287924453377 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9615786921068993 " " absolute error = 0.9615786921068993 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7173419089031912 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3589643054209533 " " Order of pole (six term test) = -1.06018516047361 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9672878696046229 " " absolute error = 0.9672878696046229 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7288837032037394 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3724029883760793 " " Order of pole (six term test) = -1.0599414886744611 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.972987461272996 " " absolute error = 0.972987461272996 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7404256367792357 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3858535994150036 " " Order of pole (six term test) = -1.0596977917636163 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9786775644359078 " " absolute error = 0.9786775644359078 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7519677085453458 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3993170085969586 " " Order of pole (six term test) = -1.0594540341501375 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9843582754752874 " " absolute error = 0.9843582754752874 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7635099174229822 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4127919403603448 " " Order of pole (six term test) = -1.059210336941792 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.9900296898455623 " " absolute error = 0.9900296898455623 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.77505226233811 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4262781702669518 " " Order of pole (six term test) = -1.058966742681969 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 0.995691902087822 " " absolute error = 0.995691902087822 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7865947422217139 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.439776567354663 " " Order of pole (six term test) = -1.0587232146387198 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0013450058436955 " " absolute error = 1.0013450058436955 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7981373560097642 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4532866427086348 " " Order of pole (six term test) = -1.058479813978769 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0069890938689479 " " absolute error = 1.0069890938689479 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.809680102643187 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4668082635958724 " " Order of pole (six term test) = -1.0582365757634768 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.012624258046806 " " absolute error = 1.012624258046806 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8212229810677003 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4803407961996584 " " Order of pole (six term test) = -1.0579935688912023 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0182505894010172 " " absolute error = 1.0182505894010172 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8327659902338456 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4938850439686429 " " Order of pole (six term test) = -1.057750760305673 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0238681781086512 " " absolute error = 1.0238681781086512 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8443091290969338 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5074405014087178 " " Order of pole (six term test) = -1.0575082094934913 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0294771135126475 " " absolute error = 1.0294771135126475 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8558523966169038 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5210068831832186 " " Order of pole (six term test) = -1.0572659591304205 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.035077484134119 " " absolute error = 1.035077484134119 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8673957917583395 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5345845843821198 " " Order of pole (six term test) = -1.0570240036929128 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0406693776844147 " " absolute error = 1.0406693776844147 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8789393134904326 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.548172169980179 " " Order of pole (six term test) = -1.056782464816406 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.046252881076949 " " absolute error = 1.046252881076949 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8904829607868963 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5617716927271676 " " Order of pole (six term test) = -1.0565412219867572 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0518280804388025 " " absolute error = 1.0518280804388025 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.902026732625863 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5753818037601677 " " Order of pole (six term test) = -1.0563003887556572 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0573950611221017 " " absolute error = 1.0573950611221017 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9135706279899343 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5890024496373985 " " Order of pole (six term test) = -1.0560599892549476 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0629539077151795 " " absolute error = 1.0629539077151795 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.925114645866072 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6026334214985818 " " Order of pole (six term test) = -1.0558200583284112 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0685047040535263 " " absolute error = 1.0685047040535263 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9366587852455668 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.616275074241856 " " Order of pole (six term test) = -1.0555805904005222 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0740475332305321 " " absolute error = 1.0740475332305321 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9482030451239811 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.629926522340912 " " Order of pole (six term test) = -1.055341664571456 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0795824776080292 " " absolute error = 1.0795824776080292 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9597474245010662 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6435890419463832 " " Order of pole (six term test) = -1.0551032136191836 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.0851096188266354 " " absolute error = 1.0851096188266354 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9712919223808458 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.657261313452709 " " Order of pole (six term test) = -1.0548653447789214 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.090629037815908 " " absolute error = 1.090629037815908 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9828365377713881 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6709437557040188 " " Order of pole (six term test) = -1.0546280472131606 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.096140814804307 " " absolute error = 1.096140814804307 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.994381269684917 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6846361723369057 " " Order of pole (six term test) = -1.0543913520290396 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1016450293289772 " " absolute error = 1.1016450293289772 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.00592611713767 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.698338272198507 " " Order of pole (six term test) = -1.0541552944673818 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1071417602453497 " " absolute error = 1.1071417602453497 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0174710791499217 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7120503940433849 " " Order of pole (six term test) = -1.0539198699147239 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.11263108573657 " " absolute error = 1.11263108573657 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0290161547459014 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7257719182089997 " " Order of pole (six term test) = -1.0536851348450629 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.118113083322754 " " absolute error = 1.118113083322754 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0405613429537217 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7395036091218992 " " Order of pole (six term test) = -1.053451055379215 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1235878298700768 " " absolute error = 1.1235878298700768 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.052106642805429 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7532444914634238 " " Order of pole (six term test) = -1.0532177105211176 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1290554015997003 " " absolute error = 1.1290554015997003 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0636520533369045 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7669947829030375 " " Order of pole (six term test) = -1.0529851010762652 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.134515874096539 " " absolute error = 1.134515874096539 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.075197573587831 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7807544918299945 " " Order of pole (six term test) = -1.0527532422912191 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1399693223178715 " " absolute error = 1.1399693223178715 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.086743202601633 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7945239674994364 " " Order of pole (six term test) = -1.0525221259000617 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1454158206017984 " " absolute error = 1.1454158206017984 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.098288939425495 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.808301909284422 " " Order of pole (six term test) = -1.0522918489632662 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1508554426755524 " " absolute error = 1.1508554426755524 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.109834783110284 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.822089208181265 " " Order of pole (six term test) = -1.052062368741856 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.156288261663663 " " absolute error = 1.156288261663663 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1213807327104885 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8358858097492206 " " Order of pole (six term test) = -1.0518337029439913 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1617143500959766 " " absolute error = 1.1617143500959766 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.132926787284268 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8496910084152824 " " Order of pole (six term test) = -1.0516059087734657 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.16713377991554 " " absolute error = 1.16713377991554 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.144472945893361 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8635053382958713 " " Order of pole (six term test) = -1.05137896661223 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1725466224863452 " " absolute error = 1.1725466224863452 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.156019207603004 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8773284819787373 " " Order of pole (six term test) = -1.0511529087376896 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1779529486009441 " " absolute error = 1.1779529486009441 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1675655714819535 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8911598878480544 " " Order of pole (six term test) = -1.0509277806284292 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1833528284879284 " " absolute error = 1.1833528284879284 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.179112036602546 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9050002876739536 " " Order of pole (six term test) = -1.0507035514033873 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1887463318192864 " " absolute error = 1.1887463318192864 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1906586020404526 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9188493702362888 " " Order of pole (six term test) = -1.0504802516077252 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.1941335277176315 " " absolute error = 1.1941335277176315 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2022052668747847 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9327067699728648 " " Order of pole (six term test) = -1.0502579143583226 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.199514484763311 " " absolute error = 1.199514484763311 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.213752030188076 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.94657233790137 " " Order of pole (six term test) = -1.0500365606155047 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2048892710013934 " " absolute error = 1.2048892710013934 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2252988910661635 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.960446738289119 " " Order of pole (six term test) = -1.0498161624532045 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.21025795394854 " " absolute error = 1.21025795394854 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2368458485982896 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9743288129346064 " " Order of pole (six term test) = -1.0495967991877286 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2156206005997614 " " absolute error = 1.2156206005997614 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.248392901876883 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.988219037654732 " " Order of pole (six term test) = -1.0493784531754589 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2209772774350613 " " absolute error = 1.2209772774350613 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2599400499976854 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.002117868414139 " " Order of pole (six term test) = -1.0491611089451762 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2263280504259717 " " absolute error = 1.2263280504259717 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2714872920596747 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.016024747065562 " " Order of pole (six term test) = -1.0489448096770015 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.231672985041979 " " absolute error = 1.231672985041979 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.283034627165034 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.029939050937737 " " Order of pole (six term test) = -1.048729600861023 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2370121462568457 " " absolute error = 1.2370121462568457 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2945820544190876 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0438613544038153 " " Order of pole (six term test) = -1.0485154593691757 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2423455985548295 " " absolute error = 1.2423455985548295 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.306129572930373 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0577916423300064 " " Order of pole (six term test) = -1.0483023963759948 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2476734059367989 " " absolute error = 1.2476734059367989 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3176771818104753 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0717294554113703 " " Order of pole (six term test) = -1.048090447293971 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.252995631926253 " " absolute error = 1.252995631926253 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.329224880174092 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0856751503211757 " " Order of pole (six term test) = -1.0478796009631548 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2583123395752416 " " absolute error = 1.2583123395752416 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.340772667139004 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.09962838718592 " " Order of pole (six term test) = -1.047669886068027 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2636235914701917 " " absolute error = 1.2636235914701917 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.352320541826043 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.113589381891826 " " Order of pole (six term test) = -1.0474612995172699 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2689294497376404 " " absolute error = 1.2689294497376404 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3638685033590114 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.127557130064683 " " Order of pole (six term test) = -1.0472539054390921 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2742299760498765 " " absolute error = 1.2742299760498765 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.375416550864732 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.14153269433279 " " Order of pole (six term test) = -1.047047653986727 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2795252316304926 " " absolute error = 1.2795252316304926 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3869646834729914 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.155515206353938 " " Order of pole (six term test) = -1.0468426004617761 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2848152772598496 " " absolute error = 1.2848152772598496 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.398512900316451 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1695056887879476 " " Order of pole (six term test) = -1.0466386986175866 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2901001732804547 " " absolute error = 1.2901001732804547 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4100612005308233 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.183502942294289 " " Order of pole (six term test) = -1.046436020657211 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.2953799796022563 " " absolute error = 1.2953799796022563 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4216095832545657 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1975073231338675 " " Order of pole (six term test) = -1.046234555242826 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.300654755707855 " " absolute error = 1.300654755707855 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4331580476290773 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2115185608374115 " " Order of pole (six term test) = -1.0460343245559276 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3059245606576342 " " absolute error = 1.3059245606576342 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4447065927985725 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.225536623351794 " " Order of pole (six term test) = -1.0458353373373654 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3111894530948107 " " absolute error = 1.3111894530948107 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4562552179101345 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2395623092423538 " " Order of pole (six term test) = -1.0456375601279753 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3164494912504086 " " absolute error = 1.3164494912504086 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.467803922113542 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2535946848999697 " " Order of pole (six term test) = -1.0454410484882057 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3217047329481546 " " absolute error = 1.3217047329481546 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.479352704561478 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2676336552143614 " " Order of pole (six term test) = -1.0452458136624134 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.326955235609301 " " absolute error = 1.326955235609301 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4909015644093033 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.281679382933144 " " Order of pole (six term test) = -1.045051855097995 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3322010562573727 " " absolute error = 1.3322010562573727 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5024505008151072 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2957317277354625 " " Order of pole (six term test) = -1.0448591860432117 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3374422515228432 " " absolute error = 1.3374422515228432 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.513999512939718 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3097909160131342 " " Order of pole (six term test) = -1.044667802310645 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.34267887764774 " " absolute error = 1.34267887764774 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5255485999465996 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3238565872182737 " " Order of pole (six term test) = -1.0444777279895163 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.34791099049018 " " absolute error = 1.34791099049018 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.537097761001988 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.337928459962941 " " Order of pole (six term test) = -1.0442889835155427 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.353138645528837 " " absolute error = 1.353138645528837 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5486469952746655 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3520071335476946 " " Order of pole (six term test) = -1.0441015460195917 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3583618978673417 " " absolute error = 1.3583618978673417 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.56019630193609 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.366091947062097 " " Order of pole (six term test) = -1.0439154527168437 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3635808022386173 " " absolute error = 1.3635808022386173 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.571745680160318 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3801830941303708 " " Order of pole (six term test) = -1.0437307013027795 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.368795413009149 " " absolute error = 1.368795413009149 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5832951291240254 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3942805024201563 " " Order of pole (six term test) = -1.0435473004890934 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.374005784183192 " " absolute error = 1.374005784183192 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.594844648006401 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.408384364568057 " " Order of pole (six term test) = -1.0433652473077828 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3792119694069156 " " absolute error = 1.3792119694069156 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6063942359892165 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.422494016229532 " " Order of pole (six term test) = -1.043184577936831 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3844140219724876 " " absolute error = 1.3844140219724876 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6179438922567955 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.4366099880424708 " " Order of pole (six term test) = -1.0430052738114703 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3896119948220984 " " absolute error = 1.3896119948220984 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6294936159959175 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.4507322083459147 " " Order of pole (six term test) = -1.0428273431916377 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3948059405519262 " " absolute error = 1.3948059405519262 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.64104340639593 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.4648601700482566 " " Order of pole (six term test) = -1.0426508147848423 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.3999959114160447 " " absolute error = 1.3999959114160447 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.652593262648596 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.4789940479121224 " " Order of pole (six term test) = -1.0424756856195163 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4051819593302741 " " absolute error = 1.4051819593302741 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6641431839481906 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.493133814649908 " " Order of pole (six term test) = -1.0423019619606801 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4103641358759758 " " absolute error = 1.4103641358759758 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6756931694913977 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.507279553607109 " " Order of pole (six term test) = -1.042129645194784 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4155424923037934 " " absolute error = 1.4155424923037934 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.687243218477335 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.5214308520445825 " " Order of pole (six term test) = -1.0419587581395913 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4207170795373392 " " absolute error = 1.4207170795373392 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6987933301075406 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.5355875061454594 " " Order of pole (six term test) = -1.0417893139785388 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4258879481768285 " " absolute error = 1.4258879481768285 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7103435035858965 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.549750289040029 " " Order of pole (six term test) = -1.0416212840743473 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4310551485026612 " " absolute error = 1.4310551485026612 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7218937381187307 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.5639189711370967 " " Order of pole (six term test) = -1.041454682960147 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4362187304789535 " " absolute error = 1.4362187304789535 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.733444032914693 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.5780926983751096 " " Order of pole (six term test) = -1.0412895514679725 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.441378743757019 " " absolute error = 1.441378743757019 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7449943871847537 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.5922722159462546 " " Order of pole (six term test) = -1.041125861770249 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4465352376787997 " " absolute error = 1.4465352376787997 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7565448001422945 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6064573116082954 " " Order of pole (six term test) = -1.040963627968063 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4516882612802513 " " absolute error = 1.4516882612802513 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7680952710028772 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.620647336655409 " " Order of pole (six term test) = -1.0408028798843958 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4568378632946781 " " absolute error = 1.4568378632946781 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.779645798984487 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6348432103487274 " " Order of pole (six term test) = -1.0406435845983317 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4619840921560228 " " absolute error = 1.4619840921560228 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.791196383307303 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6490443485369584 " " Order of pole (six term test) = -1.0404857694630802 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4671269960021094 " " absolute error = 1.4671269960021094 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8027470231938327 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6632509250115226 " " Order of pole (six term test) = -1.0403294313916973 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4722666226778427 " " absolute error = 1.4722666226778427 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.814297717868804 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.677462306971813 " " Order of pole (six term test) = -1.0401745996672886 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4774030197383619 " " absolute error = 1.4774030197383619 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.825848466559157 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6916791222174434 " " Order of pole (six term test) = -1.0400212521457561 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4825362344521504 " " absolute error = 1.4825362344521504 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8373992684941016 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.7059011841202154 " " Order of pole (six term test) = -1.039869400813492 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4876663138041046 " " absolute error = 1.4876663138041046 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8489501229050176 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.7201280265633176 " " Order of pole (six term test) = -1.0397190663907487 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4927933044985584 " " absolute error = 1.4927933044985584 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.860501029025521 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.734359892374879 " " Order of pole (six term test) = -1.0395702431039773 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.4979172529622675 " " absolute error = 1.4979172529622675 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8720519860913463 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.7485971977604455 " " Order of pole (six term test) = -1.0394229185684125 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.503038205347353 " " absolute error = 1.503038205347353 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.883602993340455 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.762839111558711 " " Order of pole (six term test) = -1.0392771272149481 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.508156207534204 " " absolute error = 1.508156207534204 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.895154050012921 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.7770860816224223 " " Order of pole (six term test) = -1.039132855430072 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.513271305134342 " " absolute error = 1.513271305134342 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9067051553509655 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.791337821241273 " " Order of pole (six term test) = -1.0389901166591429 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5183835434932453 " " absolute error = 1.5183835434932453 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9182563085989535 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.805594679585577 " " Order of pole (six term test) = -1.0388489017292706 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5234929676931366 " " absolute error = 1.5234929676931366 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9298075090033486 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.819855963114102 " " Order of pole (six term test) = -1.0387092379122738 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5285996225557315 " " absolute error = 1.5285996225557315 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9413587558127396 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.8341220504572413 " " Order of pole (six term test) = -1.0385711151260075 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5337035526449514 " " absolute error = 1.5337035526449514 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.952910048277737 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.848392955949933 " " Order of pole (six term test) = -1.038434535189051 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5388048022696 " " absolute error = 1.5388048022696 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9644613856510817 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.862668605613554 " " Order of pole (six term test) = -1.0382995032952547 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.543903415486003 " " absolute error = 1.543903415486003 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9760127671875884 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.8769488826701104 " " Order of pole (six term test) = -1.038166026717608 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5489994361006143 " " absolute error = 1.5489994361006143 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.987564192144069 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.8912333883381205 " " Order of pole (six term test) = -1.0380341208964516 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5540929076725858 " " absolute error = 1.5540929076725858 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9991156597794104 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.905522481511233 " " Order of pole (six term test) = -1.037903776476801 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = 0.0 " " y[1] (numeric) = 1.5591838735163046 " " absolute error = 1.5591838735163046 " " relative error = -1. "%" Correct digits = -1 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.010667169354502 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.9198163706048614 " " Order of pole (six term test) = -1.0377749884166079 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));" Iterations = 252 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 50 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 49 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 40 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 5 Minutes 40 Seconds "Time to Timeout " Unknown Percent Done = 51.63265306122424 "%" (%o58) true (%o58) diffeq.max