(%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_3D0 array_x , 1 1 1 array_tmp2 : array_const_1D0 + array_tmp1 , 1 1 1 array_tmp3_a1 : sinh(array_tmp2 ), array_tmp3_a2 : cosh(array_tmp2 ), 1 1 1 1 array_tmp3_a1 1 array_tmp3 : --------------, array_tmp4 : array_tmp3 + array_const_0D0 , 1 array_tmp3_a2 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_3D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_a2 array_tmp2 1 2 array_tmp3_a1 : --------------------------, 2 1 array_tmp3_a1 array_tmp2 1 2 array_tmp3_a2 : --------------------------, 2 1 array_tmp3_a1 - ats(2, array_tmp3_a2, array_tmp3, 2) 2 array_tmp3 : -----------------------------------------------------, 2 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp3_a2 array_tmp2 2 2 array_tmp3_a1 : --------------------------, 3 2 array_tmp3_a1 array_tmp2 2 2 array_tmp3_a2 : --------------------------, 3 2 array_tmp3_a1 - ats(3, array_tmp3_a2, array_tmp3, 2) 3 array_tmp3 : -----------------------------------------------------, 3 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3_a2 array_tmp2 3 2 array_tmp3_a1 : --------------------------, 4 3 array_tmp3_a1 array_tmp2 3 2 array_tmp3_a2 : --------------------------, 4 3 array_tmp3_a1 - ats(4, array_tmp3_a2, array_tmp3, 2) 4 array_tmp3 : -----------------------------------------------------, 4 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3_a2 array_tmp2 4 2 array_tmp3_a1 : --------------------------, 5 4 array_tmp3_a1 array_tmp2 4 2 array_tmp3_a2 : --------------------------, 5 4 array_tmp3_a1 - ats(5, array_tmp3_a2, array_tmp3, 2) 5 array_tmp3 : -----------------------------------------------------, 5 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3_a1 : kkk array_tmp3_a2 array_tmp2 kkk - 1 2 --------------------------------, array_tmp3_a2 : kkk - 1 kkk array_tmp3_a1 array_tmp2 kkk - 1 2 --------------------------------, array_tmp3 : kkk - 1 kkk array_tmp3_a1 - ats(kkk, array_tmp3_a2, array_tmp3, 2) kkk ---------------------------------------------------------, array_tmp3_a2 1 array_tmp4 : array_tmp3 , 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_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_3D0 array_x , 1 1 1 array_tmp2 : array_const_1D0 + array_tmp1 , 1 1 1 array_tmp3_a1 : sinh(array_tmp2 ), array_tmp3_a2 : cosh(array_tmp2 ), 1 1 1 1 array_tmp3_a1 1 array_tmp3 : --------------, array_tmp4 : array_tmp3 + array_const_0D0 , 1 array_tmp3_a2 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_3D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_a2 array_tmp2 1 2 array_tmp3_a1 : --------------------------, 2 1 array_tmp3_a1 array_tmp2 1 2 array_tmp3_a2 : --------------------------, 2 1 array_tmp3_a1 - ats(2, array_tmp3_a2, array_tmp3, 2) 2 array_tmp3 : -----------------------------------------------------, 2 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp3_a2 array_tmp2 2 2 array_tmp3_a1 : --------------------------, 3 2 array_tmp3_a1 array_tmp2 2 2 array_tmp3_a2 : --------------------------, 3 2 array_tmp3_a1 - ats(3, array_tmp3_a2, array_tmp3, 2) 3 array_tmp3 : -----------------------------------------------------, 3 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3_a2 array_tmp2 3 2 array_tmp3_a1 : --------------------------, 4 3 array_tmp3_a1 array_tmp2 3 2 array_tmp3_a2 : --------------------------, 4 3 array_tmp3_a1 - ats(4, array_tmp3_a2, array_tmp3, 2) 4 array_tmp3 : -----------------------------------------------------, 4 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3_a2 array_tmp2 4 2 array_tmp3_a1 : --------------------------, 5 4 array_tmp3_a1 array_tmp2 4 2 array_tmp3_a2 : --------------------------, 5 4 array_tmp3_a1 - ats(5, array_tmp3_a2, array_tmp3, 2) 5 array_tmp3 : -----------------------------------------------------, 5 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3_a1 : kkk array_tmp3_a2 array_tmp2 kkk - 1 2 --------------------------------, array_tmp3_a2 : kkk - 1 kkk array_tmp3_a1 array_tmp2 kkk - 1 2 --------------------------------, array_tmp3 : kkk - 1 kkk array_tmp3_a1 - ats(kkk, array_tmp3_a2, array_tmp3, 2) kkk ---------------------------------------------------------, array_tmp3_a2 1 array_tmp4 : array_tmp3 , 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_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i14) log10(x) := --------- log(10.0) log(x) (%o14) log10(x) := --------- log(10.0) (%i15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i16) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o16) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i17) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o17) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i18) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o18) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i21) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o21) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i22) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o22) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i23) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o23) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i24) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o24) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i25) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o25) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i26) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o26) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i27) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o27) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i28) display_pole_debug(typ, m, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_int(ALWAYS, "m", 4, m, 4, " "), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%o28) display_pole_debug(typ, m, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_int(ALWAYS, "m", 4, m, 4, " "), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i33) log_revs(file, revs) := printf(file, revs) (%o33) log_revs(file, revs) := printf(file, revs) (%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, "")) (%o35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, "")) (%i36) logstart(file) := printf(file, "") (%o36) logstart(file) := printf(file, "") (%i37) logend(file) := printf(file, "~%") (%o37) logend(file) := printf(file, "~%") (%i38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i41) factorial_2(nnn) := nnn! (%o41) factorial_2(nnn) := nnn! (%i42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i44) convfp(mmm) := mmm (%o44) convfp(mmm) := mmm (%i45) convfloat(mmm) := mmm (%o45) convfloat(mmm) := mmm (%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i47) Si(x) := 0.0 (%o47) Si(x) := 0.0 (%i48) Ci(x) := 0.0 (%o48) Ci(x) := 0.0 (%i49) ln(x) := log(x) (%o49) ln(x) := log(x) (%i50) arcsin(x) := asin(x) (%o50) arcsin(x) := asin(x) (%i51) arccos(x) := acos(x) (%o51) arccos(x) := acos(x) (%i52) arctan(x) := atan(x) (%o52) arctan(x) := atan(x) (%i53) omniabs(x) := abs(x) (%o53) omniabs(x) := abs(x) (%i54) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o54) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) ln(cosh(1.0 + 3.0 x)) (%i56) exact_soln_y(x) := block(---------------------) 3.0 ln(cosh(1.0 + 3.0 x)) (%o56) exact_soln_y(x) := block(---------------------) 3.0 (%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 0.0, float), define_variable(glob_smallish_float, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/lin_tanhpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"), 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:1.1,"), omniout_str(ALWAYS, "x_end:2.0,"), 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:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (ln(cosh(3.0*x + 1.0))/3.0) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 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_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, 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 : 1.1, iiif, jjjf x_end : 2.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h, if glob_max_h < glob_h then glob_h : glob_max_h, if glob_display_interval < glob_h then glob_h : glob_display_interval, best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"), 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, "2013-05-26T02:47:37-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_tanh"), logitem_str(html_log_file, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"), 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, "lin_tanh diffeq.max"), logitem_str(html_log_file, "lin_tanh maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 0.0, float), define_variable(glob_smallish_float, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/lin_tanhpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"), 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:1.1,"), omniout_str(ALWAYS, "x_end:2.0,"), 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:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (ln(cosh(3.0*x + 1.0))/3.0) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 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_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, 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 : 1.1, iiif, jjjf x_end : 2.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h, if glob_max_h < glob_h then glob_h : glob_max_h, if glob_display_interval < glob_h then glob_h : glob_display_interval, best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"), 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, "2013-05-26T02:47:37-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_tanh"), logitem_str(html_log_file, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"), 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, "lin_tanh diffeq.max"), logitem_str(html_log_file, "lin_tanh maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i58) main() "##############ECHO OF PROBLEM#################" "##############temp/lin_tanhpostode.ode#################" "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:1.1," "x_end:2.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (ln(cosh(3.0*x + 1.0))/3.0) " "));" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 0.8999999999999999 "" estimated_steps = 900000. "" step_error = 1.11111111111111120000000000000000E-16 "" est_needed_step_err = 1.11111111111111120000000000000000E-16 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.1149483493787170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-163 "" estimated_step_error = 4.1149483493787170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-163 "" 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 = 2.761494174506531000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-155 "" estimated_step_error = 2.761494174506531000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-155 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.8532061392314483000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-147 "" estimated_step_error = 1.8532061392314483000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-147 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.24366393579367560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-139 "" estimated_step_error = 1.24366393579367560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-139 "" 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 = 8.346065222575855000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-132 "" estimated_step_error = 8.346065222575855000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-132 "" 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 = 5.6009198032896070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-124 "" estimated_step_error = 5.6009198032896070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-124 "" 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 = 3.758673715897868400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-116 "" estimated_step_error = 3.758673715897868400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-116 "" 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 = 2.522349630320909000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-108 "" estimated_step_error = 2.522349630320909000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-108 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.69264824383644000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-100 "" estimated_step_error = 1.69264824383644000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-100 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.135820463697787800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-92 "" estimated_step_error = 1.135820463697787800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-92 "" 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 = 7.6210665995498550000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 "" estimated_step_error = 7.6210665995498550000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 "" 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 = 5.11267320850600000000000000000000000000000000000000000000000000000000000000000000000000000E-77 "" estimated_step_error = 5.11267320850600000000000000000000000000000000000000000000000000000000000000000000000000000E-77 "" 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 = 3.4287262949855773000000000000000000000000000000000000000000000000000000000000000000000E-69 "" estimated_step_error = 3.4287262949855773000000000000000000000000000000000000000000000000000000000000000000000E-69 "" 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 = 2.29785681466310150000000000000000000000000000000000000000000000000000000000000E-61 "" estimated_step_error = 2.29785681466310150000000000000000000000000000000000000000000000000000000000000E-61 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.537889880465240800000000000000000000000000000000000000000000000000000E-53 "" estimated_step_error = 1.537889880465240800000000000000000000000000000000000000000000000000000E-53 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.0264965592831055000000000000000000000000000000000000000000000E-45 "" estimated_step_error = 1.0264965592831055000000000000000000000000000000000000000000000E-45 "" 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 = 6.81511715944993600000000000000000000000000000000000000E-38 "" estimated_step_error = 6.81511715944993600000000000000000000000000000000000000E-38 "" 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 = 4.477716319818289000000000000000000000000000000E-30 "" estimated_step_error = 4.477716319818289000000000000000000000000000000E-30 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 1.1 " " y[1] (analytic) = 1.2023456360961104 " " y[1] (numeric) = 1.2023456360961104 " " 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" Radius of convergence (three term test) for eq 1 = 0.5000248574832679 " " Order of pole (three term test) = -249.52490811209682 " " Radius of convergence (six term test) for eq 1 = 1.527431609003778 " " Order of pole (six term test) = 3.16433092274941430E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.11 " " y[1] (analytic) = 1.212342062905879 " " y[1] (numeric) = 1.2123420629058792 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.83153428161033720000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7125026532630176 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.47034706228376644 " " Order of pole (three term test) = -239.39570936365794 " " Radius of convergence (six term test) for eq 1 = 1.5381067232728765 " " Order of pole (six term test) = 4.92361534210008500E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.12 " " y[1] (analytic) = 1.222338697767025 " " y[1] (numeric) = 1.2223386977670252 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.816555471332648000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6977171587685893 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.437699449129346 " " Order of pole (three term test) = -227.5412988031135 " " Radius of convergence (six term test) for eq 1 = 1.5491454065037096 " " Order of pole (six term test) = 7.19245106618977600E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000001 " " y[1] (analytic) = 1.2323355285675388 " " y[1] (numeric) = 1.232335528567539 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.801819389100425800000000000000E-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 = 0.4029126487921095 " " Order of pole (three term test) = -214.30990673895806 " " Radius of convergence (six term test) for eq 1 = 1.5605806858454525 " " Order of pole (six term test) = 0.10020399588520057 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000001 " " y[1] (analytic) = 1.242332543900312 " " y[1] (numeric) = 1.2423325439003123 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.57464039745623500000000000000E-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 = 0.36678857055149094 " " Order of pole (three term test) = -200.0490956204224 " " Radius of convergence (six term test) for eq 1 = 1.5724418838806256 " " Order of pole (six term test) = 0.13452067436039883 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000001 " " y[1] (analytic) = 1.252329733022138 " " y[1] (numeric) = 1.252329733022138 " " 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" Radius of convergence (three term test) for eq 1 = 0.33007356865902676 " " Order of pole (three term test) = -185.09196184375512 " " Radius of convergence (six term test) for eq 1 = 1.5847537123352837 " " Order of pole (six term test) = 0.17525881893762296 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000001 " " y[1] (analytic) = 1.262327085815092 " " y[1] (numeric) = 1.2623270858150921 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.75901006498371900000000000000E-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 = 0.2934401767013893 " " Order of pole (three term test) = -169.7469086880764 " " Radius of convergence (six term test) for eq 1 = 1.5975354027343165 " " Order of pole (six term test) = 0.22272900834063591 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000002 " " y[1] (analytic) = 1.2723245927501607 " " y[1] (numeric) = 1.272324592750161 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.745188344155766400000000000000E-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 = 0.25747687144808934 " " Order of pole (three term test) = -154.2909669043433 " " Radius of convergence (six term test) for eq 1 = 1.6107998882060903 " " Order of pole (six term test) = 0.2771566629944502 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000002 " " y[1] (analytic) = 1.2823222448529796 " " y[1] (numeric) = 1.2823222448529796 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.624713270984997 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.22268467774688314 " " Order of pole (three term test) = -138.96629573090505 " " Radius of convergence (six term test) for eq 1 = 1.6245530494746376 " " Order of pole (six term test) = 0.3386711053314073 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000002 " " y[1] (analytic) = 1.2923200336715641 " " y[1] (numeric) = 1.2923200336715646 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.436371783143968300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6142590568244153 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.18947911352002847 " " Order of pole (three term test) = -123.97930021338607 " " Radius of convergence (six term test) for eq 1 = 1.6387930377211342 " " Order of pole (six term test) = 0.4072952423072831 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000002 " " y[1] (analytic) = 1.3023179512459186 " " y[1] (numeric) = 1.3023179512459189 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.704995348582907500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6040891855163835 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.15819593226675296 " " Order of pole (three term test) = -109.50173044186333 " " Radius of convergence (six term test) for eq 1 = 1.6535096865344647 " " Order of pole (six term test) = 0.4829359841395888 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000002 " " y[1] (analytic) = 1.3123159900794066 " " y[1] (numeric) = 1.3123159900794066 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.594140083567807 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.12909926157174276 " " Order of pole (three term test) = -95.67315046886368 " " Radius of convergence (six term test) for eq 1 = 1.668684026000533 " " Order of pole (six term test) = 0.5653755551221149 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000002 " " y[1] (analytic) = 1.3223141431117904 " " y[1] (numeric) = 1.3223141431117906 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.67921220597773900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5843519439748295 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.10239097629615664 " " Order of pole (three term test) = -82.60424333863217 " " Radius of convergence (six term test) for eq 1 = 1.6842879124668164 " " Order of pole (six term test) = 0.6542638953578841 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000002 " " y[1] (analytic) = 1.332312403693838 " " y[1] (numeric) = 1.332312403693838 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5746679102038086 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 7.82204179983450600E-2 " " Order of pole (three term test) = -70.38052323117215 " " Radius of convergence (six term test) for eq 1 = 1.7002837892613258 " " Order of pole (six term test) = 0.7491124178231878 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000002 " " y[1] (analytic) = 1.3423107655634017 " " y[1] (numeric) = 1.342310765563402 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.65419670780807300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5650333526989864 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 5.669383324924251000E-2 " " Order of pole (three term test) = -59.06613414331726 " " Radius of convergence (six term test) for eq 1 = 1.7166245951403634 " " Order of pole (six term test) = 0.8492894501380679 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000002 " " y[1] (analytic) = 1.352309222822895 " " y[1] (numeric) = 1.352309222822895 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5553952164412657 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 3.788312812989746000E-2 " " Order of pole (three term test) = -48.7075131914769 " " Radius of convergence (six term test) for eq 1 = 1.7332538386676117 " " Order of pole (six term test) = 0.9540177555638092 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2600000000000002 " " y[1] (analytic) = 1.3623077699180726 " " y[1] (numeric) = 1.3623077699180723 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.629915132454869400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.545701421579974 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 2.18337143732530600E-2 " " Order of pole (three term test) = -39.33677872191803 " " Radius of convergence (six term test) for eq 1 = 1.7501058583421698 " " Order of pole (six term test) = 1.0623745934628666 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2700000000000002 " " y[1] (analytic) = 1.3723064016180493 " " y[1] (numeric) = 1.3723064016180495 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.618039562179587000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5359003017543231 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 8.571354547666223000E-3 " " Order of pole (three term test) = -30.97476716694117 " " Radius of convergence (six term test) for eq 1 = 1.7671062883371904 " " Order of pole (six term test) = 1.1732948182184177 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2800000000000002 " " y[1] (analytic) = 1.382305112996481 " " y[1] (numeric) = 1.382305112996481 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5259400666106713 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7841727494856345 " " Order of pole (six term test) = 1.285577540849376 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2900000000000003 " " y[1] (analytic) = 1.3923038994138357 " " y[1] (numeric) = 1.3923038994138355 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.594799849504930600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5157682762702929 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8012157825749853 " " Order of pole (six term test) = 1.3978968570739543 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3000000000000003 " " y[1] (analytic) = 1.4023027565007016 " " y[1] (numeric) = 1.4023027565007016 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.5053313162786113 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8181400366109384 " " Order of pole (six term test) = 1.5088170801163159 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3100000000000003 " " y[1] (analytic) = 1.412301680142064 " " y[1] (numeric) = 1.412301680142064 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.494573861873555 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8348457182390459 " " Order of pole (six term test) = 1.6168128011742517 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3200000000000003 " " y[1] (analytic) = 1.4223006664624958 " " y[1] (numeric) = 1.4223006664624958 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.483438320334065 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8512302989256706 " " Order of pole (six term test) = 1.720293914882813 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3300000000000003 " " y[1] (analytic) = 1.4322997118122114 " " y[1] (numeric) = 1.4322997118122114 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.471864239608343 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.867190465085602 " " Order of pole (six term test) = 1.8176355105554052 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3400000000000003 " " y[1] (analytic) = 1.4422988127539318 " " y[1] (numeric) = 1.4422988127539318 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.459787670533112 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.882624282214949 " " Order of pole (six term test) = 1.9072122304395531 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3500000000000003 " " y[1] (analytic) = 1.4522979660505129 " " y[1] (numeric) = 1.452297966050513 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.52891906561623800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4471404684580804 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 3.242357261673556300E-3 " " Order of pole (three term test) = -0.9451996246674843 " " Radius of convergence (six term test) for eq 1 = 1.8974335293896614 " " Order of pole (six term test) = 1.9874363702152902 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3600000000000003 " " y[1] (analytic) = 1.4622971686532964 " " y[1] (numeric) = 1.4622971686532964 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4338495181987192 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 1.521242999606858800E-2 " " Order of pole (three term test) = -1.778983608331185 " " Radius of convergence (six term test) for eq 1 = 1.911526143860976 " " Order of pole (six term test) = 2.0567986330809944 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3700000000000003 " " y[1] (analytic) = 1.4722964176911344 " " y[1] (numeric) = 1.4722964176911344 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4198358635423007 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 3.004015623548752500E-2 " " Order of pole (three term test) = -3.629876113665898 " " Radius of convergence (six term test) for eq 1 = 1.9248187023409589 " " Order of pole (six term test) = 2.113910139063311 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3800000000000003 " " y[1] (analytic) = 1.4822957104600576 " " y[1] (numeric) = 1.4822957104600574 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.497977787820189400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.4050137192095493 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 4.776026999087152300E-2 " " Order of pole (three term test) = -6.501964507999767 " " Radius of convergence (six term test) for eq 1 = 1.9372388518679915 " " Order of pole (six term test) = 2.1575439888948473 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3900000000000003 " " y[1] (analytic) = 1.4922950444135399 " " y[1] (numeric) = 1.4922950444135399 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3892893386630951 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 6.84161546142223400E-2 " " Order of pole (three term test) = -10.40191782406327 " " Radius of convergence (six term test) for eq 1 = 1.9487275956299142 " " Order of pole (six term test) = 2.1866745031372226 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4000000000000004 " " y[1] (analytic) = 1.5022944171533352 " " y[1] (numeric) = 1.5022944171533352 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.372559705643193 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 9.20600733529542400E-2 " " Order of pole (three term test) = -15.339156733967107 " " Radius of convergence (six term test) for eq 1 = 1.9592413368639912 " " Order of pole (six term test) = 2.200512199998169 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4100000000000004 " " y[1] (analytic) = 1.5122938264208419 " " y[1] (numeric) = 1.5122938264208419 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3547110099677957 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.11875328599375118 " " Order of pole (three term test) = -21.325968021968915 " " Radius of convergence (six term test) for eq 1 = 1.9687535855390286 " " Order of pole (six term test) = 2.1985326278409545 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4200000000000004 " " y[1] (analytic) = 1.5222932700889737 " " y[1] (numeric) = 1.5222932700889735 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.458619106370045400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.3356168588237436 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.1485660646496777 " " Order of pole (three term test) = -28.37757162330533 " " Radius of convergence (six term test) for eq 1 = 1.977256244999051 " " Order of pole (six term test) = 2.1804974389823606 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4300000000000004 " " y[1] (analytic) = 1.532292746154502 " " y[1] (numeric) = 1.532292746154502 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.315136162788252 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.18157761545289083 " " Order of pole (three term test) = -36.512145744266626 " " Radius of convergence (six term test) for eq 1 = 1.9847604107351249 " " Order of pole (six term test) = 2.1464664487559943 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4400000000000004 " " y[1] (analytic) = 1.5422922527308458 " " y[1] (numeric) = 1.5422922527308458 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2931106200932962 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.21787590729826162 " " Order of pole (three term test) = -45.75081330696437 " " Radius of convergence (six term test) for eq 1 = 1.9912966359371063 " " Order of pole (six term test) = 2.0967999306806604 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4500000000000004 " " y[1] (analytic) = 1.5522917880412788 " " y[1] (numeric) = 1.5522917880412785 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.430430841905134500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.26936170219062 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.25755740350239076 " " Order of pole (three term test) = -56.11759088130836 " " Radius of convergence (six term test) for eq 1 = 1.996914644661479 " " Order of pole (six term test) = 2.0321509801030615 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4600000000000004 " " y[1] (analytic) = 1.5622913504125329 " " y[1] (numeric) = 1.5622913504125326 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.421275262558414600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2436870167284084 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.300726687197975 " " Order of pole (three term test) = -67.63929932735905 " " Radius of convergence (six term test) for eq 1 = 2.0016825003008942 " " Order of pole (six term test) = 1.9534483639776425 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4700000000000004 " " y[1] (analytic) = 1.5722909382687755 " " y[1] (numeric) = 1.5722909382687755 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.2158558882292807 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.3474959663715173 " " Order of pole (three term test) = -80.34543353540849 " " Radius of convergence (six term test) for eq 1 = 2.00568526360988 " " Order of pole (six term test) = 1.8618708308983631 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4800000000000004 " " y[1] (analytic) = 1.5822905501259366 " " y[1] (numeric) = 1.5822905501259363 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.403311199118003300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.185603948590479 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.3979844396795777 " " Order of pole (three term test) = -94.26798691124756 " " Radius of convergence (six term test) for eq 1 = 2.009023198640431 " " Order of pole (six term test) = 1.7588143281364523 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4900000000000004 " " y[1] (analytic) = 1.5922901845863635 " " y[1] (numeric) = 1.5922901845863633 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.394498358869886700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1526264648406417 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.4523174989422321 " " Order of pole (three term test) = -109.44122442085717 " " Radius of convergence (six term test) for eq 1 = 2.0118096028005668 " " Order of pole (six term test) = 1.6458538918755412 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5000000000000004 " " y[1] (analytic) = 1.6022898403337917 " " y[1] (numeric) = 1.6022898403337913 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.771590998527140300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.1165700423844114 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.5106257394307105 " " Order of pole (three term test) = -125.90139634338077 " " Radius of convergence (six term test) for eq 1 = 2.0141683506272012 " " Order of pole (six term test) = 1.5247021676844437 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000005 " " y[1] (analytic) = 1.6122895161286035 " " y[1] (numeric) = 1.6122895161286033 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.377200575354482800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0770222192521988 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.5730437435578343 " " Order of pole (three term test) = -143.68638303295916 " " Radius of convergence (six term test) for eq 1 = 2.016231246412093 " " Order of pole (six term test) = 1.397166531970372 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000005 " " y[1] (analytic) = 1.6222892108033673 " " y[1] (numeric) = 1.6222892108033673 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.0334982948867673 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.6397085981576965 " " Order of pole (three term test) = -162.83525917512992 " " Radius of convergence (six term test) for eq 1 = 2.01813527989904 " " Order of pole (six term test) = 1.2651066514069669 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000005 " " y[1] (analytic) = 1.6322889232586333 " " y[1] (numeric) = 1.632288923258633 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.36032660493554500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9854244927779829 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.7107581001911831 " " Order of pole (three term test) = -183.38776425404058 " " Radius of convergence (six term test) for eq 1 = 2.020019873757625 " " Order of pole (six term test) = 1.130394086044447 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000005 " " y[1] (analytic) = 1.642288652458974 " " y[1] (numeric) = 1.6422886524589737 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.352043714072841400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.9321162054299906 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.7863286000316897 " " Order of pole (three term test) = -205.3836640706983 " " Radius of convergence (six term test) for eq 1 = 2.0220241999215394 " " Order of pole (six term test) = 0.9948752019660247 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000005 " " y[1] (analytic) = 1.652288397429258 " " y[1] (numeric) = 1.6522883974292577 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.34386106729614100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8727495569280104 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.8665524265725182 " " Order of pole (three term test) = -228.8619865176338 " " Radius of convergence (six term test) for eq 1 = 2.024284628781997 " " Order of pole (six term test) = 0.8603383017766664 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000005 " " y[1] (analytic) = 1.6622881572511379 " " y[1] (numeric) = 1.6622881572511379 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8063237562244785 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 0.9515548337621156 " " Order of pole (three term test) = -253.8601132423904 " " Radius of convergence (six term test) for eq 1 = 2.0269323588430845 " " Order of pole (six term test) = 0.7284854916276977 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000005 " " y[1] (analytic) = 1.6722879310597447 " " y[1] (numeric) = 1.6722879310597445 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.32778931666581800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.7316105599513827 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 1.0414504049971693 " " Order of pole (three term test) = -280.41270769326593 " " Radius of convergence (six term test) for eq 1 = 2.030091260077687 " " Order of pole (six term test) = 0.6009094739892653 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000005 " " y[1] (analytic) = 1.6822877180405724 " " y[1] (numeric) = 1.6822877180405722 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.319896724822169600000000000000E-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 = 1.13633884967405 " " Order of pole (three term test) = -308.55045920788774 " " Radius of convergence (six term test) for eq 1 = 2.033875947945914 " " Order of pole (six term test) = 0.4790751305386092 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000005 " " y[1] (analytic) = 1.6922875174265464 " " y[1] (numeric) = 1.6922875174265462 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.312097398571452600000000000000E-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 = 1.236300128275036 " " Order of pole (three term test) = -338.2986231721371 " " Radius of convergence (six term test) for eq 1 = 2.038390093318875 " " Order of pole (six term test) = 0.36430553788427567 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000005 " " y[1] (analytic) = 1.7022873284952613 " " y[1] (numeric) = 1.702287328495261 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.304389695018806600000000000000E-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 = 1.341388846360271 " " Order of pole (three term test) = -369.67533826863405 " " Radius of convergence (six term test) for eq 1 = 2.0437249614869946 " " Order of pole (six term test) = 0.2577718680376062 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000005 " " y[1] (analytic) = 1.71228715056638 " " y[1] (numeric) = 1.7122871505663797 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.29677200959888500000000000000E-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 = 1.4516278679649606 " " Order of pole (three term test) = -402.68970456836064 " " Radius of convergence (six term test) for eq 1 = 2.049958165808413 " " Order of pole (six term test) = 0.1604865279931218 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000006 " " y[1] (analytic) = 1.7222869829991831 " " y[1] (numeric) = 1.722286982999183 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.289242774966363500000000000000E-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 = 1.5670011160272188 " " Order of pole (three term test) = -437.33961107775644 " " Radius of convergence (six term test) for eq 1 = 2.0571526147714825 " " Order of pole (six term test) = 7.3298828594047900E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000006 " " y[1] (analytic) = 1.732286825190263 " " y[1] (numeric) = 1.732286825190263 " " 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" Radius of convergence (three term test) for eq 1 = 1.6874455520601044 " " Order of pole (three term test) = -473.60930846533563 " " Radius of convergence (six term test) for eq 1 = 2.0653556276391796 " " Order of pole (six term test) = -3.107525085727758000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000006 " " y[1] (analytic) = 1.742286676571351 " " y[1] (numeric) = 1.7422866765713507 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.274443568391358500000000000000E-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 = 1.8128423632608661 " " Order of pole (three term test) = -511.4667331550547 " " Radius of convergence (six term test) for eq 1 = 2.0745981929289097 " " Order of pole (six term test) = -6.82157834934500300E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000006 " " y[1] (analytic) = 1.7522865366072697 " " y[1] (numeric) = 1.7522865366072695 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.267170638398832400000000000000E-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 = 1.9430074332535905 " " Order of pole (three term test) = -550.8606031701772 " " Radius of convergence (six term test) for eq 1 = 2.0848943424903563 " " Order of pole (six term test) = -0.12167695870203588 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000006 " " y[1] (analytic) = 1.7622864047940086 " " y[1] (numeric) = 1.762286404794008 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.519960482257546000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8009304315344435 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 2.077681235292009 " " Order of pole (three term test) = -591.7173246722605 " " Radius of convergence (six term test) for eq 1 = 2.096240618030941 " " Order of pole (six term test) = -0.16331058609365634 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000006 " " y[1] (analytic) = 1.772286280656906 " " y[1] (numeric) = 1.7722862806569057 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.252870979979202000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 0.8898609674934483 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 2.216518364200017 " " Order of pole (three term test) = -633.9377713543659 " " Radius of convergence (six term test) for eq 1 = 2.1086156080668745 " " Order of pole (six term test) = -0.19310585955835968 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000006 " " y[1] (analytic) = 1.7822861637489436 " " y[1] (numeric) = 1.7822861637489433 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.245841489662761900000000000000E-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 = 2.3590770173461917 " " Order of pole (three term test) = -677.3940270509445 " " Radius of convergence (six term test) for eq 1 = 2.121979540231462 " " Order of pole (six term test) = -0.21122341924982457 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000006 " " y[1] (analytic) = 1.7922860536491336 " " y[1] (numeric) = 1.7922860536491332 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.47778087067009900000000000000E-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 = 2.504808841689518 " " Order of pole (three term test) = -721.9262143476691 " " Radius of convergence (six term test) for eq 1 = 2.136273917667051 " " Order of pole (six term test) = -0.21799796109707437 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000006 " " y[1] (analytic) = 1.8022859499610038 " " y[1] (numeric) = 1.8022859499610036 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.232016511751843300000000000000E-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 = 2.653049684621667 " " Order of pole (three term test) = -767.3395687589103 " " Radius of convergence (six term test) for eq 1 = 2.1514211969841965 " " Order of pole (six term test) = -0.21394169456217327 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000006 " " y[1] (analytic) = 1.8122858523111711 " " y[1] (numeric) = 1.812285852311171 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.225218442454110400000000000000E-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 = 2.803011903632405 " " Order of pole (three term test) = -813.4019541384715 " " Radius of convergence (six term test) for eq 1 = 2.16732451263256 " " Order of pole (six term test) = -0.1997485307223812 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000006 " " y[1] (analytic) = 1.8222857603479958 " " y[1] (numeric) = 1.8222857603479956 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.218494978979741300000000000000E-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 = 2.9537790116450644 " " Order of pole (three term test) = -859.8420530131128 " " Radius of convergence (six term test) for eq 1 = 2.183867461664153 " " Order of pole (six term test) = -0.1762987426803182 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000006 " " y[1] (analytic) = 1.832285673740316 " " y[1] (numeric) = 1.8322856737403157 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.211844900100992600000000000000E-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 = 3.104303522094764 " " Order of pole (three term test) = -906.3484935057664 " " Radius of convergence (six term test) for eq 1 = 2.2009139731194827 " " Order of pole (six term test) = -0.14466367241580258 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000007 " " y[1] (analytic) = 1.8422855921762542 " " y[1] (numeric) = 1.8422855921762538 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.410534022173343700000000000000E-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 = 3.25340891989136 " " Order of pole (three term test) = -952.5701953782672 " " Radius of convergence (six term test) for eq 1 = 2.218308295819787 " " Order of pole (six term test) = -0.1061099134418857 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000007 " " y[1] (analytic) = 1.8522855153620947 " " y[1] (numeric) = 1.8522855153620947 " " 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" Radius of convergence (three term test) for eq 1 = 3.3997966707188 " " Order of pole (three term test) = -998.1182163118249 " " Radius of convergence (six term test) for eq 1 = 2.2358751492596745 " " Order of pole (six term test) = -6.21022230375540800E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000007 " " y[1] (analytic) = 1.8622854430212283 " " y[1] (numeric) = 1.862285443021228 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.384646303896391700000000000000E-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 = 3.5420590989583682 " " Order of pole (three term test) = -1042.5693577650695 " " Radius of convergence (six term test) for eq 1 = 2.2534200932146193 " " Order of pole (six term test) = -1.430426371836546200E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000007 " " y[1] (analytic) = 1.8722853748931512 " " y[1] (numeric) = 1.872285374893151 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.18595491853213400000000000000E-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 = 3.6786987723953732 " " Order of pole (three term test) = -1085.4717349618788 " " Radius of convergence (six term test) for eq 1 = 2.2707301755162557 " " Order of pole (six term test) = 3.5423830505273200E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000007 " " y[1] (analytic) = 1.8822853107325317 " " y[1] (numeric) = 1.8822853107325315 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.179654347079922100000000000000E-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 = 3.8081547174695536 " " Order of pole (three term test) = -1126.352423563001 " " Radius of convergence (six term test) for eq 1 = 2.287574932630452 " " Order of pole (six term test) = 8.50322398586467200E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000007 " " y[1] (analytic) = 1.8922852503083245 " " y[1] (numeric) = 1.8922852503083243 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.173420365078953600000000000000E-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 = 3.928835379202078 " " Order of pole (three term test) = -1164.727174624347 " " Radius of convergence (six term test) for eq 1 = 2.3037078084893547 " " Order of pole (six term test) = 0.13229373347671114 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000007 " " y[1] (analytic) = 1.9022851934029392 " " y[1] (numeric) = 1.902285193402939 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.167251922556483600000000000000E-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 = 4.039157702728942 " " Order of pole (three term test) = -1200.11202852322 " " Radius of convergence (six term test) for eq 1 = 2.3188680664949985 " " Order of pole (six term test) = 0.17482263383046615 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000007 " " y[1] (analytic) = 1.912285139811457 " " y[1] (numeric) = 1.9122851398114564 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.48344397447324100000000000000E-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 = 4.1375911321598196 " " Order of pole (three term test) = -1232.0364831064967 " " Radius of convergence (six term test) for eq 1 = 2.3327832533275012 " " Order of pole (six term test) = 0.21010149485918284 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000007 " " y[1] (analytic) = 1.9222850893408916 " " y[1] (numeric) = 1.922285089340891 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.465322695727179000000000000000E-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 = 4.222704722897534 " " Order of pole (three term test) = -1260.0576883220658 " " Radius of convergence (six term test) for eq 1 = 2.345172261785845 " " Order of pole (six term test) = 0.2355162961235493 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000007 " " y[1] (analytic) = 1.932285041809496 " " y[1] (numeric) = 1.9322850418094955 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.29825931599715500000000000000E-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 = 4.293215023559784 " " Order of pole (three term test) = -1283.774972856553 " " Radius of convergence (six term test) for eq 1 = 2.355749015304912 " " Order of pole (six term test) = 0.24840059056900543 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000007 " " y[1] (analytic) = 1.9422849970461071 " " y[1] (numeric) = 1.9422849970461067 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.286426608481497400000000000000E-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 = 4.348032006455834 " " Order of pole (three term test) = -1302.8438879986436 " " Radius of convergence (six term test) for eq 1 = 2.3642267658228198 " " Order of pole (six term test) = 0.24608850830572493 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000008 " " y[1] (analytic) = 1.95228495488953 " " y[1] (numeric) = 1.9522849548895294 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.41207267467154700000000000000E-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 = 4.3863001379843976 " " Order of pole (three term test) = -1316.988890264851 " " Radius of convergence (six term test) for eq 1 = 2.370322954385051 " " Order of pole (six term test) = 0.22597587006942277 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000008 " " y[1] (analytic) = 1.962284915187956 " " y[1] (numeric) = 1.9622849151879551 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.526245973893407400000000000000E-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 = 4.407431797482315 " " Order of pole (three term test) = -1326.0138110937874 " " Radius of convergence (six term test) for eq 1 = 2.373764542720101 " " Order of pole (six term test) = 0.18558793232433146 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000008 " " y[1] (analytic) = 1.9722848777984165 " " y[1] (numeric) = 1.972284877798416 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.251648404594481200000000000000E-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 = 4.411130637014032 " " Order of pole (three term test) = -1329.8093692414204 " " Radius of convergence (six term test) for eq 1 = 2.374293676113695 " " Order of pole (six term test) = 0.12265150965850857 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000008 " " y[1] (analytic) = 1.9822848425862711 " " y[1] (numeric) = 1.9822848425862707 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24028959062544720000000000000E-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 = 4.397403152907758 " " Order of pole (three term test) = -1328.3571798501634 " " Radius of convergence (six term test) for eq 1 = 2.371673482230325 " " Order of pole (six term test) = 3.51683872952008870E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000008 " " y[1] (analytic) = 1.9922848094247183 " " y[1] (numeric) = 1.9922848094247174 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.458089603948699500000000000000E-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 = 4.366557598595556 " " Order of pole (three term test) = -1321.7299675021454 " " Radius of convergence (six term test) for eq 1 = 2.3656937875247457 " " Order of pole (six term test) = -7.85135554894562700E-2 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000008 " " y[1] (analytic) = 2.002284778194341 " " y[1] (numeric) = 2.0022847781943396 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.65373699115680100000000000000E-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 = 4.319190356730422 " " Order of pole (three term test) = -1310.0879875412165 " " Radius of convergence (six term test) for eq 1 = 2.3561764851979983 " " Order of pole (six term test) = -0.21963563447601864 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000008 " " y[1] (analytic) = 2.0122847487826756 " " y[1] (numeric) = 2.0122847487826747 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.413781003098223000000000000000E-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 = 4.256160832499684 " " Order of pole (three term test) = -1293.671945495428 " " Radius of convergence (six term test) for eq 1 = 2.3429802970279776 " " Order of pole (six term test) = -0.38897412230596373 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000008 " " y[1] (analytic) = 2.022284721083811 " " y[1] (numeric) = 2.0222847210838095 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.58793302278514300000000000000E-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 = 4.1785567744987056 " " Order of pole (three term test) = -1272.792963198461 " " Radius of convergence (six term test) for eq 1 = 2.3260046606488345 " " Order of pole (six term test) = -0.5868003992178181 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000008 " " y[1] (analytic) = 2.032284694998 " " y[1] (numeric) = 2.0322846949979985 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.55551671883992100000000000000E-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 = 4.087652516092003 " " Order of pole (three term test) = -1247.8203235952099 " " Radius of convergence (six term test) for eq 1 = 2.3051925316391193 " " Order of pole (six term test) = -0.812858521278276 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000008 " " y[1] (analytic) = 2.0422846704313065 " " y[1] (numeric) = 2.042284670431305 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.52341786059055500000000000000E-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 = 3.9848629680181817 " " Order of pole (three term test) = -1219.1678363691099 " " Radius of convergence (six term test) for eq 1 = 2.280531909869058 " " Order of pole (six term test) = -1.0663624449307854 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000008 " " y[1] (analytic) = 2.0522846472952643 " " y[1] (numeric) = 2.052284647295263 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.49163180802430400000000000000E-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 = 3.8716962105641466 " " Order of pole (three term test) = -1187.279678737375 " " Radius of convergence (six term test) for eq 1 = 2.2520560177729996 " " Order of pole (six term test) = -1.3460134736011522 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000009 " " y[1] (analytic) = 2.062284625506559 " " y[1] (numeric) = 2.0622846255065577 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.46015401110282200000000000000E-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 = 3.749707329910878 " " Order of pole (three term test) = -1152.6165135344122 " " Radius of convergence (six term test) for eq 1 = 2.219842082945478 " " Order of pole (six term test) = -1.65003749737299 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000009 " " y[1] (analytic) = 2.0722846049867276 " " y[1] (numeric) = 2.0722846049867263 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.42898000759273400000000000000E-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 = 3.6204556877029286 " " Order of pole (three term test) = -1115.6425542102372 " " Radius of convergence (six term test) for eq 1 = 2.184008822879211 " " Order of pole (six term test) = -1.9762397219290762 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000009 " " y[1] (analytic) = 2.0822845856618772 " " y[1] (numeric) = 2.082284585661876 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.39810542095864300000000000000E-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 = 3.4854672968743947 " " Order of pole (three term test) = -1076.8140953732766 " " Radius of convergence (six term test) for eq 1 = 2.1447127646817514 " " Order of pole (six term test) = -2.322073733576902 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000009 " " y[1] (analytic) = 2.092284567462417 " " y[1] (numeric) = 2.092284567462416 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.245017305544311000000000000000E-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 = 3.3462033517972407 " " Order of pole (three term test) = -1036.5698424991028 " " Radius of convergence (six term test) for eq 1 = 2.1021436205227504 " " Order of pole (six term test) = -2.6847206840903954 " " "Finished!" "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;" Iterations = 90 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 0 Minutes 58 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 0 Minutes 47 Seconds "Time to Timeout "= 0 Years 0 Days 0 Hours 2 Minutes 1 Seconds Percent Done = 101.11111111111119 "%" (%o58) true (%o58) diffeq.max