(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) display_poles() := block([rad_given], if glob_type_given_pole = 4 then (rad_given : sqrt(expt(array_given_rad_poles , 2.0) 1, 2 + expt(array_x - array_given_rad_poles , 2.0)), 1 1, 1 omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_poles # glob_large_float then (omniout_float(ALWAYS, 1, 1 "Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4, 1, 1 " "), omniout_str(ALWAYS, "Order of pole (ratio test) Not computed")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if (array_real_poles > 0.0) and (array_real_poles # glob_large_float) 1, 1 1, 1 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles , 1, 1 4, " "), omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles , 1, 2 4, " ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if (array_complex_poles > 0.0) and (array_complex_poles # 1, 1 1, 1 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles , 4, " "), omniout_float(ALWAYS, 1, 1 "Order of pole (six term test) ", 4, array_complex_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO COMPLEX POLE (six term test) for Equation 1")) (%o3) display_poles() := block([rad_given], if glob_type_given_pole = 4 then (rad_given : sqrt(expt(array_given_rad_poles , 2.0) 1, 2 + expt(array_x - array_given_rad_poles , 2.0)), 1 1, 1 omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_poles # glob_large_float then (omniout_float(ALWAYS, 1, 1 "Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4, 1, 1 " "), omniout_str(ALWAYS, "Order of pole (ratio test) Not computed")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if (array_real_poles > 0.0) and (array_real_poles # glob_large_float) 1, 1 1, 1 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles , 1, 1 4, " "), omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles , 1, 2 4, " ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if (array_complex_poles > 0.0) and (array_complex_poles # 1, 1 1, 1 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles , 4, " "), omniout_float(ALWAYS, 1, 1 "Order of pole (six term test) ", 4, array_complex_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO COMPLEX POLE (six term test) for Equation 1")) (%i4) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o4) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i5) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o5) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), est_tmp : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%o6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), est_tmp : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%i7) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o7) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i8) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o8) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > 1, 1 glob_small_float then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > 1, 1 glob_small_float then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i11) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad], array_pole : glob_large_float, array_pole : glob_large_float, 1 2 tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float, tmp_ratio : glob_large_float, rad_c : glob_large_float, array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0, while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) = 1, n 0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0 1, 1 + n array_y_higher glob_h 1, n tmp_rad else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------, array_y_higher prev_tmp_rad 1, 1 + n if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5) then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0 then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0 then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n), if found_sing = 1 then (if rad_c < array_pole 1 then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms, 1 1, 1 m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0) 1, m or (omniabs(array_y_higher ) = 0.0) 1, m - 1 or (omniabs(array_y_higher ) = 0.0)) do m : m - 1, 1, m - 2 array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, glob_h if omniabs(hdrc) > 0.0 then (rcs : ------, hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) ord_no : -----------------------------------------------------, hdrc array_real_poles : rcs, array_real_poles : ord_no) 1, 1 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float)) 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) # 1, n 0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) = 0.0) rm4 rm3 rm2 or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_poles : rad_c, 1, 1 array_complex_poles : ord_no), if array_pole glob_ratio_of_radius < 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()) (%o11) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad], array_pole : glob_large_float, array_pole : glob_large_float, 1 2 tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float, tmp_ratio : glob_large_float, rad_c : glob_large_float, array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0, while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) = 1, n 0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0 1, 1 + n array_y_higher glob_h 1, n tmp_rad else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------, array_y_higher prev_tmp_rad 1, 1 + n if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5) then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0 then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0 then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n), if found_sing = 1 then (if rad_c < array_pole 1 then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms, 1 1, 1 m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0) 1, m or (omniabs(array_y_higher ) = 0.0) 1, m - 1 or (omniabs(array_y_higher ) = 0.0)) do m : m - 1, 1, m - 2 array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, glob_h if omniabs(hdrc) > 0.0 then (rcs : ------, hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) ord_no : -----------------------------------------------------, hdrc array_real_poles : rcs, array_real_poles : ord_no) 1, 1 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float)) 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) # 1, n 0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) = 0.0) rm4 rm3 rm2 or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_poles : rad_c, 1, 1 array_complex_poles : ord_no), if array_pole glob_ratio_of_radius < 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()) (%i12) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o12) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4 : exp(array_tmp3 ), array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4 : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp5 : array_tmp4 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp5 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, array_tmp3 : 0.0, 2, 2 3 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 3 2.0 array_tmp4 : att(2, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 4 4 2.0 array_tmp4 : att(3, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 5 5 2.0 array_tmp4 : att(4, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4 : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , 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_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4 : exp(array_tmp3 ), array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4 : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp5 : array_tmp4 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp5 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, array_tmp3 : 0.0, 2, 2 3 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 3 2.0 array_tmp4 : att(2, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 4 4 2.0 array_tmp4 : att(3, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 5 5 2.0 array_tmp4 : att(4, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4 : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , 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_tmp5 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(20.0 exp(sqrt(0.2 + 0.1 x)) sqrt(0.2 + 0.1 x) - 20.0 exp(sqrt(0.2 + 0.1 x))) (%o56) exact_soln_y(x) := block(20.0 exp(sqrt(0.2 + 0.1 x)) sqrt(0.2 + 0.1 x) - 20.0 exp(sqrt(0.2 + 0.1 x))) (%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 0.0, float), define_variable(glob_smallish_float, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/exp_sqrtpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), 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:0.0,"), 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, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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, " (20.\ 0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x \ + 0.2))) "), 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, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_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 : 0.0, 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_display_interval : 0.1, glob_max_minutes : 10, 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 ) = exp(sqrt(0.1 * x + 0.2));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-05-26T00:55:11-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "exp_sqrt"), logitem_str(html_log_file, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 189 "), logitem_str(html_log_file, "exp_sqrt diffeq.max"), logitem_str(html_log_file, "exp_sqrt 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/exp_sqrtpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), 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:0.0,"), 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, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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, " (20.\ 0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x \ + 0.2))) "), 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, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_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 : 0.0, 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_display_interval : 0.1, glob_max_minutes : 10, 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 ) = exp(sqrt(0.1 * x + 0.2));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-05-26T00:55:11-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "exp_sqrt"), logitem_str(html_log_file, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 189 "), logitem_str(html_log_file, "exp_sqrt diffeq.max"), logitem_str(html_log_file, "exp_sqrt 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/exp_sqrtpostode.ode#################" "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.0," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* 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(" " (20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 5. "" estimated_steps = 5000000. "" step_error = 2.00000000000000000E-17 "" est_needed_step_err = 2.00000000000000000E-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 = 1.1720747881514175000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 "" estimated_step_error = 1.1720747881514175000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 "" 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 = 7.86565897109439200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 "" estimated_step_error = 7.86565897109439200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 "" 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 = 5.278551986510086000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 "" estimated_step_error = 5.278551986510086000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 "" 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 = 3.54237305914462700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 "" estimated_step_error = 3.54237305914462700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 "" 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 = 2.377242004013287700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" estimated_step_error = 2.377242004013287700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" 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 = 1.5953343124698974000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 "" estimated_step_error = 1.5953343124698974000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 "" 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 = 1.07060296169847770000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 "" estimated_step_error = 1.07060296169847770000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 "" 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 = 7.184590538324873000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" estimated_step_error = 7.184590538324873000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" 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 = 4.821357087351180000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" estimated_step_error = 4.821357087351180000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" 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 = 3.235370074304397000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" estimated_step_error = 3.235370074304397000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" 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 = 2.17096795689045000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" estimated_step_error = 2.17096795689045000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" 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 = 1.45657362721387460000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" estimated_step_error = 1.45657362721387460000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" 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 = 9.770362651387945000000000000000000000000000000000000000000000000000000000000000000000000000E-75 "" estimated_step_error = 9.770362651387945000000000000000000000000000000000000000000000000000000000000000000000000000E-75 "" 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 = 6.5506977943914160000000000000000000000000000000000000000000000000000000000000000000E-67 "" estimated_step_error = 6.5506977943914160000000000000000000000000000000000000000000000000000000000000000000E-67 "" 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 = 4.387959204904177700000000000000000000000000000000000000000000000000000000000E-59 "" estimated_step_error = 4.387959204904177700000000000000000000000000000000000000000000000000000000000E-59 "" 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 = 2.933846174711976000000000000000000000000000000000000000000000000000E-51 "" estimated_step_error = 2.933846174711976000000000000000000000000000000000000000000000000000E-51 "" 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 = 1.95445525958865360000000000000000000000000000000000000000000E-43 "" estimated_step_error = 1.95445525958865360000000000000000000000000000000000000000000E-43 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.292707456262763300000000000000000000000000000000000E-35 "" estimated_step_error = 1.292707456262763300000000000000000000000000000000000E-35 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.0 " " y[1] (analytic) = -17.290587327796203 " " y[1] (numeric) = -17.290587327796203 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.243621849784292 " " "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 = 26.491795563639077 " " Order of pole (six term test) = -2.494529568939207 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.00E-2 " " y[1] (analytic) = -17.274939105918932 " " y[1] (numeric) = -17.27493910591893 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.056570883994161500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.254838549445759 " " "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 = 26.559783936302743 " " Order of pole (six term test) = -2.494723469874927 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.00E-2 " " y[1] (analytic) = -17.259273422614413 " " y[1] (numeric) = -17.259273422614413 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.26605523508521 " " "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 = 26.62540421328101 " " Order of pole (six term test) = -2.4946248144561096 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.00E-2 " " y[1] (analytic) = -17.243590301745535 " " y[1] (numeric) = -17.243590301745535 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.277271906702706 " " "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 = 26.69062694698068 " " Order of pole (six term test) = -2.4944954806442805 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.00E-2 " " y[1] (analytic) = -17.22788976697712 " " y[1] (numeric) = -17.227889766977118 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.062187375734454400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2884885642983024 " " "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 = 26.75576850559894 " " Order of pole (six term test) = -2.494377161503003 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.00E-2 " " y[1] (analytic) = -17.2121718417784 " " y[1] (numeric) = -17.2121718417784 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.299705207872049 " " "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 = 26.8223211672933 " " Order of pole (six term test) = -2.494465457557439 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.000000000000001000E-2 " " y[1] (analytic) = -17.196436549425442 " " y[1] (numeric) = -17.196436549425442 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.310921837424006 " " "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 = 26.887359670519317 " " Order of pole (six term test) = -2.494375733515696 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.00E-2 " " y[1] (analytic) = -17.18068391300352 " " y[1] (numeric) = -17.18068391300352 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3221384529542277 " " "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 = 26.953199162318707 " " Order of pole (six term test) = -2.494411508495059 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.00E-2 " " y[1] (analytic) = -17.164913955409432 " " y[1] (numeric) = -17.164913955409435 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.069753269972484700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3333550544627704 " " "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 = 27.019293284316348 " " Order of pole (six term test) = -2.4945005413979846 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.00E-2 " " y[1] (analytic) = -17.149126699353832 " " y[1] (numeric) = -17.149126699353832 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.344571641949686 " " "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 = 27.082988878249218 " " Order of pole (six term test) = -2.4942974146651515 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.99999999999999900E-2 " " y[1] (analytic) = -17.13332216736344 " " y[1] (numeric) = -17.133322167363442 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.073569646386454500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.355788215415036 " " "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 = 27.147737459892507 " " Order of pole (six term test) = -2.494251669694707 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10999999999999999 " " y[1] (analytic) = -17.1175003817833 " " y[1] (numeric) = -17.117500381783305 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.07548625649884720000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3670047748588705 " " "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 = 27.213122604554034 " " Order of pole (six term test) = -2.494308177492247 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11999999999999998 " " y[1] (analytic) = -17.10166136477895 " " y[1] (numeric) = -17.101661364778955 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.15481701224344470000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.378221320281248 " " "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 = 27.278178587906396 " " Order of pole (six term test) = -2.494341418954347 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12999999999999998 " " y[1] (analytic) = -17.085805138338557 " " y[1] (numeric) = -17.08580513833856 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.079336414078974400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.389437851682221 " " "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 = 27.343038643012996 " " Order of pole (six term test) = -2.494368576533317 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13999999999999999 " " y[1] (analytic) = -17.069931724275037 " " y[1] (numeric) = -17.06993172427504 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.081269999310079400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4006543690618454 " " "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 = 27.405623092497706 " " Order of pole (six term test) = -2.4941223673461845 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15 " " y[1] (analytic) = -17.05404114422813 " " y[1] (numeric) = -17.054041144228137 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16641856174118900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.41187087242018 " " "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 = 27.47055042339306 " " Order of pole (six term test) = -2.494196553311278 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16 " " y[1] (analytic) = -17.038133419666444 " " y[1] (numeric) = -17.03813341966645 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17030855586533200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.423087361757281 " " "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 = 27.534540772318486 " " Order of pole (six term test) = -2.4941693414789796 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17 " " y[1] (analytic) = -17.02220857188945 " " y[1] (numeric) = -17.022208571889458 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17421001957110070000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.434303837073197 " " "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 = 27.598044906382007 " " Order of pole (six term test) = -2.494098806706438 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000002 " " y[1] (analytic) = -17.006266622029468 " " y[1] (numeric) = -17.00626662202948 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.26718448750840400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.445520298367987 " " "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 = 27.662564700006712 " " Order of pole (six term test) = -2.4941763193673943 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000003 " " y[1] (analytic) = -16.990307591053615 " " y[1] (numeric) = -16.990307591053625 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.27307126682840800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4567367456417077 " " "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 = 27.726175719864674 " " Order of pole (six term test) = -2.494156301720439 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000004 " " y[1] (analytic) = -16.9743314997657 " " y[1] (numeric) = -16.974331499765714 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37196723499724200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.467953178894412 " " "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 = 27.789460629900493 " " Order of pole (six term test) = -2.4941131361595907 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000005 " " y[1] (analytic) = -16.95833836880813 " " y[1] (numeric) = -16.958338368808143 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37986270007465100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4791695981261586 " " "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 = 27.852442576145464 " " Order of pole (six term test) = -2.494049777513059 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000006 " " y[1] (analytic) = -16.942328218663732 " " y[1] (numeric) = -16.942328218663743 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29083612290101700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.490386003337003 " " "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 = 27.915381061011526 " " Order of pole (six term test) = -2.493998984659349 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000007 " " y[1] (analytic) = -16.926301069657594 " " y[1] (numeric) = -16.926301069657608 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.3957237063900800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.501602394526995 " " "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 = 27.978216650546106 " " Order of pole (six term test) = -2.49395306386214 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000007 " " y[1] (analytic) = -16.91025694195887 " " y[1] (numeric) = -16.91025694195888 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.30276705610297600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.512818771696197 " " "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 = 28.040793531407402 " " Order of pole (six term test) = -2.4938922955750034 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.25000000000000006 " " y[1] (analytic) = -16.89419585558251 " " y[1] (numeric) = -16.894195855582517 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.20583934171278600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5240351348446617 " " "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 = 28.10443781169593 " " Order of pole (six term test) = -2.4939828600463 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.26000000000000006 " " y[1] (analytic) = -16.87811783039102 " " y[1] (numeric) = -16.87811783039103 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.3147687102943900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5352514839724396 " " "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 = 28.16619306666224 " " Order of pole (six term test) = -2.4938539272222773 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2700000000000001 " " y[1] (analytic) = -16.86202288609618 " " y[1] (numeric) = -16.86202288609619 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.32079621074991200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5464678190795924 " " "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 = 28.228329407600423 " " Order of pole (six term test) = -2.493790090175974 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2800000000000001 " " y[1] (analytic) = -16.84591104226071 " " y[1] (numeric) = -16.84591104226072 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.32684157577694800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5576841401661747 " " "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 = 28.29171997491138 " " Order of pole (six term test) = -2.493899531010859 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2900000000000001 " " y[1] (analytic) = -16.829782318299934 " " y[1] (numeric) = -16.829782318299944 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.33290486758841100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5689004472322416 " " "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 = 28.354032026586214 " " Order of pole (six term test) = -2.4938911896779263 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3000000000000001 " " y[1] (analytic) = -16.81363673348341 " " y[1] (numeric) = -16.813636733483424 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.45198153169438100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5801167402778464 " " "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 = 28.41632378843707 " " Order of pole (six term test) = -2.493896908203313 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3100000000000001 " " y[1] (analytic) = -16.79747430693655 " " y[1] (numeric) = -16.797474306936564 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.4601139763813200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.591333019303042 " " "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 = 28.477090329383497 " " Order of pole (six term test) = -2.493730313126946 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000001 " " y[1] (analytic) = -16.781295057642183 " " y[1] (numeric) = -16.781295057642197 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.46827057529770000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6025492843078974 " " "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 = 28.53918685982627 " " Order of pole (six term test) = -2.493744865311889 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000001 " " y[1] (analytic) = -16.765099004442128 " " y[1] (numeric) = -16.76509900444214 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.35733856005114700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6137655352924525 " " "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 = 28.60016473058112 " " Order of pole (six term test) = -2.4936376728217624 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.34000000000000014 " " y[1] (analytic) = -16.748886166038716 " " y[1] (numeric) = -16.74888616603873 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.48465657615906900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.624981772256768 " " "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 = 28.662588923388025 " " Order of pole (six term test) = -2.4937246967291102 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.35000000000000014 " " y[1] (analytic) = -16.73265656099632 " " y[1] (numeric) = -16.732656560996336 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.06161076869343230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6361979952009036 " " "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 = 28.724085000035213 " " Order of pole (six term test) = -2.4937133409531587 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.36000000000000015 " " y[1] (analytic) = -16.716410207742825 " " y[1] (numeric) = -16.716410207742843 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.06264252750717060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.647414204124907 " " "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 = 28.7851878382812 " " Order of pole (six term test) = -2.4936696064177486 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.37000000000000016 " " y[1] (analytic) = -16.700147124571117 " " y[1] (numeric) = -16.70014712457113 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.50941887469566800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6586303990288407 " " "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 = 28.84636022420589 " " Order of pole (six term test) = -2.4936501186709616 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.38000000000000017 " " y[1] (analytic) = -16.683867329640492 " " y[1] (numeric) = -16.68386732964051 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.06471527512352130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6698465799127518 " " "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 = 28.907058506341695 " " Order of pole (six term test) = -2.4935883628999065 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3900000000000002 " " y[1] (analytic) = -16.667570840978126 " " y[1] (numeric) = -16.66757084097814 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.52605028698234100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6810627467767074 " " "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 = 28.968106169284653 " " Order of pole (six term test) = -2.4935846728260813 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4000000000000002 " " y[1] (analytic) = -16.65125767648043 " " y[1] (numeric) = -16.651257676480448 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.06680040265626250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.692278899620752 " " "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 = 29.028410349259225 " " Order of pole (six term test) = -2.4935059239628306 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4100000000000002 " " y[1] (analytic) = -16.634927853914483 " " y[1] (numeric) = -16.634927853914498 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.5427810928906100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.703495038444949 " " "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 = 29.089176550939385 " " Order of pole (six term test) = -2.493498534777938 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4200000000000002 " " y[1] (analytic) = -16.618581390919342 " " y[1] (numeric) = -16.618581390919356 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.55118399153314100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7147111632493472 " " "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 = 29.14962099908049 " " Order of pole (six term test) = -2.4934671984331747 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4300000000000002 " " y[1] (analytic) = -16.60221830500742 " " y[1] (numeric) = -16.602218305007437 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.06995150091748940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.725927274034008 " " "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 = 29.210258500615392 " " Order of pole (six term test) = -2.493474098070646 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000002 " " y[1] (analytic) = -16.585838613565798 " " y[1] (numeric) = -16.585838613565816 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.0710081538761280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7371433707989814 " " "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 = 29.270489948385343 " " Order of pole (six term test) = -2.4934467521503176 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.45000000000000023 " " y[1] (analytic) = -16.569442333857523 " " y[1] (numeric) = -16.56944233385754 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.0720679692221710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7483594535443254 " " "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 = 29.33033471086217 " " Order of pole (six term test) = -2.4933876214009434 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.46000000000000024 " " y[1] (analytic) = -16.5530294830229 " " y[1] (numeric) = -16.553029483022918 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.07313095842795150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7595755222700977 " " "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 = 29.389942444290924 " " Order of pole (six term test) = -2.4933147552183907 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.47000000000000025 " " y[1] (analytic) = -16.536600078080745 " " y[1] (numeric) = -16.536600078080767 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.28903655964068030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7707915769763467 " " "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 = 29.4502014171349 " " Order of pole (six term test) = -2.493334444960837 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.48000000000000026 " " y[1] (analytic) = -16.520154135929666 " " y[1] (numeric) = -16.520154135929683 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.07526650464892080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.782007617663137 " " "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 = 29.510073886362786 " " Order of pole (six term test) = -2.4933221045312095 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.49000000000000027 " " y[1] (analytic) = -16.50369167334924 " " y[1] (numeric) = -16.50369167334926 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.07633908495077850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.793223644330521 " " "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 = 29.568373196254925 " " Order of pole (six term test) = -2.493136393421029 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000002 " " y[1] (analytic) = -16.487212707001284 " " y[1] (numeric) = -16.487212707001298 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.61931908549185800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8044396569785444 " " "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 = 29.629704282856416 " " Order of pole (six term test) = -2.4933260684605116 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000002 " " y[1] (analytic) = -16.470717253430994 " " y[1] (numeric) = -16.470717253431012 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.07849391867267940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.815655655607278 " " "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 = 29.688616875916793 " " Order of pole (six term test) = -2.493241722733652 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000002 " " y[1] (analytic) = -16.454205329068184 " " y[1] (numeric) = -16.454205329068202 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.07957619579604900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.826871640216772 " " "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 = 29.746924054032583 " " Order of pole (six term test) = -2.493099732916974 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000002 " " y[1] (analytic) = -16.437676950228397 " " y[1] (numeric) = -16.437676950228415 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.08066172901370240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8380876108070736 " " "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 = 29.807654674622814 " " Order of pole (six term test) = -2.4932585548200166 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000003 " " y[1] (analytic) = -16.421132133114074 " " y[1] (numeric) = -16.421132133114092 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.08175053035358850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.849303567378249 " " "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 = 29.865359266485143 " " Order of pole (six term test) = -2.493073128590501 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000003 " " y[1] (analytic) = -16.404570893815684 " " y[1] (numeric) = -16.404570893815702 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.0828426119148990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.860519509930342 " " "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 = 29.92460353248269 " " Order of pole (six term test) = -2.4930832399402423 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000003 " " y[1] (analytic) = -16.38799324831284 " " y[1] (numeric) = -16.387993248312856 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.08393798586848240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.871735438463419 " " "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 = 29.984076224043918 " " Order of pole (six term test) = -2.493133501674837 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000003 " " y[1] (analytic) = -16.37139921247539 " " y[1] (numeric) = -16.371399212475406 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.08503666445725980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8829513529775346 " " "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 = 30.043150333588102 " " Order of pole (six term test) = -2.4931500240157725 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000003 " " y[1] (analytic) = -16.3547888020645 " " y[1] (numeric) = -16.354788802064522 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.30336639199597650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.894167253472738 " " "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 = 30.101063986870656 " " Order of pole (six term test) = -2.493043689738128 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000003 " " y[1] (analytic) = -16.338162032733752 " " y[1] (numeric) = -16.33816203273377 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.08724398487497740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9053831399490884 " " "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 = 30.15882372966298 " " Order of pole (six term test) = -2.492932794575589 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000003 " " y[1] (analytic) = -16.321518920030147 " " y[1] (numeric) = -16.321518920030165 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.08835265155393350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9165990124066425 " " "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 = 30.218368703238845 " " Order of pole (six term test) = -2.493043539494055 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000003 " " y[1] (analytic) = -16.30485947939519 " " y[1] (numeric) = -16.304859479395212 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.30735760708277550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9278148708454474 " " "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 = 30.275600302973054 " " Order of pole (six term test) = -2.4928972811492027 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000003 " " y[1] (analytic) = -16.288183726165908 " " y[1] (numeric) = -16.288183726165926 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.09058006052979910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9390307152655697 " " "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 = 30.334754195246333 " " Order of pole (six term test) = -2.4929877375406075 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000003 " " y[1] (analytic) = -16.271491675575838 " " y[1] (numeric) = -16.271491675575856 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.09169882812073920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9502465456670586 " " "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 = 30.39241823441828 " " Order of pole (six term test) = -2.4929176359262417 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000003 " " y[1] (analytic) = -16.254783342756053 " " y[1] (numeric) = -16.254783342756074 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.3113851857215070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9614623620499745 " " "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 = 30.45020913413644 " " Order of pole (six term test) = -2.492875012664795 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000004 " " y[1] (analytic) = -16.23805874273614 " " y[1] (numeric) = -16.23805874273616 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.31273586396763950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.972678164414366 " " "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 = 30.50769220129725 " " Order of pole (six term test) = -2.49280940423124 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000004 " " y[1] (analytic) = -16.221317890445167 " " y[1] (numeric) = -16.221317890445192 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.5331057513059450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9838939527602877 " " "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 = 30.565395101531745 " " Order of pole (six term test) = -2.492781745412419 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000004 " " y[1] (analytic) = -16.204560800712656 " " y[1] (numeric) = -16.204560800712677 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.31544954133317460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.995109727087802 " " "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 = 30.62396099627864 " " Order of pole (six term test) = -2.4928658171736604 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000004 " " y[1] (analytic) = -16.187787488269503 " " y[1] (numeric) = -16.187787488269525 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.31681257171493450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.0063254873969627 " " "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 = 30.680918530639065 " " Order of pole (six term test) = -2.492776866841883 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000004 " " y[1] (analytic) = -16.170997967748946 " " y[1] (numeric) = -16.170997967748967 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.3181797508920410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.017541233687821 " " "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 = 30.737721555957112 " " Order of pole (six term test) = -2.4926825833337283 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000004 " " y[1] (analytic) = -16.15419225368746 " " y[1] (numeric) = -16.15419225368748 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.31955109472819440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.0287569659604383 " " "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 = 30.79548692126662 " " Order of pole (six term test) = -2.492710827331388 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000004 " " y[1] (analytic) = -16.137370360525683 " " y[1] (numeric) = -16.137370360525704 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.32092661918113280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.039972684214864 " " "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 = 30.85310362738749 " " Order of pole (six term test) = -2.4927338679204567 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000004 " " y[1] (analytic) = -16.120532302609313 " " y[1] (numeric) = -16.120532302609334 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.32230634030321040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.051188388451154 " " "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 = 30.909799450792484 " " Order of pole (six term test) = -2.4926635399005193 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000004 " " y[1] (analytic) = -16.10367809418999 " " y[1] (numeric) = -16.10367809419001 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.1030752285349879000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.06240407866937 " " "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 = 30.966597254457458 " " Order of pole (six term test) = -2.4926168015638837 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000004 " " y[1] (analytic) = -16.086807749426164 " " y[1] (numeric) = -16.086807749426185 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.3250784372408120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.0736197548695605 " " "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 = 31.02373988243167 " " Order of pole (six term test) = -2.492621062820941 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000004 " " y[1] (analytic) = -16.06992128238398 " " y[1] (numeric) = -16.069921282383998 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.10539237136619450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.084835417051786 " " "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 = 31.080549468545957 " " Order of pole (six term test) = -2.492599053528746 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000005 " " y[1] (analytic) = -16.053018707038106 " " y[1] (numeric) = -16.053018707038124 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.10655626322882460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.0960510652160984 " " "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 = 31.137339822536415 " " Order of pole (six term test) = -2.492586405626744 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000005 " " y[1] (analytic) = -16.036100037272597 " " y[1] (numeric) = -16.036100037272615 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.10772372040051910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1072666993625564 " " "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 = 31.19439277579946 " " Order of pole (six term test) = -2.492614867770973 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000005 " " y[1] (analytic) = -16.019165286881712 " " y[1] (numeric) = -16.01916528688173 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.10889475674174520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.11848231949121 " " "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 = 31.249309240495105 " " Order of pole (six term test) = -2.4924133548002096 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000005 " " y[1] (analytic) = -16.00221446957074 " " y[1] (numeric) = -16.002214469570756 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.11006938619533550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1296979256021227 " " "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 = 31.305879180030704 " " Order of pole (six term test) = -2.492410080274446 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000005 " " y[1] (analytic) = -15.985247598956803 " " y[1] (numeric) = -15.985247598956821 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.11124762278700980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1409135176953376 " " "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 = 31.36286543897913 " " Order of pole (six term test) = -2.492464782142509 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000005 " " y[1] (analytic) = -15.968264688569676 " " y[1] (numeric) = -15.968264688569693 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.11242948062590260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1521290957709254 " " "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 = 31.418364817559468 " " Order of pole (six term test) = -2.492363386447792 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000005 " " y[1] (analytic) = -15.951265751852546 " " y[1] (numeric) = -15.951265751852567 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.33633796868611380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.163344659828927 " " "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 = 31.475363062580573 " " Order of pole (six term test) = -2.4924413206564573 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000005 " " y[1] (analytic) = -15.934250802162829 " " y[1] (numeric) = -15.934250802162847 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.11480411690214970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1745602098694063 " " "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 = 31.53069576402944 " " Order of pole (six term test) = -2.4923435191730565 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000005 " " y[1] (analytic) = -15.917219852772899 " " y[1] (numeric) = -15.917219852772918 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.22759661637762420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.185775745892419 " " "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 = 31.586857348013005 " " Order of pole (six term test) = -2.492349461127569 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000005 " " y[1] (analytic) = -15.900172916870886 " " y[1] (numeric) = -15.900172916870908 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.34063209150293900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1969912678980164 " " "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 = 31.642203824359548 " " Order of pole (six term test) = -2.4922752324627737 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000005 " " y[1] (analytic) = -15.883110007561413 " " y[1] (numeric) = -15.883110007561429 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.00655422942932980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2082067758862585 " " "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 = 31.69876548636717 " " Order of pole (six term test) = -2.4923471950151956 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000006 " " y[1] (analytic) = -15.866031137866319 " " y[1] (numeric) = -15.866031137866335 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.00763772714694370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.219422269857191 " " "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 = 31.753815131372043 " " Order of pole (six term test) = -2.492261481239126 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000006 " " y[1] (analytic) = -15.848936320725425 " " y[1] (numeric) = -15.848936320725443 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.12080508335271320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2306377498108843 " " "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 = 31.80834156784323 " " Order of pole (six term test) = -2.492128543642549 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000006 " " y[1] (analytic) = -15.831825568997242 " " y[1] (numeric) = -15.831825568997262 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.2342180722144210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2418532157473825 " " "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 = 31.864352596458453 " " Order of pole (six term test) = -2.4921709069998546 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000006 " " y[1] (analytic) = -15.814698895459685 " " y[1] (numeric) = -15.814698895459705 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.23555468002065880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2530686676667466 " " "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 = 31.92017802211326 " " Order of pole (six term test) = -2.492202979641794 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000006 " " y[1] (analytic) = -15.79755631281078 " " y[1] (numeric) = -15.797556312810798 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.12445039234311300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2642841055690246 " " "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 = 31.975726222140334 " " Order of pole (six term test) = -2.4922146419369486 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000006 " " y[1] (analytic) = -15.780397833669362 " " y[1] (numeric) = -15.780397833669378 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.01310573555323370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2754995294542795 " " "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 = 32.02970109466014 " " Order of pole (six term test) = -2.492063157921544 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000006 " " y[1] (analytic) = -15.76322347057576 " " y[1] (numeric) = -15.763223470575781 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.35227938071123570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.286714939322564 " " "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 = 32.08552154190726 " " Order of pole (six term test) = -2.4921253372829195 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000006 " " y[1] (analytic) = -15.746033235992506 " " y[1] (numeric) = -15.746033235992524 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.12812974085424180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.297930335173936 " " "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 = 32.14011738382202 " " Order of pole (six term test) = -2.4920629272143042 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000006 " " y[1] (analytic) = -15.728827142304958 " " y[1] (numeric) = -15.728827142304976 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.12936382562338770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3091457170084446 " " "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 = 32.19493301090976 " " Order of pole (six term test) = -2.492034837545372 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000006 " " y[1] (analytic) = -15.711605201822007 " " y[1] (numeric) = -15.711605201822026 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.24366192902662760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.320361084826153 " " "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 = 32.249454327604056 " " Order of pole (six term test) = -2.491984593094445 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000006 " " y[1] (analytic) = -15.694367426776722 " " y[1] (numeric) = -15.694367426776738 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.01865918643690610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3315764386271125 " " "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 = 32.30434110893241 " " Order of pole (six term test) = -2.491984326760038 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000006 " " y[1] (analytic) = -15.67711382932698 " " y[1] (numeric) = -15.677113829326998 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.13308920171086720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.342791778411379 " " "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 = 32.358443697921906 " " Order of pole (six term test) = -2.491908347022477 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000007 " " y[1] (analytic) = -15.659844421556144 " " y[1] (numeric) = -15.659844421556162 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.13433875304345520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3540071041790056 " " "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 = 32.41339996668814 " " Order of pole (six term test) = -2.491935327664846 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = -15.642559215473664 " " y[1] (numeric) = -15.642559215473684 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.24915143131271030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3652224159300497 " " "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 = 32.46715551801376 " " Order of pole (six term test) = -2.491841370782124 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = -15.625258223015724 " " y[1] (numeric) = -15.62525822301574 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.0231646303965320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.376437713664567 " " "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 = 32.52238067274521 " " Order of pole (six term test) = -2.4919168555113878 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = -15.60794145604584 " " y[1] (numeric) = -15.607941456045857 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.13811090617088840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3876529973826117 " " "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 = 32.57574390071928 " " Order of pole (six term test) = -2.491799888833471 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = -15.590608926355497 " " y[1] (numeric) = -15.590608926355516 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.2533137945863712000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3988682670842407 " " "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 = 32.63032915910951 " " Order of pole (six term test) = -2.4918250036280387 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = -15.573260645664739 " " y[1] (numeric) = -15.573260645664758 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.25470995946133170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4100835227695097 " " "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 = 32.684030194640286 " " Order of pole (six term test) = -2.4917639697206493 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = -15.555896625622768 " " y[1] (numeric) = -15.555896625622786 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.14191864484001440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.421298764438473 " " "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 = 32.73854050975469 " " Order of pole (six term test) = -2.4917997666000176 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = -15.538516877808533 " " y[1] (numeric) = -15.53851687780855 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.14319587472158940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4325139920911867 " " "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 = 32.79183816759758 " " Order of pole (six term test) = -2.4917142028121333 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = -15.521121413731318 " " y[1] (numeric) = -15.521121413731336 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.1444771238170540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4437292057277022 " " "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 = 32.845847173389274 " " Order of pole (six term test) = -2.491714620162483 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = -15.503710244831321 " " y[1] (numeric) = -15.503710244831339 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.14576240870630190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.454944405348083 " " "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 = 32.89965583252583 " " Order of pole (six term test) = -2.491702731211527 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = -15.48628338248022 " " y[1] (numeric) = -15.486283382480236 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.03234657146263630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4661595909523792 " " "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 = 32.95274466077872 " " Order of pole (six term test) = -2.4916228744338547 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = -15.468840837981734 " " y[1] (numeric) = -15.46884083798175 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.03351063741943280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.477374762540647 " " "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 = 33.006759372048094 " " Order of pole (six term test) = -2.491651387465714 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = -15.45138262257219 " " y[1] (numeric) = -15.451382622572206 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.03467838090083250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.488589920112938 " " "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 = 33.060277425553956 " " Order of pole (six term test) = -2.4916357824764557 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = -15.433908747421068 " " y[1] (numeric) = -15.433908747421084 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.03584981719382270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4998050636693145 " " "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 = 33.11297531689983 " " Order of pole (six term test) = -2.4915417179039956 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = -15.416419223631546 " " y[1] (numeric) = -15.416419223631562 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.03702496167824440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.511020193209826 " " "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 = 33.16642773387664 " " Order of pole (six term test) = -2.491537169203351 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = -15.398914062241044 " " y[1] (numeric) = -15.39891406224106 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.03820382982743880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5222353087345306 " " "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 = 33.21978653151495 " " Order of pole (six term test) = -2.491531523448323 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = -15.381393274221747 " " y[1] (numeric) = -15.381393274221761 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.23899055296798600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5334504102434874 " " "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 = 33.27236075114206 " " Order of pole (six term test) = -2.4914514103668655 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = -15.363856870481136 " " y[1] (numeric) = -15.363856870481154 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.15619199942769450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.544665497736743 " " "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 = 33.32555790048391 " " Order of pole (six term test) = -2.4914462800385504 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = -15.346304861862528 " " y[1] (numeric) = -15.346304861862542 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.2601149547848100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.555880571214356 " " "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 = 33.378669843748995 " " Order of pole (six term test) = -2.4914408194263054 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = -15.328737259145544 " " y[1] (numeric) = -15.328737259145562 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.15884094649768180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5670956306763917 " " "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 = 33.43240426931365 " " Order of pole (six term test) = -2.4915097486203557 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = -15.31115407304668 " " y[1] (numeric) = -15.311154073046696 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.04415457373952540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5783106761228907 " " "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 = 33.484145085067965 " " Order of pole (six term test) = -2.491376756141804 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = -15.293555314219752 " " y[1] (numeric) = -15.293555314219772 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.27765747283333000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.589525707553915 " " "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 = 33.53715007904121 " " Order of pole (six term test) = -2.4913858062570284 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = -15.275940993256441 " " y[1] (numeric) = -15.27594099325646 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.27913070900369740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6007407249695254 " " "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 = 33.5894366538282 " " Order of pole (six term test) = -2.4913277435579495 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = -15.258311120686756 " " y[1] (numeric) = -15.258311120686775 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.28060865182589660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6119557283697663 " " "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 = 33.64173482387841 " " Order of pole (six term test) = -2.4912794780063745 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = -15.240665706979534 " " y[1] (numeric) = -15.24066570697955 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.04898380831756160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6231707177547015 " " "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 = 33.694597647116964 " " Order of pole (six term test) = -2.491298900261963 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = -15.223004762542914 " " y[1] (numeric) = -15.22300476254293 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.05020078519187720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.63438569312438 " " "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 = 33.746791203631254 " " Order of pole (six term test) = -2.491256502443388 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = -15.205328297724826 " " y[1] (numeric) = -15.20532829772484 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.34597033155040500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.645600654478864 " " "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 = 33.79875067351287 " " Order of pole (six term test) = -2.491198021381482 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = -15.187636322813447 " " y[1] (numeric) = -15.187636322813464 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.16960717365346270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6568156018182028 " " "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 = 33.85134794021141 " " Order of pole (six term test) = -2.49121446490817 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = -15.169928848037692 " " y[1] (numeric) = -15.169928848037705 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.19680698595380600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.668030535142456 " " "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 = 33.90316693880635 " " Order of pole (six term test) = -2.491157912888376 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = -15.152205883567639 " " y[1] (numeric) = -15.15220588356765 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.03405241342457700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6792454544516766 " " "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 = 33.955807576420234 " " Order of pole (six term test) = -2.491195104807442 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = -15.13446743951501 " " y[1] (numeric) = -15.134467439515024 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.38972895610352400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6904603597459205 " " "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 = 34.007350563136 " " Order of pole (six term test) = -2.4911262062680386 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = -15.116713525933633 " " y[1] (numeric) = -15.116713525933648 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.40075677879482700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7016752510252506 " " "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 = 34.05928347804848 " " Order of pole (six term test) = -2.491105954342224 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = -15.098944152819861 " " y[1] (numeric) = -15.098944152819874 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.23534265041936800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.712890128289708 " " "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 = 34.11060723756675 " " Order of pole (six term test) = -2.4910306188103206 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = -15.081159330113024 " " y[1] (numeric) = -15.081159330113037 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.24505437786430700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7241049915393543 " " "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 = 34.1630571576624 " " Order of pole (six term test) = -2.4910798693142215 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = -15.063359067695881 " " y[1] (numeric) = -15.06335906769589 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.8962839278316600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.735319840774246 " " "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 = 34.21382976849232 " " Order of pole (six term test) = -2.490963618043306 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = -15.04554337539502 " " y[1] (numeric) = -15.045543375395033 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.26457214974150800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7465346759944436 " " "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 = 34.26583163152804 " " Order of pole (six term test) = -2.4909822678481834 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = -15.027712262981332 " " y[1] (numeric) = -15.027712262981344 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.27437846706208200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7577494971999954 " " "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 = 34.31711006571927 " " Order of pole (six term test) = -2.4909341330826447 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = -15.00986574017039 " " y[1] (numeric) = -15.009865740170403 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.28421658864258300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7689643043909555 " " "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 = 34.36928620055485 " " Order of pole (six term test) = -2.4909861449079678 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = -14.992003816622894 " " y[1] (numeric) = -14.992003816622907 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.29408665305606500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7801790975673852 " " "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 = 34.42005761267204 " " Order of pole (six term test) = -2.4909014610218616 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = -14.97412650194508 " " y[1] (numeric) = -14.974126501945088 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.93142057124169700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.791393876729331 " " "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 = 34.47129414432607 " " Order of pole (six term test) = -2.4908723198491067 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = -14.956233805689113 " " y[1] (numeric) = -14.956233805689125 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.31392316899450300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8026086418768568 " " "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 = 34.52272062759761 " " Order of pole (six term test) = -2.490870281038818 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = -14.938325737353534 " " y[1] (numeric) = -14.938325737353546 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.32388990200493700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8138233930100207 " " "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 = 34.573424931927995 " " Order of pole (six term test) = -2.4908019673261492 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = -14.920402306383622 " " y[1] (numeric) = -14.92040230638363 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.95277795773725500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8250381301288683 " " "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 = 34.62442252717009 " " Order of pole (six term test) = -2.490771265557729 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = -14.902463522171796 " " y[1] (numeric) = -14.902463522171809 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.34392102842713300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8362528532334594 " " "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 = 34.675653067110424 " " Order of pole (six term test) = -2.490771834412211 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = -14.884509394058043 " " y[1] (numeric) = -14.884509394058055 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.3539857086358890000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8474675623238497 " " "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 = 34.72708725274784 " " Order of pole (six term test) = -2.4908005231368264 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = -14.866539931330266 " " y[1] (numeric) = -14.866539931330275 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.974345233004399000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8586822574000936 " " "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 = 34.77804663061308 " " Order of pole (six term test) = -2.490788231954399 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = -14.848555143224683 " " y[1] (numeric) = -14.848555143224694 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.17789773725206900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.869896938462248 " " "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 = 34.82850369068344 " " Order of pole (six term test) = -2.4907323142735684 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = -14.830555038926224 " " y[1] (numeric) = -14.830555038926235 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.18660967740367400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.88111160551037 " " "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 = 34.87838720922488 " " Order of pole (six term test) = -2.4906257054135033 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = -14.812539627568889 " " y[1] (numeric) = -14.812539627568901 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.39457526423007300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8923262585445078 " " "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 = 34.92908849026937 " " Order of pole (six term test) = -2.4906093715824547 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = -14.794508918236136 " " y[1] (numeric) = -14.794508918236145 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.00343292642401300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9035408975647248 " " "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 = 34.980057681202275 " " Order of pole (six term test) = -2.490627340741103 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = -14.776462919961233 " " y[1] (numeric) = -14.776462919961242 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.01076471758544100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.91475552257107 " " "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 = 35.030228620010135 " " Order of pole (six term test) = -2.490571857459992 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = -14.758401641727641 " " y[1] (numeric) = -14.758401641727652 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.22174480349339800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.925970133563606 " " "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 = 35.081063742727586 " " Order of pole (six term test) = -2.4905905592086217 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = -14.740325092469373 " " y[1] (numeric) = -14.740325092469384 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.23060106852500800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.937184730542384 " " "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 = 35.13060034927032 " " Order of pole (six term test) = -2.490485606589294 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = -14.72223328107135 " " y[1] (numeric) = -14.72223328107136 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.03290548888443900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9483993135074527 " " "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 = 35.18087950574662 " " Order of pole (six term test) = -2.4904625813165584 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = -14.704126216369751 " " y[1] (numeric) = -14.70412621636976 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.04033457432742600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9596138824588807 " " "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 = 35.23143373801798 " " Order of pole (six term test) = -2.490474203865878 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = -14.686003907152372 " " y[1] (numeric) = -14.686003907152385 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.46690355961699600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9708284373967118 " " "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 = 35.28143311377126 " " Order of pole (six term test) = -2.4904371369311633 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = -14.667866362158982 " " y[1] (numeric) = -14.667866362158994 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.47737330623695700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9820429783210085 " " "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 = 35.331064581110475 " " Order of pole (six term test) = -2.490370265959152 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = -14.64971359008165 " " y[1] (numeric) = -14.64971359008166 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.27532382859513600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9932575052318233 " " "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 = 35.381335103596996 " " Order of pole (six term test) = -2.4903742950826064 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = -14.631545599565086 " " y[1] (numeric) = -14.6315455995651 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.71247679781991900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.004472018129212 " " "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 = 35.43102489249522 " " Order of pole (six term test) = -2.4903271874403234 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = -14.613362399207013 " " y[1] (numeric) = -14.613362399207023 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.2934214216023700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.015686517013231 " " "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 = 35.48114415484366 " " Order of pole (six term test) = -2.49032979466997 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = -14.595163997558444 " " y[1] (numeric) = -14.595163997558457 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.51960134047268100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.02690100188394 " " "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 = 35.530806603490674 " " Order of pole (six term test) = -2.490293683866623 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = -14.57695040312407 " " y[1] (numeric) = -14.576950403124082 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.53024640403307200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.0381154727413815 " " "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 = 35.581013444362824 " " Order of pole (six term test) = -2.490318481741685 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = -14.558721624362548 " " y[1] (numeric) = -14.558721624362564 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.09811918704793930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.049329929585618 " " "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 = 35.63031035189604 " " Order of pole (six term test) = -2.4902595813532553 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = -14.540477669686858 " " y[1] (numeric) = -14.540477669686869 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.32997999001159000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.0605443724167065 " " "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 = 35.680163547316496 " " Order of pole (six term test) = -2.490262606958467 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = -14.522218547464583 " " y[1] (numeric) = -14.522218547464595 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.56239550118372200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.071758801234705 " " "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 = 35.72950717873806 " " Order of pole (six term test) = -2.490221793743183 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = -14.503944266018273 " " y[1] (numeric) = -14.503944266018285 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.57318371316064100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.082973216039666 " " "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 = 35.77876696963847 " " Order of pole (six term test) = -2.4901793682091498 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = -14.485654833625727 " " y[1] (numeric) = -14.485654833625743 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.10365818723575720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.094187616831642 " " "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 = 35.82815650664353 " " Order of pole (six term test) = -2.4901563894479857 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = -14.467350258520334 " " y[1] (numeric) = -14.467350258520344 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.3670304830869400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.105402003610688 " " "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 = 35.87759828439977 " " Order of pole (six term test) = -2.4901451104650025 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = -14.449030548891344 " " y[1] (numeric) = -14.44903054889135 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.91758068720132400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.116616376376865 " " "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 = 35.92683561663666 " " Order of pole (six term test) = -2.4901201934104478 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = -14.430695712884198 " " y[1] (numeric) = -14.430695712884212 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.84765738114350600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.127830735130222 " " "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 = 35.9759115383029 " " Order of pole (six term test) = -2.490085892950418 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = -14.412345758600857 " " y[1] (numeric) = -14.412345758600871 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.86019552488281900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.139045079870819 " " "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 = 36.024561766770695 " " Order of pole (six term test) = -2.4900162786784037 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = -14.393980694100048 " " y[1] (numeric) = -14.393980694100062 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.87277600075349300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.150259410598707 " " "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 = 36.07342403555885 " " Order of pole (six term test) = -2.4899739877736025 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = -14.375600527397598 " " y[1] (numeric) = -14.37560052739761 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.64972412950929400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.161473727313946 " " "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 = 36.12273990080011 " " Order of pole (six term test) = -2.489982538236678 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = -14.357205266466714 " " y[1] (numeric) = -14.357205266466728 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.89806473575568800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.1726880300165945 " " "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 = 36.17146464720748 " " Order of pole (six term test) = -2.489939545055039 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = -14.338794919238293 " " y[1] (numeric) = -14.338794919238305 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.6719267175782300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.183902318706696 " " "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 = 36.22031691510522 " " Order of pole (six term test) = -2.4899153651645918 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = -14.320369493601184 " " y[1] (numeric) = -14.320369493601197 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.68308452610660600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.195116593384316 " " "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 = 36.269145570961435 " " Order of pole (six term test) = -2.489895160552754 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = -14.301928997402499 " " y[1] (numeric) = -14.301928997402511 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.69428024573474900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.206330854049506 " " "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 = 36.3183728851675 " " Order of pole (six term test) = -2.489920018114608 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = -14.283473438447878 " " y[1] (numeric) = -14.283473438447892 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.94915891883104500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.217545100702328 " " "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 = 36.36669568479637 " " Order of pole (six term test) = -2.48986297656028 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = -14.265002824501792 " " y[1] (numeric) = -14.265002824501805 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.71678612950855100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.228759333342824 " " "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 = 36.41468328141088 " " Order of pole (six term test) = -2.489779634909926 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = -14.246517163287795 " " y[1] (numeric) = -14.246517163287805 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.4812257018625800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.239973551971056 " " "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 = 36.46336392525375 " " Order of pole (six term test) = -2.48976982876626 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = -14.228016462488814 " " y[1] (numeric) = -14.228016462488828 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 9.98793806056377800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.251187756587082 " " "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 = 36.51169169030352 " " Order of pole (six term test) = -2.4897319041948247 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = -14.209500729747436 " " y[1] (numeric) = -14.209500729747447 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.50071465501162900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.262401947190956 " " "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 = 36.55975485623723 " " Order of pole (six term test) = -2.489674498154553 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = -14.190969972666146 " " y[1] (numeric) = -14.190969972666156 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.51050918783608100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.273616123782731 " " "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 = 36.60905454073531 " " Order of pole (six term test) = -2.4897427185184373 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = -14.172424198807619 " " y[1] (numeric) = -14.172424198807631 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.77372685249423800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.284830286362467 " " "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 = 36.6570404489139 " " Order of pole (six term test) = -2.489689917108681 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = -14.153863415694989 " " y[1] (numeric) = -14.153863415695 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.53019915720174600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.296044434930213 " " "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 = 36.70512485403099 " " Order of pole (six term test) = -2.4896526707918447 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = -14.135287630812087 " " y[1] (numeric) = -14.1352876308121 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.79677739892398500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.307258569486036 " " "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 = 36.75333617061396 " " Order of pole (six term test) = -2.489633629284448 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = -14.11669685160373 " " y[1] (numeric) = -14.116696851603745 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.00666996426912560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.318472690029975 " " "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 = 36.801104766952314 " " Order of pole (six term test) = -2.489577930951052 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = -14.098091085475971 " " y[1] (numeric) = -14.098091085475982 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.5599887756305200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.329686796562093 " " "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 = 36.84893695576351 " " Order of pole (six term test) = -2.489534312150436 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = -14.079470339796337 " " y[1] (numeric) = -14.079470339796345 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.04665813849342800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.34090088908245 " " "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 = 36.897487651490096 " " Order of pole (six term test) = -2.489565510576721 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = -14.060834621894099 " " y[1] (numeric) = -14.06083462189411 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.58002019297327600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.352114967591096 " " "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 = 36.9452315541166 " " Order of pole (six term test) = -2.4895251265419027 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = -14.042183939060536 " " y[1] (numeric) = -14.042183939060546 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.59008789705012500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.363329032088094 " " "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 = 36.99307567188273 " " Order of pole (six term test) = -2.48950017169466 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = -14.02351829854916 " " y[1] (numeric) = -14.023518298549167 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.06679365786267300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.374543082573479 " " "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 = 37.04089208674456 " " Order of pole (six term test) = -2.4894783439273365 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = -14.004837707575966 " " y[1] (numeric) = -14.004837707575975 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.34194010845025400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.385757119047334 " " "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 = 37.08860399947158 " " Order of pole (six term test) = -2.489452278494353 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = -13.986142173319696 " " y[1] (numeric) = -13.986142173319704 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.35041749678789900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.396971141509694 " " "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 = 37.13643542783489 " " Order of pole (six term test) = -2.4894433196872523 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = -13.967431702922056 " " y[1] (numeric) = -13.967431702922068 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.9024941308289300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.408185149960622 " " "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 = 37.18342899326214 " " Order of pole (six term test) = -2.4893602626358575 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = -13.948706303487988 " " y[1] (numeric) = -13.948706303487995 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.09396871867911600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.419399144400172 " " "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 = 37.23103416025799 " " Order of pole (six term test) = -2.4893411470377877 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = -13.92996598208586 " " y[1] (numeric) = -13.92996598208587 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.376027198073101000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.4306131248283975 " " "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 = 37.27868402827863 " " Order of pole (six term test) = -2.4893318867659016 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = -13.911210745747756 " " y[1] (numeric) = -13.911210745747766 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 7.66154810763641100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.441827091245365 " " "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 = 37.32540867974432 " " Order of pole (six term test) = -2.489240457308428 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = -13.892440601469673 " " y[1] (numeric) = -13.892440601469682 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.39324971888787800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.453041043651113 " " "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 = 37.373041704103905 " " Order of pole (six term test) = -2.4892407891466206 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = -13.873655556211766 " " y[1] (numeric) = -13.873655556211773 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.12152498583520700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.464254982045705 " " "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 = 37.42043146514794 " " Order of pole (six term test) = -2.489223595075794 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = -13.854855616898572 " " y[1] (numeric) = -13.85485561689858 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.41059311088616900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.4754689064292 " " "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 = 37.4680100734079 " " Order of pole (six term test) = -2.4892297351607713 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = -13.83604079041925 " " y[1] (numeric) = -13.83604079041926 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.4193105032990590000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.486682816801644 " " "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 = 37.51484260394302 " " Order of pole (six term test) = -2.4891708945239426 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = -13.817211083627793 " " y[1] (numeric) = -13.817211083627802 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.42805855917291700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.497896713163100 " " "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 = 37.56216589720835 " " Order of pole (six term test) = -2.4891638447845708 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = -13.79836650334326 " " y[1] (numeric) = -13.798366503343265 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.862102457497088600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.509110595513627 " " "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 = 37.60913912475762 " " Order of pole (six term test) = -2.489129234157673 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = -13.779507056349981 " " y[1] (numeric) = -13.779507056349988 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.15651781195367400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.520324463853265 " " "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 = 37.65647746918363 " " Order of pole (six term test) = -2.4891343765649108 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = -13.76063274939781 " " y[1] (numeric) = -13.760632749397818 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.16359057537666500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.531538318182087 " " "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 = 37.703027951076166 " " Order of pole (six term test) = -2.489070851270741 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = -13.741743589202315 " " y[1] (numeric) = -13.741743589202319 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.585344178297777600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.542752158500136 " " "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 = 37.74990623117165 " " Order of pole (six term test) = -2.4890435106685445 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = -13.722839582444987 " " y[1] (numeric) = -13.722839582444996 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.47226409930734800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.55396598480747 " " "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 = 37.796880782369826 " " Order of pole (six term test) = -2.489030523656071 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = -13.703920735773497 " " y[1] (numeric) = -13.703920735773504 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.18495946860856300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.56517979710415 " " "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 = 37.84377985528494 " " Order of pole (six term test) = -2.4890157468716403 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = -13.684987055801862 " " y[1] (numeric) = -13.684987055801866 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.596066524808512000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.5763935953902255 " " "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 = 37.8910066419184 " " Order of pole (six term test) = -2.4890368398324387 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = -13.66603854911067 " " y[1] (numeric) = -13.666038549110672 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.299833037216076600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.587607379665756 " " "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 = 37.9368276196728 " " Order of pole (six term test) = -2.488931868915664 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = -13.647075222247299 " " y[1] (numeric) = -13.6470752222473 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.301639223402575600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.59882114993079 " " "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 = 37.983947759577774 " " Order of pole (six term test) = -2.4889534195055543 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = -13.628097081726118 " " y[1] (numeric) = -13.628097081726118 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.610034906185391 " " "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 = 38.03034896532453 " " Order of pole (six term test) = -2.4889131161439355 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = -13.60910413402868 " " y[1] (numeric) = -13.609104134028684 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.61054191650806100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.621248648429614 " " "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 = 38.07690678207057 " " Order of pole (six term test) = -2.4888925862887827 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = -13.590096385603953 " " y[1] (numeric) = -13.590096385603953 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.632462376663503 " " "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 = 38.12301559654523 " " Order of pole (six term test) = -2.48883548708778 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = -13.57107384286848 " " y[1] (numeric) = -13.571073842868485 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.92678617764735500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.643676090887125 " " "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 = 38.16963917588022 " " Order of pole (six term test) = -2.4888313448571076 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = -13.55203651220663 " " y[1] (numeric) = -13.55203651220663 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.654889791100534 " " "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 = 38.215431276752824 " " Order of pole (six term test) = -2.488755202296989 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = -13.532984399970744 " " y[1] (numeric) = -13.532984399970742 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.312612788797784300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.66610347730378 " " "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 = 38.26217873421923 " " Order of pole (six term test) = -2.4887726779815846 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = -13.513917512481356 " " y[1] (numeric) = -13.513917512481362 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.94339429205399600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.677317149496926 " " "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 = 38.308553665166556 " " Order of pole (six term test) = -2.488760665033727 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = -13.494835856027418 " " y[1] (numeric) = -13.494835856027418 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.688530807680016 " " "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 = 38.35416677997511 " " Order of pole (six term test) = -2.488683299726052 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = -13.475739436866423 " " y[1] (numeric) = -13.475739436866423 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.699744451853114 " " "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 = 38.40084888584776 " " Order of pole (six term test) = -2.488709649111529 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = -13.456628261224658 " " y[1] (numeric) = -13.456628261224658 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.7109580820162815 " " "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 = 38.44694677481401 " " Order of pole (six term test) = -2.4886870382406965 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = -13.437502335297363 " " y[1] (numeric) = -13.437502335297365 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.321939743767821800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.7221716981695545 " " "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 = 38.49254074892534 " " Order of pole (six term test) = -2.4886230077670177 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = -13.418361665248934 " " y[1] (numeric) = -13.418361665248936 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.32382542944917410000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.733385300313006 " " "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 = 38.53846649254625 " " Order of pole (six term test) = -2.4885944892155365 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = -13.399206257213098 " " y[1] (numeric) = -13.399206257213098 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.744598888446684 " " "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 = 38.58421290274209 " " Order of pole (six term test) = -2.4885544222032934 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = -13.380036117293102 " " y[1] (numeric) = -13.3800361172931 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.327617372500503300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.755812462570645 " " "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 = 38.62980975341769 " " Order of pole (six term test) = -2.488505560735563 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = -13.360851251561897 " " y[1] (numeric) = -13.360851251561893 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.659047400430556400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.767026022684945 " " "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 = 38.67590933103745 " " Order of pole (six term test) = -2.4885076594324147 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = -13.341651666062322 " " y[1] (numeric) = -13.341651666062317 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.99431093809510500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.778239568789635 " " "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 = 38.72191484226784 " " Order of pole (six term test) = -2.488505923774337 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = -13.322437366807275 " " y[1] (numeric) = -13.322437366807275 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.789453100884776 " " "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 = 38.767096228320696 " " Order of pole (six term test) = -2.488433648707989 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = -13.30320835977992 " " y[1] (numeric) = -13.303208359779918 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.335284535398825700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.800666618970419 " " "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 = 38.81341847027498 " " Order of pole (six term test) = -2.488470397294071 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = -13.283964650933822 " " y[1] (numeric) = -13.283964650933816 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.01165665389371100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.811880123046626 " " "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 = 38.858710719265225 " " Order of pole (six term test) = -2.4884178749215167 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = -13.26470624619315 " " y[1] (numeric) = -13.264706246193144 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.01748098999941800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.823093613113448 " " "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 = 38.90438083060304 " " Order of pole (six term test) = -2.4884045726966573 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = -13.245433151452847 " " y[1] (numeric) = -13.245433151452845 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.341108908322419000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.83430708917094 " " "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 = 38.94952601148859 " " Order of pole (six term test) = -2.4883482222190647 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = -13.226145372578813 " " y[1] (numeric) = -13.226145372578808 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.029193970035502300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.845520551219148 " " "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 = 38.994976766028564 " " Order of pole (six term test) = -2.488324409234904 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = -13.20684291540805 " " y[1] (numeric) = -13.206842915408043 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.380110449645238000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.856733999258150 " " "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 = 39.04006147497633 " " Order of pole (six term test) = -2.488272055687178 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = -13.187525785748846 " " y[1] (numeric) = -13.187525785748845 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.34699781313025200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.867947433287986 " " "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 = 39.085654723629176 " " Order of pole (six term test) = -2.4882705251088204 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = -13.16819398938097 " " y[1] (numeric) = -13.168193989380967 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.697950593426451000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.879160853308705 " " "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 = 39.13068176372606 " " Order of pole (six term test) = -2.4882223066937463 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = -13.14884753205579 " " y[1] (numeric) = -13.148847532055786 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.701920202617973000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.890374259320373 " " "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 = 39.176286248312174 " " Order of pole (six term test) = -2.488230992572946 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = -13.129486419496473 " " y[1] (numeric) = -13.12948641949647 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.705904530679084000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.901587651323045 " " "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 = 39.22135945056875 " " Order of pole (six term test) = -2.4881961932232546 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = -13.110110657398145 " " y[1] (numeric) = -13.110110657398142 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.709903655005135300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.9128010293167765 " " "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 = 39.26657931987944 " " Order of pole (six term test) = -2.4881792323214764 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = -13.09072025142805 " " y[1] (numeric) = -13.090720251428044 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.07087648032155470000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.924014393301620 " " "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 = 39.31195550322500 " " Order of pole (six term test) = -2.488180899734388 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = -13.071315207225702 " " y[1] (numeric) = -13.071315207225696 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.07691990722929700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.935227743277626 " " "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 = 39.35622306740204 " " Order of pole (six term test) = -2.488087214797943 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = -13.051895530403069 " " y[1] (numeric) = -13.051895530403064 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.08298588184928530000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.946441079244871 " " "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 = 39.40114552673955 " " Order of pole (six term test) = -2.4880571008025605 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = -13.032461226544715 " " y[1] (numeric) = -13.03246122654471 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.08907452365668200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.957654401203387 " " "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 = 39.44634076032635 " " Order of pole (six term test) = -2.488055998484896 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = -13.013012301207961 " " y[1] (numeric) = -13.013012301207958 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.73012396866074800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.968867709153238 " " "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 = 39.49165405498418 " " Order of pole (six term test) = -2.488069909115076 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = -12.993548759923055 " " y[1] (numeric) = -12.993548759923048 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.46842705475257600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.980081003094474 " " "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 = 39.535943536351155 " " Order of pole (six term test) = -2.4879964131961927 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = -12.974070608193301 " " y[1] (numeric) = -12.974070608193292 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.84579609994744800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.991294283027160 " " "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 = 39.58076506601988 " " Order of pole (six term test) = -2.487975091717198 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = -12.954577851495237 " " y[1] (numeric) = -12.954577851495229 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.85609697113835600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.002507548951346 " " "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 = 39.62547060640303 " " Order of pole (six term test) = -2.4879478033603295 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = -12.93507049527878 " " y[1] (numeric) = -12.935070495278772 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.49314931077835100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.013720800867078 " " "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 = 39.67018038215863 " " Order of pole (six term test) = -2.487925291163263 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = -12.915548544967383 " " y[1] (numeric) = -12.915548544967374 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.87681530991735600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.024934038774437 " " "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 = 39.71494791612733 " " Order of pole (six term test) = -2.487912302115536 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = -12.896012005958173 " " y[1] (numeric) = -12.896012005958164 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.88723319495803800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.03614726267345 " " "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 = 39.75933818597846 " " Order of pole (six term test) = -2.4878700048437175 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = -12.876460883622116 " " y[1] (numeric) = -12.876460883622107 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.89769050461544900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.047360472564187 " " "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 = 39.80397997112044 " " Order of pole (six term test) = -2.487854476425321 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = -12.85689518330415 " " y[1] (numeric) = -12.856895183304143 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.526549961166399000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.058573668446705 " " "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 = 39.84837015403967 " " Order of pole (six term test) = -2.4878208650646947 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = -12.837314910323357 " " y[1] (numeric) = -12.837314910323347 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.30246909953931800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.0697868503210515 " " "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 = 39.892850259976676 " " Order of pole (six term test) = -2.4877995558053847 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = -12.817720069973074 " " y[1] (numeric) = -12.817720069973062 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 9.7010215607149500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.081000018187286 " " "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 = 39.93732420982945 " " Order of pole (six term test) = -2.4877819689368597 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = -12.798110667521062 " " y[1] (numeric) = -12.798110667521051 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.32790191715535400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.092213172045465 " " "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 = 39.98119806013107 " " Order of pole (six term test) = -2.4877154168142432 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = -12.778486708209655 " " y[1] (numeric) = -12.778486708209643 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 9.73080628382474900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.103426311895636 " " "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 = 40.025618374281564 " " Order of pole (six term test) = -2.487701591542228 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = -12.758848197255883 " " y[1] (numeric) = -12.758848197255869 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.11380388695732050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.114639437737872 " " "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 = 40.069550120996354 " " Order of pole (six term test) = -2.487648739075034 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = -12.739195139851617 " " y[1] (numeric) = -12.739195139851608 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.97201361584975700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.125852549572208 " " "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 = 40.11423400460492 " " Order of pole (six term test) = -2.487666622313835 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = -12.719527541163739 " " y[1] (numeric) = -12.719527541163725 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.11724705726780640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.137065647398716 " " "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 = 40.15843367463441 " " Order of pole (six term test) = -2.4876458514451087 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = -12.69984540633423 " " y[1] (numeric) = -12.699845406334214 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.2588508791318362000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.148278731217437 " " "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 = 40.20213477385218 " " Order of pole (six term test) = -2.4875852600744413 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = -12.680148740480352 " " y[1] (numeric) = -12.680148740480334 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.4008959009521510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.159491801028433 " " "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 = 40.246292069194205 " " Order of pole (six term test) = -2.487569088765113 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = -12.660437548694762 " " y[1] (numeric) = -12.660437548694746 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.26276927579414250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.170704856831764 " " "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 = 40.290459870274645 " " Order of pole (six term test) = -2.4875579469198428 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y[1] (analytic) = -12.640711836045664 " " y[1] (numeric) = -12.64071183604565 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.12421316928363120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.181917898627474 " " "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 = 40.33464540759891 " " Order of pole (six term test) = -2.4875524475498185 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y[1] (analytic) = -12.620971607576937 " " y[1] (numeric) = -12.62097160757692 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.40746441290924340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.193130926415634 " " "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 = 40.378385849700315 " " Order of pole (six term test) = -2.4875119194999797 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y[1] (analytic) = -12.601216868308253 " " y[1] (numeric) = -12.601216868308237 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.268703786442220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.204343940196285 " " "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 = 40.42206434914379 " " Order of pole (six term test) = -2.4874700589346386 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y[1] (analytic) = -12.581447623235242 " " y[1] (numeric) = -12.581447623235224 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.41188589150877950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.2155569399694865 " " "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 = 40.46597075748372 " " Order of pole (six term test) = -2.4874522675911184 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y[1] (analytic) = -12.561663877329597 " " y[1] (numeric) = -12.561663877329579 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.4141095134746390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.226769925735298 " " "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 = 40.50945649223546 " " Order of pole (six term test) = -2.4874016757318937 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y[1] (analytic) = -12.541865635539217 " " y[1] (numeric) = -12.541865635539201 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.27470760883453770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.237982897493769 " " "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 = 40.55360674260508 " " Order of pole (six term test) = -2.4874132740279897 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y[1] (analytic) = -12.522052902788346 " " y[1] (numeric) = -12.522052902788328 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.41858276210021480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.249195855244956 " " "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 = 40.597040498889285 " " Order of pole (six term test) = -2.487366209067437 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y[1] (analytic) = -12.502225683977677 " " y[1] (numeric) = -12.502225683977658 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.56291573415158370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.260408798988918 " " "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 = 40.64043362458742 " " Order of pole (six term test) = -2.487319632428772 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y[1] (analytic) = -12.482383983984501 " " y[1] (numeric) = -12.482383983984482 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.56540010774171180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.271621728725713 " " "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 = 40.6844559677897 " " Order of pole (six term test) = -2.487331932486452 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y[1] (analytic) = -12.46252780766283 " " y[1] (numeric) = -12.46252780766281 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.71043005093206470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.282834644455380 " " "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 = 40.727591955806695 " " Order of pole (six term test) = -2.4872709138935853 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y[1] (analytic) = -12.442657159843513 " " y[1] (numeric) = -12.442657159843495 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.42763464152426360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.294047546178 " " "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 = 40.77090658067073 " " Order of pole (six term test) = -2.4872294533502295 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y[1] (analytic) = -12.422772045334387 " " y[1] (numeric) = -12.422772045334368 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.57291183981286600000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.305260433893599 " " "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 = 40.81428405806914 " " Order of pole (six term test) = -2.487197411908296 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y[1] (analytic) = -12.402872468920364 " " y[1] (numeric) = -12.402872468920345 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.5754354712883420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.316473307602259 " " "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 = 40.858002726359054 " " Order of pole (six term test) = -2.487198910980533 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y[1] (analytic) = -12.382958435363584 " " y[1] (numeric) = -12.382958435363566 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.4345173236851730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.327686167304019 " " "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 = 40.90138498254867 " " Order of pole (six term test) = -2.4871750699872752 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y[1] (analytic) = -12.363029949403526 " " y[1] (numeric) = -12.36302994940351 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.29314671403619660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.338899012998944 " " "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 = 40.94454203188879 " " Order of pole (six term test) = -2.4871355854183665 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y[1] (analytic) = -12.343087015757138 " " y[1] (numeric) = -12.343087015757117 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.72698143062515240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.350111844687073 " " "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 = 40.98749954681755 " " Order of pole (six term test) = -2.4870827190300187 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y[1] (analytic) = -12.323129639118935 " " y[1] (numeric) = -12.323129639118914 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.7297782866079670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.361324662368482 " " "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 = 41.03092366125053 " " Order of pole (six term test) = -2.48707409286696 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y[1] (analytic) = -12.303157824161147 " " y[1] (numeric) = -12.303157824161127 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.5882040621335380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.372537466043218 " " "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 = 41.07456515287451 " " Order of pole (six term test) = -2.4870880327109504 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y[1] (analytic) = -12.283171575533828 " " y[1] (numeric) = -12.283171575533805 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.88002249827725370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.383750255711333 " " "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 = 41.11725645546329 " " Order of pole (six term test) = -2.4870237158856057 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y[1] (analytic) = -12.263170897864963 " " y[1] (numeric) = -12.263170897864937 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 2.17279468849632950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.394963031372883 " " "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 = 41.16057311418870 " " Order of pole (six term test) = -2.487017175175577 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y[1] (analytic) = -12.24315579576059 " " y[1] (numeric) = -12.243155795760565 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.0312569868803630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.40617579302792 " " "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 = 41.20371568497029 " " Order of pole (six term test) = -2.4869993844837044 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y[1] (analytic) = -12.223126273804933 " " y[1] (numeric) = -12.223126273804908 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.03458552210980660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.417388540676512 " " "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 = 41.246899494824966 " " Order of pole (six term test) = -2.486988883789895 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y[1] (analytic) = -12.203082336560499 " " y[1] (numeric) = -12.203082336560474 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.03792739127030780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.4286012743187095 " " "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 = 41.289261578615786 " " Order of pole (six term test) = -2.4869114891874666 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y[1] (analytic) = -12.183023988568191 " " y[1] (numeric) = -12.18302398856817 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.7496708610936748000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.43981399395456 " " "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 = 41.33219894762604 " " Order of pole (six term test) = -2.4868873180982405 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999983 " " y[1] (analytic) = -12.162951234347442 " " y[1] (numeric) = -12.162951234347421 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.75255837683596950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.451026699584129 " " "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 = 41.37505455883807 " " Order of pole (six term test) = -2.486859844794358 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999983 " " y[1] (analytic) = -12.142864078396304 " " y[1] (numeric) = -12.142864078396283 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.75545752099188680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.4622393912074605 " " "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 = 41.41804445635606 " " Order of pole (six term test) = -2.486847583299765 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999826 " " y[1] (analytic) = -12.122762525191575 " " y[1] (numeric) = -12.12276252519155 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.05142975455674900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.473452068824616 " " "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 = 41.46088170117701 " " Order of pole (six term test) = -2.486825917988453 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999999824 " " y[1] (analytic) = -12.102646579188903 " " y[1] (numeric) = -12.102646579188875 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 2.34838795336521970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.484664732435658 " " "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 = 41.50314023453923 " " Order of pole (six term test) = -2.4867584296221317 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999982 " " y[1] (analytic) = -12.082516244822894 " " y[1] (numeric) = -12.082516244822868 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 2.20528175183879700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.495877382040624 " " "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 = 41.54611497434012 " " Order of pole (six term test) = -2.486755856919345 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.909999999999982 " " y[1] (analytic) = -12.062371526507246 " " y[1] (numeric) = -12.062371526507215 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 2.50349329760267700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.507090017639584 " " "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 = 41.58899307786512 " " Order of pole (six term test) = -2.486748634617763 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999817 " " y[1] (analytic) = -12.042212428634816 " " y[1] (numeric) = -12.042212428634786 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 2.507684235663970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.518302639232593 " " "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 = 41.63134889905973 " " Order of pole (six term test) = -2.4867004810830977 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999999815 " " y[1] (analytic) = -12.022038955577766 " " y[1] (numeric) = -12.022038955577734 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 2.6596505989834280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.529515246819698 " " "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 = 41.67392642879587 " " Order of pole (six term test) = -2.4866748604223243 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999999813 " " y[1] (analytic) = -12.00185111168765 " " y[1] (numeric) = -12.001851111687618 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 2.6641242931323450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.540727840400964 " " "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 = 41.71667885870552 " " Order of pole (six term test) = -2.4866677190078814 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999981 " " y[1] (analytic) = -11.981648901295525 " " y[1] (numeric) = -11.981648901295493 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 2.6686162624701220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.5519404199764395 " " "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 = 41.75869419951709 " " Order of pole (six term test) = -2.4866014717686475 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999981 " " y[1] (analytic) = -11.96143232871206 " " y[1] (numeric) = -11.961432328712027 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 2.82163364897277800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.563152985546177 " " "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 = 41.80124165732473 " " Order of pole (six term test) = -2.4865840583535945 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999807 " " y[1] (analytic) = -11.941201398227633 " " y[1] (numeric) = -11.941201398227602 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 2.67765545885109150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.574365537110240 " " "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 = 41.84357554805224 " " Order of pole (six term test) = -2.486552064549029 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9799999999999804 " " y[1] (analytic) = -11.920956114112453 " " y[1] (numeric) = -11.920956114112418 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.9802254490264180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.585578074668676 " " "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 = 41.88635551397228 " " Order of pole (six term test) = -2.4865614227598734 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999999802 " " y[1] (analytic) = -11.90069648061663 " " y[1] (numeric) = -11.900696480616599 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 2.6867690610615220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.596790598221554 " " "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 = 41.928453251062045 " " Order of pole (six term test) = -2.4865164774348667 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999998 " " y[1] (analytic) = -11.880422501970326 " " y[1] (numeric) = -11.880422501970292 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 2.84087370992128550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.608003107768905 " " "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 = 41.97088287467346 " " Order of pole (six term test) = -2.486503157159204 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.00999999999998 " " y[1] (analytic) = -11.860134182383806 " " y[1] (numeric) = -11.860134182383772 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 2.8457333980871610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.619215603310815 " " "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 = 42.01291685181719 " " Order of pole (six term test) = -2.4864598734620706 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999999796 " " y[1] (analytic) = -11.839831526047579 " " y[1] (numeric) = -11.839831526047542 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 3.1506777394034480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.630428084847317 " " "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 = 42.054814807054335 " " Order of pole (six term test) = -2.4864086263748533 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999999794 " " y[1] (analytic) = -11.81951453713247 " " y[1] (numeric) = -11.819514537132434 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 3.00580338358162700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.641640552378469 " " "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 = 42.09735022960871 " " Order of pole (six term test) = -2.48641465955105 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999979 " " y[1] (analytic) = -11.799183219789743 " " y[1] (numeric) = -11.79918321978971 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 2.8604335842499257000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.652853005904336 " " "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 = 42.13949897664887 " " Order of pole (six term test) = -2.486391508236986 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999979 " " y[1] (analytic) = -11.77883757815119 " " y[1] (numeric) = -11.778837578151155 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 3.01618360490045600000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.664065445424965 " " "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 = 42.18129099766142 " " Order of pole (six term test) = -2.4863417658039335 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999787 " " y[1] (analytic) = -11.758477616329223 " " y[1] (numeric) = -11.758477616329188 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 3.0214061672973540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.675277870940410 " " "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 = 42.22359229730736 " " Order of pole (six term test) = -2.4863383218065955 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0699999999999785 " " y[1] (analytic) = -11.738103338416984 " " y[1] (numeric) = -11.738103338416947 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 3.17798306522968900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.686490282450734 " " "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 = 42.26545850395873 " " Order of pole (six term test) = -2.4863017001502055 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0799999999999783 " " y[1] (analytic) = -11.717714748488433 " " y[1] (numeric) = -11.717714748488394 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 3.3351085348657040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.697702679955988 " " "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 = 42.307544221838164 " " Order of pole (six term test) = -2.486286921482961 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.089999999999978 " " y[1] (analytic) = -11.697311850598446 " " y[1] (numeric) = -11.697311850598407 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 3.3409257584943460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.7089150634562245 " " "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 = 42.349080268171136 " " Order of pole (six term test) = -2.486229425992782 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.099999999999978 " " y[1] (analytic) = -11.67689464878292 " " y[1] (numeric) = -11.676894648782879 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.4988932019236980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.7201274329515 " " "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 = 42.391056030239426 " " Order of pole (six term test) = -2.4862121952145007 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999777 " " y[1] (analytic) = -11.656463147058847 " " y[1] (numeric) = -11.65646314705881 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 3.2002412015361330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.731339788441878 " " "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 = 42.432985417977264 " " Order of pole (six term test) = -2.4861944297608556 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999999775 " " y[1] (analytic) = -11.636017349424446 " " y[1] (numeric) = -11.636017349424405 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.51118480484447160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.742552129927407 " " "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 = 42.474909984912074 " " Order of pole (six term test) = -2.4861795945497924 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));" Iterations = 313 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 52 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 1 Minutes 47 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 1 Minutes 42 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 4 Minutes 43 Seconds "Time to Timeout " Unknown Percent Done = 62.79999999999954 "%" (%o58) true (%o58) diffeq.max