(%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_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : sin(array_tmp2 ), 1 1 1 1 1 array_tmp3_g : cos(array_tmp2 ), array_tmp4 : 1 1 1 expt(array_tmp3 , array_const_2D0 ), array_tmp5 : 1 1 1 array_tmp4 + array_const_0D0 , if not array_y_set_initial 1 1 1, 2 then (if 1 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary, 1 2 temporary 1.0 array_y_higher : temporary, temporary : -------------, 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_g array_tmp2 1 2 array_tmp3 : -------------------------, 2 1 - array_tmp3 array_tmp2 1 2 array_tmp3_g : -------------------------, 2 1 array_const_2D0 array_tmp4 array_tmp3 1 1 2 array_tmp4 : ----------------------------------------, 2 array_tmp3 1 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, 2, 2 array_tmp3_g array_tmp2 2 2 array_tmp3 : -------------------------, 3 2 - array_tmp3 array_tmp2 2 2 array_tmp3_g : -------------------------, 3 2 array_tmp4 : (array_const_2D0 att(2, array_tmp4, array_tmp3, 1) 3 1 - att(2, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 , 1 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 array_tmp3_g array_tmp2 3 2 array_tmp3 : -------------------------, 4 3 - array_tmp3 array_tmp2 3 2 array_tmp3_g : -------------------------, 4 3 array_tmp4 : (array_const_2D0 att(3, array_tmp4, array_tmp3, 1) 4 1 - att(3, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 , 1 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 array_tmp3_g array_tmp2 4 2 array_tmp3 : -------------------------, 5 4 - array_tmp3 array_tmp2 4 2 array_tmp3_g : -------------------------, 5 4 array_tmp4 : (array_const_2D0 att(4, array_tmp4, array_tmp3, 1) 5 1 - att(4, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 , 1 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 : kkk array_tmp3_g array_tmp2 kkk - 1 2 -------------------------------, array_tmp3_g : kkk - 1 kkk - array_tmp3 array_tmp2 kkk - 1 2 -------------------------------, array_tmp4 : kkk - 1 kkk (array_const_2D0 att(kkk - 1, array_tmp4, array_tmp3, 1) 1 - att(kkk - 1, array_tmp3, array_tmp4, 2))/array_tmp3 , 1 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_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : sin(array_tmp2 ), 1 1 1 1 1 array_tmp3_g : cos(array_tmp2 ), array_tmp4 : 1 1 1 expt(array_tmp3 , array_const_2D0 ), array_tmp5 : 1 1 1 array_tmp4 + array_const_0D0 , if not array_y_set_initial 1 1 1, 2 then (if 1 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary, 1 2 temporary 1.0 array_y_higher : temporary, temporary : -------------, 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_g array_tmp2 1 2 array_tmp3 : -------------------------, 2 1 - array_tmp3 array_tmp2 1 2 array_tmp3_g : -------------------------, 2 1 array_const_2D0 array_tmp4 array_tmp3 1 1 2 array_tmp4 : ----------------------------------------, 2 array_tmp3 1 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, 2, 2 array_tmp3_g array_tmp2 2 2 array_tmp3 : -------------------------, 3 2 - array_tmp3 array_tmp2 2 2 array_tmp3_g : -------------------------, 3 2 array_tmp4 : (array_const_2D0 att(2, array_tmp4, array_tmp3, 1) 3 1 - att(2, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 , 1 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 array_tmp3_g array_tmp2 3 2 array_tmp3 : -------------------------, 4 3 - array_tmp3 array_tmp2 3 2 array_tmp3_g : -------------------------, 4 3 array_tmp4 : (array_const_2D0 att(3, array_tmp4, array_tmp3, 1) 4 1 - att(3, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 , 1 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 array_tmp3_g array_tmp2 4 2 array_tmp3 : -------------------------, 5 4 - array_tmp3 array_tmp2 4 2 array_tmp3_g : -------------------------, 5 4 array_tmp4 : (array_const_2D0 att(4, array_tmp4, array_tmp3, 1) 5 1 - att(4, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 , 1 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 : kkk array_tmp3_g array_tmp2 kkk - 1 2 -------------------------------, array_tmp3_g : kkk - 1 kkk - array_tmp3 array_tmp2 kkk - 1 2 -------------------------------, array_tmp4 : kkk - 1 kkk (array_const_2D0 att(kkk - 1, array_tmp4, array_tmp3, 1) 1 - att(kkk - 1, array_tmp3, array_tmp4, 2))/array_tmp3 , 1 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(0.75 + 0.5 x - 2.5 sin(0.3 + 0.2 x) cos(0.3 + 0.2 x)) (%o56) exact_soln_y(x) := block(0.75 + 0.5 x - 2.5 sin(0.3 + 0.2 x) cos(0.3 + 0.2 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/expt_sin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (-2.\ 5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.300\ 00000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.3000\ 0000000000000000000000000000)+0.50000000000000000000000000000000*x+0.750000000\ 00000000000000000000000) "), 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_g, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4_c1, 1 + max_terms), array(array_tmp4_a1, 1 + max_terms), array(array_tmp4_a2, 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_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4_c1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4_a2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp5 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 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_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_c1 : 0.0, term : 1 + term), term array(array_tmp4_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_a1 : 0.0, term : 1 + term), term array(array_tmp4_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_a2 : 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_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_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h, if glob_max_h < glob_h then glob_h : glob_max_h, if glob_display_interval < glob_h then glob_h : glob_display_interval, best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"), 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, "2013-05-26T01:46:37-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_sin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 189 "), logitem_str(html_log_file, "expt_sin_c diffeq.max"), logitem_str(html_log_file, "expt_sin_c maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 0.0, float), define_variable(glob_smallish_float, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/expt_sin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (-2.\ 5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.300\ 00000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.3000\ 0000000000000000000000000000)+0.50000000000000000000000000000000*x+0.750000000\ 00000000000000000000000) "), 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_g, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4_c1, 1 + max_terms), array(array_tmp4_a1, 1 + max_terms), array(array_tmp4_a2, 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_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4_c1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4_a2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp5 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 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_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_c1 : 0.0, term : 1 + term), term array(array_tmp4_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_a1 : 0.0, term : 1 + term), term array(array_tmp4_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_a2 : 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_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_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h, if glob_max_h < glob_h then glob_h : glob_max_h, if glob_display_interval < glob_h then glob_h : glob_display_interval, best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"), 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, "2013-05-26T01:46:37-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_sin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 189 "), logitem_str(html_log_file, "expt_sin_c diffeq.max"), logitem_str(html_log_file, "expt_sin_c maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i58) main() "##############ECHO OF PROBLEM#################" "##############temp/expt_sin_cpostode.ode#################" "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (-2.5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)+0.50000000000000000000000000000000*x+0.75000000000000000000000000000000) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900000.000000001 "" step_error = 2.04081632653061200000000000000000E-17 "" est_needed_step_err = 2.04081632653061200000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 9.6231357696947530000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 "" estimated_step_error = 9.6231357696947530000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 "" best_h = 2.000000E-6 "" opt_iter = 2 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.4579753769509400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 "" estimated_step_error = 6.4579753769509400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.33387160530974000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 "" estimated_step_error = 4.33387160530974000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.90840890438994900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" estimated_step_error = 2.90840890438994900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" best_h = 1.600000E-5 "" opt_iter = 5 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.951796019297282200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" estimated_step_error = 1.951796019297282200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" 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 = 1.3098225568684294000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" estimated_step_error = 1.3098225568684294000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" 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 = 8.78999550044665600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" estimated_step_error = 8.78999550044665600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" best_h = 1.280000E-4 "" opt_iter = 8 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.898765622519023000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 "" estimated_step_error = 5.898765622519023000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.9584597127433580000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 "" estimated_step_error = 3.9584597127433580000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.656296322079278500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" estimated_step_error = 2.656296322079278500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" best_h = 1.024000E-3 "" opt_iter = 11 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.7823673712041604000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" estimated_step_error = 1.7823673712041604000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" 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 = 1.1958005943093329000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" estimated_step_error = 1.1958005943093329000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" 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 = 8.020511381323849000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" estimated_step_error = 8.020511381323849000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" best_h = 8.192000E-3 "" opt_iter = 14 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.3766176735542190000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" estimated_step_error = 5.3766176735542190000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.60035267228840300000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 3.60035267228840300000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.405710347770160800000000000000000000000000000000000000000000000000000000000000000E-66 "" estimated_step_error = 2.405710347770160800000000000000000000000000000000000000000000000000000000000000000E-66 "" 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 = 1.60061231949650400000000000000000000000000000000000000000000000000000000000E-58 "" estimated_step_error = 1.60061231949650400000000000000000000000000000000000000000000000000000000000E-58 "" 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 = 1.056089107012379400000000000000000000000000000000000000000000000000E-50 "" estimated_step_error = 1.056089107012379400000000000000000000000000000000000000000000000000E-50 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 5.35056982970100200E-2 " " y[1] (numeric) = 5.35056982970100200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y[1] (analytic) = 5.45012021486411800E-2 " " y[1] (numeric) = 5.450120214864113000E-2 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.01853076708037020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y[1] (analytic) = 5.55087139650272100E-2 " " y[1] (numeric) = 5.550871396502722000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.500109769532408700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y[1] (analytic) = 5.652829762589406000E-2 " " y[1] (numeric) = 5.65282976258940800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.455016052253698500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y[1] (analytic) = 5.75600168178178600E-2 " " y[1] (numeric) = 5.756001681781819000E-2 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.7864282500425750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y[1] (analytic) = 5.86039350332077100E-2 " " y[1] (numeric) = 5.86039350332078400E-2 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 2.36806415814068750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y[1] (analytic) = 5.966011556928708000E-2 " " y[1] (numeric) = 5.9660115569287200E-2 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 2.09352746099319450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y[1] (analytic) = 6.07286215270834700E-2 " " y[1] (numeric) = 6.07286215270835400E-2 " " absolute error = 6.24500451351650600000000000000000E-17 " " relative error = 1.0283461663511310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y[1] (analytic) = 6.18095158104174900E-2 " " y[1] (numeric) = 6.18095158104176500E-2 " " absolute error = 1.59594559789866250000000000000000E-16 " " relative error = 2.58203866665734140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y[1] (analytic) = 6.29028611248971800E-2 " " y[1] (numeric) = 6.29028611248974100E-2 " " absolute error = 2.35922392732845760000000000000000E-16 " " relative error = 3.75058285925036900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y[1] (analytic) = 6.40087199769143700E-2 " " y[1] (numeric) = 6.40087199769144400E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 1.08405447045493740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y[1] (analytic) = 6.51271546726439600E-2 " " y[1] (numeric) = 6.51271546726440500E-2 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 1.27852548242618270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y[1] (analytic) = 6.62582273170482200E-2 " " y[1] (numeric) = 6.62582273170482700E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 6.28350094913135600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y[1] (analytic) = 6.74019998128820900E-2 " " y[1] (numeric) = 6.74019998128822600E-2 " " absolute error = 1.80411241501587940000000000000000E-16 " " relative error = 2.67664523311528200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y[1] (analytic) = 6.85585338597036700E-2 " " y[1] (numeric) = 6.85585338597038400E-2 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 2.4290696477635160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 6.97278909528862300E-2 " " y[1] (numeric) = 6.97278909528862500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.98055573405809900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 7.09101323826342200E-2 " " y[1] (numeric) = 7.0910132382634300E-2 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 1.17425710612942870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 7.21053192330034500E-2 " " y[1] (numeric) = 7.21053192330036500E-2 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 2.69451728909999740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 7.33135123809234300E-2 " " y[1] (numeric) = 7.33135123809235200E-2 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 1.13576234643142260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 7.45347724952225600E-2 " " y[1] (numeric) = 7.45347724952226600E-2 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 1.30334488725953880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 7.57691600356584800E-2 " " y[1] (numeric) = 7.57691600356586300E-2 " " absolute error = 1.52655665885959020000000000000000E-16 " " relative error = 2.01474670979744560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 7.70167352519504100E-2 " " y[1] (numeric) = 7.70167352519504500E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 5.405755422798063000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 7.82775581828145700E-2 " " y[1] (numeric) = 7.82775581828146100E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 5.31868448504871200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 7.95516886550042800E-2 " " y[1] (numeric) = 7.95516886550044400E-2 " " absolute error = 1.52655665885959020000000000000000E-16 " " relative error = 1.91894940845301680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 8.08391862823527600E-2 " " y[1] (numeric) = 8.0839186282352890E-2 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.71671542552921360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 8.21401104648187300E-2 " " y[1] (numeric) = 8.21401104648187500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.37905262831571800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 8.34545203875360900E-2 " " y[1] (numeric) = 8.34545203875361800E-2 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 9.97749749926339500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 8.47824750198675800E-2 " " y[1] (numeric) = 8.47824750198677500E-2 " " absolute error = 1.80411241501587940000000000000000E-16 " " relative error = 2.12793081894944800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 8.61240331144610400E-2 " " y[1] (numeric) = 8.61240331144610500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.611372262301107000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 8.74792532063084500E-2 " " y[1] (numeric) = 8.74792532063085200E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 7.93204519881159600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.33928572811425 " " Order of pole (six term test) = -15.931575676952273 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 8.88481936118108400E-2 " " y[1] (numeric) = 8.88481936118109100E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 7.80983115337622500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 9.0230912427844200E-2 " " y[1] (numeric) = 9.02309124278442900E-2 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 9.2281818510339710000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 11.769009376208933 " " Order of pole (six term test) = -20.47801483941086 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 9.1627467530830400E-2 " " y[1] (numeric) = 9.16274675308304200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.02917633364578600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 9.30379165758106200E-2 " " y[1] (numeric) = 9.3037916575810800E-2 " " absolute error = 1.80411241501587940000000000000000E-16 " " relative error = 1.9391152353952640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 9.4462316995524100E-2 " " y[1] (numeric) = 9.44623169955241100E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.46913480943644700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 9.59007259994872900E-2 " " y[1] (numeric) = 9.59007259994873600E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 7.235496740602699000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 9.73532005730806100E-2 " " y[1] (numeric) = 9.73532005730805100E-2 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 9.97856404133084900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 9.88197974766347200E-2 " " y[1] (numeric) = 9.8819797476634710E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.404352990208846400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 0.10030057324452413 " " y[1] (numeric) = 0.10030057324452411 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.383619989287759000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 0.10179558418426127 " " y[1] (numeric) = 0.10179558418426136 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 9.54309712284364700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 0.10330488637559654 " " y[1] (numeric) = 0.10330488637559665 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.07470523764829560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 0.10482853566962036 " " y[1] (numeric) = 0.10482853566962043 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 6.6192796260895790000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 0.10636658768786966 " " y[1] (numeric) = 0.10636658768786986 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.82659830998376240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 0.1079190978214386 " " y[1] (numeric) = 0.10791909782143877 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.54313237467308460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 0.1094861212300915 " " y[1] (numeric) = 0.1094861212300915 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 11.4497891100404 " " Order of pole (six term test) = -18.35086865887306 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 0.11106771284138017 " " y[1] (numeric) = 0.11106771284138026 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 7.49693360173923500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 0.11266392734976627 " " y[1] (numeric) = 0.11266392734976634 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 6.15893131646774800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 17.599619565499815 " " Order of pole (six term test) = -27.77788740742004 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 0.11427481921574478 " " y[1] (numeric) = 0.114274819215745 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.94307553010276830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 0.1159004426649739 " " y[1] (numeric) = 0.11590044266497408 " " absolute error = 1.80411241501587940000000000000000E-16 " " relative error = 1.55660528427049530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 0.11754085168740636 " " y[1] (numeric) = 0.11754085168740641 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.722711332642610700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 0.11919610003642589 " " y[1] (numeric) = 0.11919610003642596 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 5.82141018186562200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 0.12086624122798773 " " y[1] (numeric) = 0.12086624122798778 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.59277550681403100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.282966525217671 " " Order of pole (six term test) = -11.30641653419429 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 0.1225513285397617 " " y[1] (numeric) = 0.12255132853976178 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 6.79443689750543300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 22.216525099244905 " " Order of pole (six term test) = -35.32247009288179 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 0.12425141501028025 " " y[1] (numeric) = 0.12425141501028025 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 0.12596655343808916 " " y[1] (numeric) = 0.12596655343808927 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.81363341556229900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 17.845130632193147 " " Order of pole (six term test) = -26.22112287572063 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 0.12769679638090392 " " y[1] (numeric) = 0.1276967963809039 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.173553010119175500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 0.12944219615476737 " " y[1] (numeric) = 0.12944219615476732 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.288489602330757000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.9611300200270536 " " Order of pole (six term test) = -11.76907982228754 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 0.13120280483321367 " " y[1] (numeric) = 0.1312028048332137 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.115471208935821300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (analytic) = 0.13297867424643495 " " y[1] (numeric) = 0.13297867424643509 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.04361002893563650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.970118272041615 " " Order of pole (six term test) = -11.749086485254342 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (analytic) = 0.1347698559804522 " " y[1] (numeric) = 0.13476985598045207 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.02973975202788450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.991455881419660 " " Order of pole (six term test) = -12.140319625507885 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 0.13657640137628868 " " y[1] (numeric) = 0.1365764013762885 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.42256661730386870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 0.13839836152914997 " " y[1] (numeric) = 0.13839836152914986 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.02193763248647400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1368319296305631 " " Order of pole (six term test) = -11.099164825879443 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 0.1402357872876061 " " y[1] (numeric) = 0.14023578728760594 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.18752464627473560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 0.14208872925277705 " " y[1] (numeric) = 0.14208872925277713 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.8601922393685800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 0.1439572377775249 " " y[1] (numeric) = 0.14395723777752484 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.856086160603202600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 0.14584136296564587 " " y[1] (numeric) = 0.14584136296564587 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.2903875195891796 " " Order of pole (six term test) = -11.475013263581873 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 0.14774115467107074 " " y[1] (numeric) = 0.14774115467107074 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1829986766389973 " " Order of pole (six term test) = -11.229648127433002 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (analytic) = 0.14965666249706588 " " y[1] (numeric) = 0.14965666249706605 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.11277006258935160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (analytic) = 0.1515879357954406 " " y[1] (numeric) = 0.15158793579544075 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.1549421363859400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (analytic) = 0.15353502366575644 " " y[1] (numeric) = 0.1535350236657566 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.08466100904972950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6057624312875834 " " Order of pole (six term test) = -11.05570401716818 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 0.15549797495454265 " " y[1] (numeric) = 0.15549797495454257 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.35484316572151100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (analytic) = 0.1574768382545133 " " y[1] (numeric) = 0.15747683825451322 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.287553888547817000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.3388853605696244 " " Order of pole (six term test) = -11.045607603856213 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 0.15947166190379147 " " y[1] (numeric) = 0.15947166190379133 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.70235353550580200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.663859426691291 " " Order of pole (six term test) = -11.13898346474495 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 0.16148249398513426 " " y[1] (numeric) = 0.1614824939851344 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.59398902341204600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.29070480842418 " " Order of pole (six term test) = -11.224077942921948 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 0.1635093823251652 " " y[1] (numeric) = 0.16350938232516532 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.78996525359808500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.6986373734118585 " " Order of pole (six term test) = -11.79906925082956 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (analytic) = 0.16555237449360716 " " y[1] (numeric) = 0.16555237449360727 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.70617397075164300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (analytic) = 0.16761151780252237 " " y[1] (numeric) = 0.16761151780252243 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.311893595323223000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.117207138036505 " " Order of pole (six term test) = -11.362575803898498 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (analytic) = 0.16968685930555494 " " y[1] (numeric) = 0.16968685930555513 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.14498571135403220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (analytic) = 0.17177844579717916 " " y[1] (numeric) = 0.17177844579717896 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.13104428444300710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (analytic) = 0.1738863238119479 " " y[1] (numeric) = 0.173886323811948 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.78857250078717200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (analytic) = 0.17601053962375235 " " y[1] (numeric) = 0.17601053962375227 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.730780726249760300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (analytic) = 0.17815113924507742 " " y[1] (numeric) = 0.17815113924507747 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.115958251318995400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.513129369261686 " " Order of pole (six term test) = -11.230728056749648 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (analytic) = 0.18030816842626884 " " y[1] (numeric) = 0.18030816842626865 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.07753869946746520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (analytic) = 0.1824816726547982 " " y[1] (numeric) = 0.18248167265479828 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.563018610882801400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7621780874459816 " " Order of pole (three term test) = -445.7193818052369 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (analytic) = 0.18467169715453857 " " y[1] (numeric) = 0.18467169715453838 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.05207799734907820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (analytic) = 0.18687828688503694 " " y[1] (numeric) = 0.18687828688503702 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.455666211137222500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (analytic) = 0.18910148654079895 " " y[1] (numeric) = 0.18910148654079892 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.46776083696415600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.5293480900801426 " " Order of pole (six term test) = -11.215041989056154 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (analytic) = 0.1913413405505704 " " y[1] (numeric) = 0.19134134055057034 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.90115826885756300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (analytic) = 0.19359789307662822 " " y[1] (numeric) = 0.19359789307662822 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1786231937363945 " " Order of pole (six term test) = -11.163722603031179 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (analytic) = 0.19587118801407355 " " y[1] (numeric) = 0.19587118801407366 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.668128303512336000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6697880707429085 " " Order of pole (six term test) = -11.22377194800248 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = 0.19816126899012965 " " y[1] (numeric) = 0.19816126899012948 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 8.40393556937044300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.127491411266623 " " Order of pole (six term test) = -11.15276486781826 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = 0.2004681793634422 " " y[1] (numeric) = 0.20046817936344224 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.769075441674857500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = 0.20279196222338858 " " y[1] (numeric) = 0.20279196222338852 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.73734474594750800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = 0.2051326603893855 " " y[1] (numeric) = 0.20513266038938546 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.353054923723161200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2507161368593056 " " Order of pole (six term test) = -11.074226133001623 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = 0.20749031641020588 " " y[1] (numeric) = 0.20749031641020568 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.36376370091871200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.000397542574652 " " Order of pole (six term test) = -11.130361343408843 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = 0.20986497256329661 " " y[1] (numeric) = 0.20986497256329648 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.6127222843863700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2745004688341637 " " Order of pole (six term test) = -11.155719478158808 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = 0.2122566708541035 " " y[1] (numeric) = 0.21225667085410338 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.23056834990254900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6972074739035339 " " Order of pole (six term test) = -11.100132898098385 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = 0.2146654530153982 " " y[1] (numeric) = 0.2146654530153981 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 3.878906721004330400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = 0.21709136050661082 " " y[1] (numeric) = 0.2170913605066108 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.278520506336948700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = 0.21953443451316668 " " y[1] (numeric) = 0.21953443451316668 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = 0.2219947159458272 " " y[1] (numeric) = 0.2219947159458271 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.00112365240297600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.115850886285423 " " Order of pole (six term test) = -11.059995529723027 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = 0.2244722454400352 " " y[1] (numeric) = 0.22447224544003494 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.1128332594124250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.140065502161895 " " Order of pole (six term test) = -11.060386566383936 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = 0.2269670633552644 " " y[1] (numeric) = 0.2269670633552645 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.89156007137193900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4760494113920164 " " Order of pole (six term test) = -11.058871397627554 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = 0.22947920977437586 " " y[1] (numeric) = 0.2294792097743757 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 7.25701704557503500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6705290504519903 " " Order of pole (six term test) = -11.041242159466975 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = 0.23200872450297283 " " y[1] (numeric) = 0.23200872450297272 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.785264118853990700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.225252479921726 " " Order of pole (six term test) = -11.064570224640207 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = 0.2345556470687673 " " y[1] (numeric) = 0.23455564706876725 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.366651663474254600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9746534562505386 " " Order of pole (six term test) = -11.04995465407764 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = 0.23712001672094607 " " y[1] (numeric) = 0.23712001672094588 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 8.19370005097675100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3809357142506544 " " Order of pole (six term test) = -11.065275167723236 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = 0.23970187242954233 " " y[1] (numeric) = 0.2397018724295422 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.78960342159766700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9830776988669019 " " Order of pole (six term test) = -11.10227866805159 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = 0.24230125288481352 " " y[1] (numeric) = 0.2423012528848133 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 9.16398913672097600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7726563733272795 " " Order of pole (six term test) = -11.041383133629978 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = 0.24491819649662094 " " y[1] (numeric) = 0.2449181964966207 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.01993312099252960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.806282237069342 " " Order of pole (six term test) = -11.041765195015142 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = 0.247552741393816 " " y[1] (numeric) = 0.24755274139381575 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.00907862758533920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5833422038030416 " " Order of pole (six term test) = -11.072075114448001 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = 0.2502049254236298 " " y[1] (numeric) = 0.25020492542362965 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.65588230974312100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.073202847033717 " " Order of pole (six term test) = -11.049533891164177 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = 0.25287478615106795 " " y[1] (numeric) = 0.2528747861510678 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.5856092743974090000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0441690043889036 " " Order of pole (six term test) = -11.047649180922587 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = 0.2555623608583091 " " y[1] (numeric) = 0.25556236085830886 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.68847056269522600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.975134078454191 " " Order of pole (six term test) = -11.044466669044118 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = 0.25826768654410814 " " y[1] (numeric) = 0.2582676865441082 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.149364946658837100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8886121881737162 " " Order of pole (six term test) = -11.062110054222455 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = 0.26099079992320595 " " y[1] (numeric) = 0.2609907999232059 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.126939005037398000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9246261820329059 " " Order of pole (six term test) = -11.041555177412853 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = 0.2637317374257394 " " y[1] (numeric) = 0.2637317374257393 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.20966788245487100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.979155848652091 " " Order of pole (six term test) = -11.054863978321489 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = 0.26649053519666044 " " y[1] (numeric) = 0.2664905351966602 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.33217602873476800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2497613172924018 " " Order of pole (six term test) = -11.047555535077151 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = 0.26926722909515666 " " y[1] (numeric) = 0.26926722909515644 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.24625431290648100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.283405579718395 " " Order of pole (six term test) = -11.048897161164586 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = 0.2720618546940783 " " y[1] (numeric) = 0.2720618546940782 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.08077429992364800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8624851640644079 " " Order of pole (six term test) = -11.037382596994732 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = 0.27487444727936905 " " y[1] (numeric) = 0.2748744472793688 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.07803734114855500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3498585108920307 " " Order of pole (six term test) = -11.049801970164946 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = 0.2777050418495004 " " y[1] (numeric) = 0.27770504184950034 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.998924861484566400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2572074706922955 " " Order of pole (six term test) = -11.045260170712636 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = 0.2805536731149135 " " y[1] (numeric) = 0.2805536731149133 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.91451426957731700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3662972085645382 " " Order of pole (six term test) = -11.048435306562915 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = 0.2834203754974618 " " y[1] (numeric) = 0.2834203754974616 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.83446160267400700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3321640730393691 " " Order of pole (six term test) = -11.046241135127588 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = 0.28630518312986164 " " y[1] (numeric) = 0.28630518312986153 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.877760830203287300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2338964778083887 " " Order of pole (six term test) = -11.041919165324686 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = 0.2892081298551461 " " y[1] (numeric) = 0.28920812985514593 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.75825630410818900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2260854588076535 " " Order of pole (six term test) = -11.040837349070811 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = 0.2921292492261228 " " y[1] (numeric) = 0.2921292492261225 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.14013543070360730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2849344901925255 " " Order of pole (six term test) = -11.041890972006806 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = 0.29506857450483714 " " y[1] (numeric) = 0.2950685745048368 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.12877797287113990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1542467749792615 " " Order of pole (six term test) = -11.031314315272269 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = 0.29802613866204075 " " y[1] (numeric) = 0.29802613866204053 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.45050772800932500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = 0.30100197437666365 " " y[1] (numeric) = 0.3010019743766636 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.84421219648855400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0989994707496906 " " Order of pole (six term test) = -11.030977712186466 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = 0.3039961140352919 " " y[1] (numeric) = 0.30399611403529136 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.8260480535225970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8374224546123951 " " Order of pole (six term test) = -11.034012450020013 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = 0.3070085897316468 " " y[1] (numeric) = 0.30700858973164646 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.08487813868230050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1740009378917415 " " Order of pole (six term test) = -11.034532036512884 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = 0.31003943326607575 " " y[1] (numeric) = 0.3100394332660754 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.07427272679120490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0472432360450297 " " Order of pole (six term test) = -11.028720920596639 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = 0.31308867614504 " " y[1] (numeric) = 0.3130886761450396 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.24111182621882460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.03097958735334 " " Order of pole (six term test) = -11.028208604541916 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = 0.31615634958061156 " " y[1] (numeric) = 0.3161563495806114 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.26743979409819900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0158104321938528 " " Order of pole (six term test) = -11.027484280847236 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = 0.31924248448997505 " " y[1] (numeric) = 0.31924248448997455 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.56495574791521540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0054284714987702 " " Order of pole (six term test) = -11.02705578805318 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = 0.32234711149493 " " y[1] (numeric) = 0.32234711149492973 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 8.61046202241693300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9923478474290395 " " Order of pole (six term test) = -11.026310806277744 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = 0.32547026092140485 " " y[1] (numeric) = 0.3254702609214044 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.3644540321221610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6521524693608156 " " Order of pole (six term test) = -11.027906805001994 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = 0.3286119627989682 " " y[1] (numeric) = 0.32861196279896776 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.35140913942240980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.943488316708116 " " Order of pole (six term test) = -11.02344667212123 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = 0.33177224686035034 " " y[1] (numeric) = 0.33177224686035006 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 8.36585214052331400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2969028814726418 " " Order of pole (six term test) = -11.007277785563419 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = 0.33495114254096736 " " y[1] (numeric) = 0.3349511425409671 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 8.28645497521602700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.905172069742944 " " Order of pole (six term test) = -11.021812995549126 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = 0.33814867897844914 " " y[1] (numeric) = 0.3381486789784491 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.64161963899896400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5556333519484644 " " Order of pole (six term test) = -11.022840821508604 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = 0.34136488501217477 " " y[1] (numeric) = 0.3413648850121746 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.87845882823694900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9741519587034948 " " Order of pole (six term test) = -11.015008912627689 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = 0.3445997891828092 " " y[1] (numeric) = 0.34459978918280904 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.83266266902525500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.4320006499551372 " " Order of pole (six term test) = -11.019958004909714 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = 0.34785341973184847 " " y[1] (numeric) = 0.347853419731848 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.27665615647073380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.42534843971449854 " " Order of pole (six term test) = -11.020016906545568 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = 0.3511258046011658 " " y[1] (numeric) = 0.35112580460116555 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.90473820263814300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8146907728368054 " " Order of pole (six term test) = -11.01861500709235 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = 0.354416971432567 " " y[1] (numeric) = 0.3544169714325668 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.2650669359178390000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.22477718046633197 " " Order of pole (six term test) = -11.01775163588275 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = 0.35772694756734613 " " y[1] (numeric) = 0.357726947567346 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.10354876023463300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.20866389154975637 " " Order of pole (six term test) = -11.01763520970919 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = 0.3610557600458494 " " y[1] (numeric) = 0.36105576004584905 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 9.2248052584800700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.12031569532298768 " " Order of pole (six term test) = -11.01828697490764 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = 0.3644034356070409 " " y[1] (numeric) = 0.3644034356070405 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.06634027193375020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = 0.36777000068807675 " " y[1] (numeric) = 0.36777000068807625 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.35845871100578250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6680686861438855 " " Order of pole (six term test) = -11.014557639167764 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = 0.3711554814238802 " " y[1] (numeric) = 0.3711554814238801 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.99126129126790430000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = 0.3745599036467261 " " y[1] (numeric) = 0.3745599036467258 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.41018334995279100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6528052463068843 " " Order of pole (six term test) = -10.978264409988384 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = 0.3779832928858242 " " y[1] (numeric) = 0.37798329288582383 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.02802971965266440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = 0.3814256743669132 " " y[1] (numeric) = 0.38142567436691266 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.45535958803493540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.6279994166021001 " " Order of pole (six term test) = -11.008593565276156 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = 0.38488707301185565 " " y[1] (numeric) = 0.3848870730118554 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.21135563177877000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = 0.3883675134382413 " " y[1] (numeric) = 0.38836751343824083 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.14347671853012050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5717322061989694 " " Order of pole (six term test) = -10.978683736892027 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = 0.3918670199589902 " " y[1] (numeric) = 0.39186701995898976 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.1332650803237730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = 0.39538561658196614 " " y[1] (numeric) = 0.39538561658196586 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.01987488962563000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.34275762440008545 " " Order of pole (six term test) = -11.00859586841225 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = 0.398923327009592 " " y[1] (numeric) = 0.3989233270095916 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.74067025690532200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = 0.4024801746384691 " " y[1] (numeric) = 0.40248017463846886 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.51690788557435400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = 0.4060561825590052 " " y[1] (numeric) = 0.40605618255900483 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.56956390049151300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = 0.4096513735550428 " " y[1] (numeric) = 0.40965137355504244 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 8.13049653653350800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = 0.4132657701034961 " " y[1] (numeric) = 0.41326577010349574 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 8.05938772292066300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = 0.4168993943739906 " " y[1] (numeric) = 0.4168993943739904 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.32609564613184200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.17306699846763804 " " Order of pole (six term test) = -11.003332359543752 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = 0.420552268228509 " " y[1] (numeric) = 0.4205522682285089 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.639916862894939300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = 0.424224413221041 " " y[1] (numeric) = 0.4242244132210409 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.617065378664753500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = 0.42791585059723825 " " y[1] (numeric) = 0.42791585059723813 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.59448913396320400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = 0.43162660129407515 " " y[1] (numeric) = 0.4316266012940747 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.02887358776920350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = 0.4353566859395124 " " y[1] (numeric) = 0.435356685939512 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.92551030381541200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8323016855016375 " " Order of pole (six term test) = -10.991656982115238 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = 0.4391061248521687 " " y[1] (numeric) = 0.4391061248521685 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.056741237662895000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = 0.4428749380409953 " " y[1] (numeric) = 0.442874938040995 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.52056345434286300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = 0.4466631452049544 " " y[1] (numeric) = 0.44666314520495415 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.21398382955752400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.7729686167721075 " " Order of pole (six term test) = -10.99101428984326 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = 0.45047076573270584 " " y[1] (numeric) = 0.45047076573270556 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.16145990528009900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4967525919809779 " " Order of pole (six term test) = -10.97288481559284 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = 0.4542978187022958 " " y[1] (numeric) = 0.4542978187022953 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.09971992053237590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = 0.4581443228808513 " " y[1] (numeric) = 0.45814432288085083 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.69321647505290700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = 0.46201029672428107 " " y[1] (numeric) = 0.4620102967242807 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.41059304032569600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = 0.4658957583769796 " " y[1] (numeric) = 0.4658957583769792 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.34045066159170400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = 0.4698007256715365 " " y[1] (numeric) = 0.46980072567153613 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.27112512573003100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = 0.47372521612845175 " " y[1] (numeric) = 0.4737252161284514 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.03080385100790300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8958543183500419 " " Order of pole (six term test) = -10.986049497833513 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = 0.47766924695585533 " " y[1] (numeric) = 0.47766924695585483 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.04591276132016080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = 0.48163283504923093 " " y[1] (numeric) = 0.48163283504923055 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.06793121941292900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = 0.48561599699114766 " " y[1] (numeric) = 0.485615996991147 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.37172955360289920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = 0.489618749050992 " " y[1] (numeric) = 0.4896187490509914 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 1.24713905406478210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0544915673564597 " " Order of pole (six term test) = -10.982289653859658 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = 0.4936411071847101 " " y[1] (numeric) = 0.49364110718470955 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.12452448597411330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = 0.497683087034551 " " y[1] (numeric) = 0.49768308703455044 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.11539155493552140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7355753696242318 " " Order of pole (six term test) = -10.964919186918364 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = 0.5017447039288166 " " y[1] (numeric) = 0.501744703928816 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.3276349696550050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = 0.5058259728816166 " " y[1] (numeric) = 0.5058259728816159 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.31692291516828820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = 0.5099269085926278 " " y[1] (numeric) = 0.5099269085926273 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.70887969171358600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = 0.5140475254468604 " " y[1] (numeric) = 0.5140475254468598 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.07988363883285120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = 0.5181878375144253 " " y[1] (numeric) = 0.5181878375144249 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.57004309441554700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = 0.5223478585503114 " " y[1] (numeric) = 0.522347858550311 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.50179057080003200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5247301809900002 " " Order of pole (six term test) = -10.972378774872062 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = 0.526527601994164 " " y[1] (numeric) = 0.5265276019941637 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.32572549142900700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = 0.5307270809700706 " " y[1] (numeric) = 0.5307270809700705 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.091890661761361000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = 0.5349463082863506 " " y[1] (numeric) = 0.5349463082863506 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = 0.5391852964353505 " " y[1] (numeric) = 0.5391852964353503 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.118150223921303600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = 0.5434440575932429 " " y[1] (numeric) = 0.543444057593243 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.042938935687353700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.053262379092692 " " Order of pole (six term test) = -10.867838340646022 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = 0.5477226036198342 " " y[1] (numeric) = 0.5477226036198344 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.05396095500833200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = 0.5520209460583725 " " y[1] (numeric) = 0.5520209460583726 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.011197278930350300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = 0.5563390961353631 " " y[1] (numeric) = 0.5563390961353637 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.97793461161884300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8166072008598493 " " Order of pole (six term test) = -10.9686964029688 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = 0.5606770647603914 " " y[1] (numeric) = 0.5606770647603919 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.90073515045257800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = 0.5650348625259445 " " y[1] (numeric) = 0.565034862525945 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.82437631956009500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.1993785506234795 " " Order of pole (three term test) = -900.173585610999 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = 0.5694124997072447 " " y[1] (numeric) = 0.5694124997072452 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.7990772959565300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = 0.5738099862620836 " " y[1] (numeric) = 0.5738099862620841 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.67413474151415500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = 0.5782273318306634 " " y[1] (numeric) = 0.5782273318306642 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.34403213832376130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.39297738655065 " " Order of pole (six term test) = -10.86747647960592 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = 0.5826645457354431 " " y[1] (numeric) = 0.5826645457354439 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.33379681829907450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8238425098298103 " " Order of pole (six term test) = -10.973048981501481 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = 0.5871216369809877 " " y[1] (numeric) = 0.5871216369809886 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.5127673104796280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5043271654707098 " " Order of pole (six term test) = -10.98069970665832 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = 0.5915986142538261 " " y[1] (numeric) = 0.591598614253827 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.5013193038330060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7137740070385516 " " Order of pole (six term test) = -10.977235790926333 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = 0.5960954859223102 " " y[1] (numeric) = 0.5960954859223113 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.8624919175614310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.183305355471323 " " Order of pole (six term test) = -10.832895430116182 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = 0.6006122600364832 " " y[1] (numeric) = 0.6006122600364844 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 2.03333399656791840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2944849628752872 " " Order of pole (six term test) = -10.986618118111876 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = 0.6051489443279487 " " y[1] (numeric) = 0.6051489443279499 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.83462771443503120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = 0.6097055462097478 " " y[1] (numeric) = 0.6097055462097493 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 2.36719173867608270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.868263477946317 " " Order of pole (six term test) = -10.801082039868684 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = 0.6142820727762417 " " y[1] (numeric) = 0.614282072776243 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 2.16882062588774180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.007111050160732 " " Order of pole (six term test) = -10.975674311683688 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = 0.6188785308029956 " " y[1] (numeric) = 0.6188785308029972 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 2.511498068059490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = 0.6234949267466727 " " y[1] (numeric) = 0.6234949267466745 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.84903174540502400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = 0.6281312667449301 " " y[1] (numeric) = 0.6281312667449318 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 2.65125241347679900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.391659204598538 " " Order of pole (three term test) = -351.27374309867224 " " Radius of convergence (six term test) for eq 1 = 9.66470732904689 " " Order of pole (six term test) = -10.518353902289412 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = 0.6327875566163195 " " y[1] (numeric) = 0.6327875566163214 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.98264262962924850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.7131033013573744 " " Order of pole (six term test) = -10.929570638589302 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = 0.6374638018601959 " " y[1] (numeric) = 0.6374638018601978 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.96076284858084000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = 0.6421600076566285 " " y[1] (numeric) = 0.6421600076566304 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.9391103764779647000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = 0.646876178866318 " " y[1] (numeric) = 0.64687617886632 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 3.08931061246926400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = 0.6516123200305188 " " y[1] (numeric) = 0.651612320030521 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.40761827392446540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = 0.6563684353709669 " " y[1] (numeric) = 0.6563684353709693 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 3.72121894130222060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.0035264299804005 " " Order of pole (six term test) = -10.963503002245632 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = 0.6611445287898119 " " y[1] (numeric) = 0.6611445287898142 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 3.52641253188686440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 21.889113424200325 " " Order of pole (three term test) = -3207.3812706107246 " " Radius of convergence (six term test) for eq 1 = 4.55453017364349 " " Order of pole (six term test) = -10.912061025112655 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = 0.6659406038695537 " " y[1] (numeric) = 0.6659406038695562 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 3.8344455073024040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = 0.6707566638729872 " " y[1] (numeric) = 0.6707566638729898 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.97243203476384030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = 0.6755927117431482 " " y[1] (numeric) = 0.6755927117431509 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 4.10832963902387900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = 0.6804487501032672 " " y[1] (numeric) = 0.6804487501032701 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 4.24217086678067960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = 0.6853247812567276 " " y[1] (numeric) = 0.6853247812567306 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 4.37398770403575940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = 0.6902208071870282 " " y[1] (numeric) = 0.6902208071870312 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 4.34296117311292030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = 0.6951368295577516 " " y[1] (numeric) = 0.6951368295577548 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 4.6316734123572540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = 0.7000728497125386 " " y[1] (numeric) = 0.7000728497125418 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 4.5990167633768320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = 0.705028868675065 " " y[1] (numeric) = 0.7050288686750683 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 4.7241598491345110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = 0.7100048871490265 " " y[1] (numeric) = 0.71000488714903 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 4.8474192764473056000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = 0.7150009055181272 " " y[1] (numeric) = 0.7150009055181307 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 4.8135482763395310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = 0.720016923846073 " " y[1] (numeric) = 0.7200169238460765 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.9342085736307070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = 0.7250529418765705 " " y[1] (numeric) = 0.7250529418765745 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 5.5124290349144730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26591160121256835 " " Order of pole (three term test) = -53.65808962260314 " " Radius of convergence (six term test) for eq 1 = 13.11279496542769 " " Order of pole (six term test) = -10.447112981626788 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = 0.7301089590333332 " " y[1] (numeric) = 0.730108959033337 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 5.1701300703436450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = 0.7351849744200867 " " y[1] (numeric) = 0.7351849744200906 " " absolute error = 3.885780586188048000000000000000E-15 " " relative error = 5.2854461412968190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15996278824960833 " " Order of pole (three term test) = -40.13830100486610 " " Radius of convergence (six term test) for eq 1 = 15.192579840034258 " " Order of pole (six term test) = -10.277599927149039 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = 0.7402809868205866 " " y[1] (numeric) = 0.7402809868205907 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 5.5490080986081650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = 0.7453969946986367 " " y[1] (numeric) = 0.7453969946986411 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 5.8088103746496490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = 0.7505329961981138 " " y[1] (numeric) = 0.7505329961981181 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 5.7690598787414020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = 0.7556889891429961 " " y[1] (numeric) = 0.7556889891430006 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 6.0235288145793010000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = 0.7608649710374005 " " y[1] (numeric) = 0.7608649710374049 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 5.8366362857337180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.961335711054927 " " Order of pole (three term test) = -151.53988332518188 " " Radius of convergence (six term test) for eq 1 = 6.675221596637786 " " Order of pole (six term test) = -10.910107507432853 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = 0.7660609390656199 " " y[1] (numeric) = 0.7660609390656244 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 5.9419742853815320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 37.36771265831955 " " Order of pole (six term test) = -8.109150052716101 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = 0.7712768900921703 " " y[1] (numeric) = 0.7712768900921749 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 6.0457363150974490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = 0.7765128206618395 " " y[1] (numeric) = 0.7765128206618445 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 6.4338971332823550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = 0.7817687269997438 " " y[1] (numeric) = 0.7817687269997491 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.8166841856830860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = 0.7870446050113875 " " y[1] (numeric) = 0.7870446050113927 " " absolute error = 5.218048215738236000000000000000E-15 " " relative error = 6.6299269222012360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = 0.792340450282728 " " y[1] (numeric) = 0.7923404502827331 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 6.4454943723413320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1711161609510222 " " Order of pole (three term test) = -43.231151112881065 " " Radius of convergence (six term test) for eq 1 = 11.056512369597582 " " Order of pole (six term test) = -10.737721699873969 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = 0.7976562580802471 " " y[1] (numeric) = 0.7976562580802523 " " absolute error = 5.218048215738236000000000000000E-15 " " relative error = 6.5417254147754470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = 0.8029920233510268 " " y[1] (numeric) = 0.8029920233510323 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 6.7747781577714850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 20.06056237975701 " " Order of pole (six term test) = -10.550675485257173 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = 0.8083477407228301 " " y[1] (numeric) = 0.8083477407228358 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 7.0045812468346560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y[1] (analytic) = 0.8137234045041868 " " y[1] (numeric) = 0.8137234045041924 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 6.9583072014971960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3530518620313056 " " Order of pole (three term test) = -67.42795600717768 " " Radius of convergence (six term test) for eq 1 = 8.264902168115336 " " Order of pole (six term test) = -10.90632253412107 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y[1] (analytic) = 0.8191190086844842 " " y[1] (numeric) = 0.8191190086844898 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 6.912472260510429000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y[1] (analytic) = 0.8245345469340635 " " y[1] (numeric) = 0.8245345469340695 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 7.2710165453567970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.852368938696343 " " Order of pole (three term test) = -272.10391340192024 " " Radius of convergence (six term test) for eq 1 = 4.38386593814535 " " Order of pole (six term test) = -11.01724539649919 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y[1] (analytic) = 0.8299700126043221 " " y[1] (numeric) = 0.8299700126043282 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 7.3571653706836130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.5366757797007966 " " Order of pole (three term test) = -92.16563110396804 " " Radius of convergence (six term test) for eq 1 = 6.8869435382470305 " " Order of pole (six term test) = -10.96772640894236 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y[1] (analytic) = 0.8354253987278186 " " y[1] (numeric) = 0.8354253987278247 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 7.3091225676606080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y[1] (analytic) = 0.8409006980183844 " " y[1] (numeric) = 0.8409006980183907 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.5255868561843420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y[1] (analytic) = 0.8463959028712413 " " y[1] (numeric) = 0.8463959028712477 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.4767271662066230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y[1] (analytic) = 0.8519110053631218 " " y[1] (numeric) = 0.8519110053631284 " " absolute error = 6.5503158452884240000000000000000E-15 " " relative error = 7.6889672795063750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35911091768108055 " " Order of pole (three term test) = -68.29779817284481 " " Radius of convergence (six term test) for eq 1 = 7.485283078283195 " " Order of pole (six term test) = -10.970946079134798 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y[1] (analytic) = 0.8574459972523973 " " y[1] (numeric) = 0.8574459972524041 " " absolute error = 6.772360450213455000000000000000E-15 " " relative error = 7.8982938539742760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y[1] (analytic) = 0.8630008699792093 " " y[1] (numeric) = 0.863000869979216 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 7.718808148955190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 13.090104973133776 " " Order of pole (six term test) = -10.690334582394502 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y[1] (analytic) = 0.8685756146656054 " " y[1] (numeric) = 0.8685756146656122 " " absolute error = 6.772360450213455000000000000000E-15 " " relative error = 7.7970879401452680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3434155353548978 " " Order of pole (three term test) = -66.20156324421974 " " Radius of convergence (six term test) for eq 1 = 7.322234905956942 " " Order of pole (six term test) = -10.99020748168093 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y[1] (analytic) = 0.8741702221156831 " " y[1] (numeric) = 0.8741702221156901 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 8.0011934497270990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.53651575592232870E-2 " " Order of pole (three term test) = -28.318007526631003 " " Radius of convergence (six term test) for eq 1 = 11.04412454148616 " " Order of pole (six term test) = -10.843203340967449 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y[1] (analytic) = 0.8797846828157361 " " y[1] (numeric) = 0.8797846828157431 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 7.9501327901652150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 31.08953716325002 " " Order of pole (six term test) = -10.743341581515034 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y[1] (analytic) = 0.885418986934406 " " y[1] (numeric) = 0.8854189869344131 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 8.024932221300320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.625305213415886 " " Order of pole (six term test) = -11.292290648297097 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y[1] (analytic) = 0.8910731243228405 " " y[1] (numeric) = 0.8910731243228478 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 8.2231993789448550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 15.517195764530006 " " Order of pole (six term test) = -11.099951343559578 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y[1] (analytic) = 0.8967470845148555 " " y[1] (numeric) = 0.896747084514863 " " absolute error = 7.438494264988549000000000000000E-15 " " relative error = 8.2949745735864980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 11.192667812120128 " " Order of pole (six term test) = -11.178060349810531 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y[1] (analytic) = 0.9024408567271023 " " y[1] (numeric) = 0.9024408567271098 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 8.3656635348171460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.57290577020069 " " Order of pole (six term test) = -11.245237095531838 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y[1] (analytic) = 0.9081544298592399 " " y[1] (numeric) = 0.9081544298592478 " " absolute error = 7.882583474838611000000000000000E-15 " " relative error = 8.6797831025945440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 27.317362240931843 " " Order of pole (six term test) = -11.079903107215268 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y[1] (analytic) = 0.913887792494114 " " y[1] (numeric) = 0.913887792494122 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 8.7468131678240040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 18.27180874427844 " " Order of pole (six term test) = -11.149471582667076 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y[1] (analytic) = 0.919640932897938 " " y[1] (numeric) = 0.9196409328979459 " " absolute error = 7.882583474838611000000000000000E-15 " " relative error = 8.5713708392680070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3401268777181713 " " Order of pole (three term test) = -65.56988840985923 " " Radius of convergence (six term test) for eq 1 = 6.674597673213837 " " Order of pole (six term test) = -11.044174013853201 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y[1] (analytic) = 0.9254138390204811 " " y[1] (numeric) = 0.9254138390204891 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 8.6378714476131950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 10.947175094458501 " " Order of pole (six term test) = -11.216756036133209 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y[1] (analytic) = 0.9312064984952619 " " y[1] (numeric) = 0.9312064984952702 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 8.8225870368192670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11884571230940368 " " Order of pole (three term test) = -37.846714152130566 " " Radius of convergence (six term test) for eq 1 = 8.322524733845778 " " Order of pole (six term test) = -11.015454096126636 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y[1] (analytic) = 0.9370188986397459 " " y[1] (numeric) = 0.9370188986397544 " " absolute error = 8.548717289613705000000000000000E-15 " " relative error = 9.1233136300919130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.79749565900586300E-2 " " Order of pole (three term test) = -0.6157782192890909 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y[1] (analytic) = 0.9428510264555481 " " y[1] (numeric) = 0.9428510264555569 " " absolute error = 8.770761894538737000000000000000E-15 " " relative error = 9.3023835669040820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 10.059206471449293 " " Order of pole (six term test) = -11.245426761285618 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);" Iterations = 276 "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 51 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 19 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 11 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 5 Minutes 13 Seconds "Time to Timeout " Unknown Percent Done = 56.530612244897604 "%" (%o58) true (%o58) diffeq.max