(%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) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) 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) (%o4) 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) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 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, ""), value3 : 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 value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 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, ""), value3 : 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 value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) 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)) (%o6) 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)) (%i7) 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 : 2 - 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, " ")))) (%o7) 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 : 2 - 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, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 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 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 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 (%i9) 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, "%")) (%o9) 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, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : 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 glob_small_float 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) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 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) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float 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_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 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_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : 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 glob_small_float 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) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 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) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float 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_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 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_pole()) (%i11) 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 (%o11) 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 (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : cos(array_x ), array_tmp1_g : sin(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp2 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_g array_x array_tmp1 array_x 1 2 1 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 2 1 2 1 array_tmp2 : array_tmp1 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp2 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_tmp1_g array_x array_tmp1 array_x 2 2 2 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 3 2 3 2 array_tmp2 : array_tmp1 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp2 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_tmp1_g array_x array_tmp1 array_x 3 2 3 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 4 3 4 3 array_tmp2 : array_tmp1 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp2 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_tmp1_g array_x array_tmp1 array_x 4 2 4 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 5 4 5 4 array_tmp2 : array_tmp1 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp2 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_tmp1 : kkk - array_tmp1_g array_x array_tmp1 array_x kkk - 1 2 kkk - 1 2 ------------------------------, array_tmp1_g : --------------------------, kkk - 1 kkk kkk - 1 array_tmp2 : array_tmp1 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp2 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)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : cos(array_x ), array_tmp1_g : sin(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp2 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_g array_x array_tmp1 array_x 1 2 1 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 2 1 2 1 array_tmp2 : array_tmp1 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp2 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_tmp1_g array_x array_tmp1 array_x 2 2 2 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 3 2 3 2 array_tmp2 : array_tmp1 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp2 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_tmp1_g array_x array_tmp1 array_x 3 2 3 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 4 3 4 3 array_tmp2 : array_tmp1 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp2 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_tmp1_g array_x array_tmp1 array_x 4 2 4 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 5 4 5 4 array_tmp2 : array_tmp1 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp2 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_tmp1 : kkk - array_tmp1_g array_x array_tmp1 array_x kkk - 1 2 kkk - 1 2 ------------------------------, array_tmp1_g : --------------------------, kkk - 1 kkk kkk - 1 array_tmp2 : array_tmp1 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp2 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) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) 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)) (%o17) 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)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) 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 (%o20) 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 (%i21) 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 (%o21) 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 (%i22) 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)) (%o22) 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)) (%i23) 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, "~%")) (%o23) 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, "~%")) (%i24) 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~%")) (%o24) 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~%")) (%i25) 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) (%o25) 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) (%i26) 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) (%o26) 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) (%i27) display_pole_debug(typ, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%o27) display_pole_debug(typ, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%i28) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o28) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%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") else printf(file, "No Pole"), 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") else printf(file, "No Pole"), printf(file, "")) (%i36) logstart(file) := printf(file, "") (%o36) logstart(file) := printf(file, "") (%i37) logend(file) := printf(file, "~%") (%o37) logend(file) := printf(file, "~%") (%i38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i41) factorial_2(nnn) := nnn! (%o41) factorial_2(nnn) := nnn! (%i42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i44) convfp(mmm) := mmm (%o44) convfp(mmm) := mmm (%i45) convfloat(mmm) := mmm (%o45) convfloat(mmm) := mmm (%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i47) Si(x) := 0.0 (%o47) Si(x) := 0.0 (%i48) Ci(x) := 0.0 (%o48) Ci(x) := 0.0 (%i49) ln(x) := log(x) (%o49) ln(x) := log(x) (%i50) arcsin(x) := asin(x) (%o50) arcsin(x) := asin(x) (%i51) arccos(x) := acos(x) (%o51) arccos(x) := acos(x) (%i52) arctan(x) := atan(x) (%o52) arctan(x) := atan(x) (%i53) omniabs(x) := abs(x) (%o53) omniabs(x) := abs(x) (%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i56) exact_soln_y(x) := block(sin(x) + 1.0) (%o56) exact_soln_y(x) := block(sin(x) + 1.0) (%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, value3, 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(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_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, 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_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, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, 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/cospostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), 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, " (1.0 + sin(x)) "), 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 : 1.0E-200, glob_smallish_float : 1.0E-64, 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 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 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 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 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 <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 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_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 <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 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_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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 10000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, 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), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) 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(), 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, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), 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 ) = cos ( x ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T12:26:29-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "cos"), logitem_str(html_log_file, "diff ( y , x , 1 ) = cos ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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, " 165 "), logitem_str(html_log_file, "cos diffeq.max"), logitem_str(html_log_file, "cos 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, value3, 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(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_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, 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_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, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, 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/cospostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), 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, " (1.0 + sin(x)) "), 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 : 1.0E-200, glob_smallish_float : 1.0E-64, 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 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 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 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 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 <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 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_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 <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 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_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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 10000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, 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), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) 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(), 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, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), 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 ) = cos ( x ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T12:26:29-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "cos"), logitem_str(html_log_file, "diff ( y , x , 1 ) = cos ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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, " 165 "), logitem_str(html_log_file, "cos diffeq.max"), logitem_str(html_log_file, "cos 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/cospostode.ode#################" "diff ( y , x , 1 ) = cos ( x ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-5.0," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:10000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "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(" " (1.0 + sin(x)) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 10. "" estimated_steps = 10000. "" step_error = 1.00000000000000E-14 "" est_needed_step_err = 1.00000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 2.3777580727116668000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" max_value3 = 2.3777580727116668000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" value3 = 2.3777580727116668000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -5. " " y[1] (analytic) = 1.9589242746631386 " " y[1] (numeric) = 1.9589242746631386 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.999 " " y[1] (analytic) = 1.9592074573392275 " " y[1] (numeric) = 1.9592074573392273 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.133338912595744200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.998000000000000 " " y[1] (analytic) = 1.959489680807939 " " y[1] (numeric) = 1.9594896808079387 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.13317567885061590000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.996999999999999 " " y[1] (analytic) = 1.9597709447870497 " " y[1] (numeric) = 1.9597709447870493 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26602609366839900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.995999999999999 " " y[1] (analytic) = 1.9600512489952955 " " y[1] (numeric) = 1.960051248995295 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.2657020324223600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.994999999999998 " " y[1] (analytic) = 1.9603305931523722 " " y[1] (numeric) = 1.9603305931523718 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.265379173295106200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.993999999999998 " " y[1] (analytic) = 1.960608976978936 " " y[1] (numeric) = 1.9606089769789354 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.397586273431872400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.992999999999998 " " y[1] (analytic) = 1.9608864001966029 " " y[1] (numeric) = 1.9608864001966022 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.397105588107020600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.991999999999997 " " y[1] (analytic) = 1.9611628625279494 " " y[1] (numeric) = 1.9611628625279487 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.396626702977864000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.990999999999997 " " y[1] (analytic) = 1.9614383636965136 " " y[1] (numeric) = 1.961438363696513 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.396149617058078500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.989999999999997 " " y[1] (analytic) = 1.9617129034267944 " " y[1] (numeric) = 1.9617129034267935 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.527565772487001000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.988999999999996 " " y[1] (analytic) = 1.9619864814442518 " " y[1] (numeric) = 1.9619864814442507 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.65866806486812500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.987999999999996 " " y[1] (analytic) = 1.9622590974753078 " " y[1] (numeric) = 1.9622590974753067 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.65788190791724500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.986999999999996 " " y[1] (analytic) = 1.9625307512473467 " " y[1] (numeric) = 1.9625307512473453 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.78851849176592200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.985999999999995 " " y[1] (analytic) = 1.9628014424887144 " " y[1] (numeric) = 1.962801442488713 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.78758228270380900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.984999999999995 " " y[1] (analytic) = 1.96307117092872 " " y[1] (numeric) = 1.9630711709287185 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.91775793711993100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.983999999999995 " " y[1] (analytic) = 1.963339936297635 " " y[1] (numeric) = 1.9633399362976334 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.91667406005228400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.982999999999994 " " y[1] (analytic) = 1.9636077383266937 " " y[1] (numeric) = 1.963607738326692 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.91559436305613900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.981999999999994 " " y[1] (analytic) = 1.9638745767480945 " " y[1] (numeric) = 1.9638745767480927 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.04516439304210800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.980999999999994 " " y[1] (analytic) = 1.964140451294999 " " y[1] (numeric) = 1.964140451294997 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.01744325005255800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.979999999999993 " " y[1] (analytic) = 1.9644053617015325 " " y[1] (numeric) = 1.9644053617015302 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.1303400471921961000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.978999999999993 " " y[1] (analytic) = 1.9646693077027844 " " y[1] (numeric) = 1.9646693077027821 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.13018819021843380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.977999999999993 " " y[1] (analytic) = 1.964932289034809 " " y[1] (numeric) = 1.9649322890348069 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.13003692882517310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.976999999999992 " " y[1] (analytic) = 1.9651943054346255 " " y[1] (numeric) = 1.965194305434623 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.24287488897193770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.975999999999992 " " y[1] (analytic) = 1.9654553566402164 " " y[1] (numeric) = 1.9654553566402142 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.1297361915388311000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.974999999999992 " " y[1] (analytic) = 1.9657154423905316 " " y[1] (numeric) = 1.965715442390529 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.35550405803395450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.973999999999991 " " y[1] (analytic) = 1.9659745624254845 " " y[1] (numeric) = 1.9659745624254819 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.35532539943602070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.972999999999991 " " y[1] (analytic) = 1.9662327164859557 " " y[1] (numeric) = 1.966232716485953 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.3551474536861660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.971999999999990 " " y[1] (analytic) = 1.966489904313791 " " y[1] (numeric) = 1.966489904313788 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.46788440545423640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.97099999999999 " " y[1] (analytic) = 1.9667461256518024 " " y[1] (numeric) = 1.9667461256517993 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.58059264915048680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.96999999999999 " " y[1] (analytic) = 1.9670013802437687 " " y[1] (numeric) = 1.9670013802437656 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.58038753819541770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.96899999999999 " " y[1] (analytic) = 1.967255667834435 " " y[1] (numeric) = 1.9672556678344322 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.46731302454600030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.967999999999990 " " y[1] (analytic) = 1.9675089881695147 " " y[1] (numeric) = 1.9675089881695116 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.57997980575558530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.966999999999989 " " y[1] (analytic) = 1.9677613409956864 " " y[1] (numeric) = 1.9677613409956833 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.5797771834349970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.965999999999989 " " y[1] (analytic) = 1.968012726060598 " " y[1] (numeric) = 1.9680127260605949 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.57957538982637620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.964999999999988 " " y[1] (analytic) = 1.968263143112864 " " y[1] (numeric) = 1.968263143112861 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.57937442451625660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.963999999999988 " " y[1] (analytic) = 1.9685125919020678 " " y[1] (numeric) = 1.9685125919020645 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.69197245045672930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.962999999999988 " " y[1] (analytic) = 1.9687610721787603 " " y[1] (numeric) = 1.968761072178757 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.6917589040855690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.961999999999987 " " y[1] (analytic) = 1.9690085836944613 " " y[1] (numeric) = 1.969008583694458 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.69154624385949470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.960999999999987 " " y[1] (analytic) = 1.9692551262016593 " " y[1] (numeric) = 1.969255126201656 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.69133446934310340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.959999999999987 " " y[1] (analytic) = 1.9695006994538122 " " y[1] (numeric) = 1.9695006994538087 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.80386515210974540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.958999999999986 " " y[1] (analytic) = 1.9697453032053462 " " y[1] (numeric) = 1.9697453032053427 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.8036411474210431000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.957999999999986 " " y[1] (analytic) = 1.9699889372116577 " " y[1] (numeric) = 1.9699889372116541 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.80341808610816250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.956999999999986 " " y[1] (analytic) = 1.970231601229113 " " y[1] (numeric) = 1.9702316012291092 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.9158957156969159000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.955999999999985 " " y[1] (analytic) = 1.9704732950150479 " " y[1] (numeric) = 1.970473295015044 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.9156607162730951000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.954999999999985 " " y[1] (analytic) = 1.9707140183277685 " " y[1] (numeric) = 1.9707140183277647 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.91542671773785280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.953999999999985 " " y[1] (analytic) = 1.9709537709265517 " " y[1] (numeric) = 1.9709537709265479 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.91519371961271640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.952999999999984 " " y[1] (analytic) = 1.9711925525716452 " " y[1] (numeric) = 1.9711925525716412 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.02760652856377680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.951999999999984 " " y[1] (analytic) = 1.9714303630242667 " " y[1] (numeric) = 1.9714303630242627 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.02736194167126500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.950999999999984 " " y[1] (analytic) = 1.9716672020466062 " " y[1] (numeric) = 1.9716672020466022 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.0271184125301928000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.949999999999983 " " y[1] (analytic) = 1.9719030694018247 " " y[1] (numeric) = 1.9719030694018205 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.13948015956756900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.948999999999983 " " y[1] (analytic) = 1.972137964854055 " " y[1] (numeric) = 1.9721379648540505 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.2518161394602370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.947999999999983 " " y[1] (analytic) = 1.972371888168401 " " y[1] (numeric) = 1.9723718881683967 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.13897162035367160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.946999999999982 " " y[1] (analytic) = 1.97260483911094 " " y[1] (numeric) = 1.9726048391109356 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.25128318173555300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.945999999999982 " " y[1] (analytic) = 1.9728368174487212 " " y[1] (numeric) = 1.9728368174487165 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.3635693850522220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.944999999999982 " " y[1] (analytic) = 1.9730678229497658 " " y[1] (numeric) = 1.9730678229497611 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.3632926598815532000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.943999999999981 " " y[1] (analytic) = 1.9732978553830685 " " y[1] (numeric) = 1.9732978553830638 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.36301716474549170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.942999999999981 " " y[1] (analytic) = 1.973526914518597 " " y[1] (numeric) = 1.9735269145185923 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.3627428990818142000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.941999999999980 " " y[1] (analytic) = 1.973755000127292 " " y[1] (numeric) = 1.9737550001272874 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.3624698623309040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.94099999999998 " " y[1] (analytic) = 1.9739821119810683 " " y[1] (numeric) = 1.9739821119810634 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 2.4746836755517362000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.93999999999998 " " y[1] (analytic) = 1.9742082498528135 " " y[1] (numeric) = 1.9742082498528086 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 2.47440021016774040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.93899999999998 " " y[1] (analytic) = 1.9744334135163903 " " y[1] (numeric) = 1.9744334135163852 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.58657794094980500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.937999999999980 " " y[1] (analytic) = 1.9746576027466347 " " y[1] (numeric) = 1.9746576027466296 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.5862842784349760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.936999999999979 " " y[1] (analytic) = 1.9748808173193575 " " y[1] (numeric) = 1.9748808173193524 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.58599195885037770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.935999999999979 " " y[1] (analytic) = 1.9751030570113444 " " y[1] (numeric) = 1.975103057011339 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.6981227634088684000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.934999999999978 " " y[1] (analytic) = 1.9753243216003553 " " y[1] (numeric) = 1.97532432160035 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.6978205350518240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.933999999999978 " " y[1] (analytic) = 1.9755446108651258 " " y[1] (numeric) = 1.9755446108651207 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.58512305173370040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.932999999999978 " " y[1] (analytic) = 1.9757639245853669 " " y[1] (numeric) = 1.9757639245853618 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.5848360979399293000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.931999999999977 " " y[1] (analytic) = 1.9759822625417647 " " y[1] (numeric) = 1.9759822625417596 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.58455048412550070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.930999999999977 " " y[1] (analytic) = 1.9761996245159814 " " y[1] (numeric) = 1.976199624515976 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.69662561013084330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.929999999999977 " " y[1] (analytic) = 1.9764160102906547 " " y[1] (numeric) = 1.9764160102906494 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.69633037298511350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.928999999999976 " " y[1] (analytic) = 1.9766314196493993 " " y[1] (numeric) = 1.976631419649394 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.6960365322665890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.927999999999976 " " y[1] (analytic) = 1.9768458523768055 " " y[1] (numeric) = 1.9768458523768 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 2.8080667576844970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.926999999999976 " " y[1] (analytic) = 1.9770593082584407 " " y[1] (numeric) = 1.9770593082584351 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 2.807763580959880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.925999999999975 " " y[1] (analytic) = 1.9772717870808494 " " y[1] (numeric) = 1.9772717870808434 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.0320588055458380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.924999999999975 " " y[1] (analytic) = 1.9774832886315519 " " y[1] (numeric) = 1.977483288631546 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 2.9194480485576830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.923999999999975 " " y[1] (analytic) = 1.9776938126990475 " " y[1] (numeric) = 1.9776938126990415 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.031411786030680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.922999999999974 " " y[1] (analytic) = 1.977903359072812 " " y[1] (numeric) = 1.977903359072806 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.03109062709021160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.921999999999974 " " y[1] (analytic) = 1.9781119275432988 " " y[1] (numeric) = 1.9781119275432926 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.14302181354436440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.920999999999974 " " y[1] (analytic) = 1.9783195179019395 " " y[1] (numeric) = 1.9783195179019333 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.1426920078584850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.919999999999973 " " y[1] (analytic) = 1.978526129941144 " " y[1] (numeric) = 1.9785261299411376 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.25459110465094570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.918999999999973 " " y[1] (analytic) = 1.9787317634543 " " y[1] (numeric) = 1.9787317634542936 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.2542528814439920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.917999999999973 " " y[1] (analytic) = 1.978936418235774 " " y[1] (numeric) = 1.9789364182357676 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.253916337830880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.916999999999972 " " y[1] (analytic) = 1.9791400940809116 " " y[1] (numeric) = 1.979140094080905 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 3.36577393771833160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.915999999999972 " " y[1] (analytic) = 1.9793427907860366 " " y[1] (numeric) = 1.97934279078603 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 3.3654292620560120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.914999999999972 " " y[1] (analytic) = 1.9795445081484524 " " y[1] (numeric) = 1.9795445081484457 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 3.3650863217930660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.913999999999971 " " y[1] (analytic) = 1.9797452459664417 " " y[1] (numeric) = 1.9797452459664349 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.47690328677402460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.912999999999971 " " y[1] (analytic) = 1.9799450040392665 " " y[1] (numeric) = 1.9799450040392597 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.47655249950541500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.911999999999970 " " y[1] (analytic) = 1.9801437821671692 " " y[1] (numeric) = 1.9801437821671621 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.5883391002164820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.91099999999997 " " y[1] (analytic) = 1.980341580151371 " " y[1] (numeric) = 1.9803415801513642 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.4758562975533880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.90999999999997 " " y[1] (analytic) = 1.9805383977940747 " " y[1] (numeric) = 1.9805383977940678 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.4755108814566220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.90899999999997 " " y[1] (analytic) = 1.9807342348984625 " " y[1] (numeric) = 1.9807342348984553 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.5872694238382990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.907999999999970 " " y[1] (analytic) = 1.9809290912686968 " " y[1] (numeric) = 1.9809290912686897 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.5869165579522550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.906999999999969 " " y[1] (analytic) = 1.9811229667099215 " " y[1] (numeric) = 1.9811229667099144 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.58656553732304900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.905999999999969 " " y[1] (analytic) = 1.9813158610282615 " " y[1] (numeric) = 1.9813158610282542 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 3.69828562252725760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.904999999999968 " " y[1] (analytic) = 1.9815077740308222 " " y[1] (numeric) = 1.9815077740308147 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.80998584330239030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.903999999999968 " " y[1] (analytic) = 1.9816987055256905 " " y[1] (numeric) = 1.981698705525683 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.8096187611165560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.902999999999968 " " y[1] (analytic) = 1.981888655321935 " " y[1] (numeric) = 1.9818886553219275 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.80925363651407170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.901999999999967 " " y[1] (analytic) = 1.9820776232296065 " " y[1] (numeric) = 1.9820776232295987 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 3.9209166590121120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.900999999999967 " " y[1] (analytic) = 1.9822656090597361 " " y[1] (numeric) = 1.9822656090597284 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 3.9205448234873236000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.899999999999967 " " y[1] (analytic) = 1.9824526126243387 " " y[1] (numeric) = 1.982452612624331 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 3.9201750008481810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.898999999999966 " " y[1] (analytic) = 1.9826386337364106 " " y[1] (numeric) = 1.9826386337364026 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.0318016814978835000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.897999999999966 " " y[1] (analytic) = 1.9828236722099306 " " y[1] (numeric) = 1.9828236722099226 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.0314254309824515000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.896999999999966 " " y[1] (analytic) = 1.9830077278598601 " " y[1] (numeric) = 1.9830077278598521 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.0310512485637867000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.895999999999965 " " y[1] (analytic) = 1.983190800502144 " " y[1] (numeric) = 1.9831908005021357 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 4.1426424427472920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.894999999999965 " " y[1] (analytic) = 1.983372889953709 " " y[1] (numeric) = 1.9833728899537009 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 4.14226211512748240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.893999999999965 " " y[1] (analytic) = 1.9835539960324664 " " y[1] (numeric) = 1.983553996032458 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.25382671912556460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.892999999999964 " " y[1] (analytic) = 1.9837341185573094 " " y[1] (numeric) = 1.983734118557301 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.253440472802670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.891999999999964 " " y[1] (analytic) = 1.983913257348116 " " y[1] (numeric) = 1.9839132573481075 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.2530564055153310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.890999999999964 " " y[1] (analytic) = 1.9840914122257471 " " y[1] (numeric) = 1.9840914122257387 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.2526745164860180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.889999999999963 " " y[1] (analytic) = 1.9842685830120481 " " y[1] (numeric) = 1.9842685830120397 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.2522948049417150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.888999999999963 " " y[1] (analytic) = 1.984444769529848 " " y[1] (numeric) = 1.9844447695298395 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.25191727011391600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.887999999999963 " " y[1] (analytic) = 1.9846199716029602 " " y[1] (numeric) = 1.9846199716029518 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.2515419112386220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.886999999999962 " " y[1] (analytic) = 1.984794189056183 " " y[1] (numeric) = 1.9847941890561747 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.2511687275563390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.885999999999962 " " y[1] (analytic) = 1.9849674217152993 " " y[1] (numeric) = 1.9849674217152906 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.36266081616238900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.884999999999962 " " y[1] (analytic) = 1.9851396694070753 " " y[1] (numeric) = 1.9851396694070669 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.2504288827553250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.883999999999961 " " y[1] (analytic) = 1.9853109319592643 " " y[1] (numeric) = 1.9853109319592557 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.36190596277536000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.882999999999961 " " y[1] (analytic) = 1.9854812092006036 " " y[1] (numeric) = 1.9854812092005947 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.47336603128933500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.881999999999960 " " y[1] (analytic) = 1.9856505009608156 " " y[1] (numeric) = 1.9856505009608068 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.4729846429185490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.88099999999996 " " y[1] (analytic) = 1.9858188070706086 " " y[1] (numeric) = 1.9858188070706 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.36079040103899640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.87999999999996 " " y[1] (analytic) = 1.985986127361677 " " y[1] (numeric) = 1.9859861273616681 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.47222872034883530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.87899999999996 " " y[1] (analytic) = 1.9861524616667001 " " y[1] (numeric) = 1.9861524616666912 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.47185418462186570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.877999999999960 " " y[1] (analytic) = 1.9863178098193437 " " y[1] (numeric) = 1.9863178098193348 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.47148193158931300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.876999999999959 " " y[1] (analytic) = 1.9864821716542598 " " y[1] (numeric) = 1.9864821716542507 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 4.5828897595114043000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.875999999999959 " " y[1] (analytic) = 1.986645547007086 " " y[1] (numeric) = 1.9866455470070772 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.4707442706031810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.874999999999958 " " y[1] (analytic) = 1.986807935714448 " " y[1] (numeric) = 1.9868079357144388 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 4.5821383326881990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.873999999999958 " " y[1] (analytic) = 1.986969337613956 " " y[1] (numeric) = 1.986969337613947 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 4.5817661247146263000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.872999999999958 " " y[1] (analytic) = 1.987129752544209 " " y[1] (numeric) = 1.9871297525441998 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.6931376247127254000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.871999999999957 " " y[1] (analytic) = 1.9872891803447916 " " y[1] (numeric) = 1.9872891803447823 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.6927611235891150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.870999999999957 " " y[1] (analytic) = 1.9874476208562761 " " y[1] (numeric) = 1.9874476208562668 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.6923870138692436000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.869999999999957 " " y[1] (analytic) = 1.9876050739202222 " " y[1] (numeric) = 1.9876050739202127 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8037299446738970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.868999999999956 " " y[1] (analytic) = 1.9877615393791763 " " y[1] (numeric) = 1.987761539379167 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.6916459656242270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.867999999999956 " " y[1] (analytic) = 1.9879170170766738 " " y[1] (numeric) = 1.9879170170766642 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8029761452603353000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.866999999999956 " " y[1] (analytic) = 1.9880715068572363 " " y[1] (numeric) = 1.9880715068572268 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8026029138508164000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.865999999999955 " " y[1] (analytic) = 1.9882250085663742 " " y[1] (numeric) = 1.9882250085663646 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8022321269668317000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.864999999999955 " " y[1] (analytic) = 1.9883775220505862 " " y[1] (numeric) = 1.9883775220505764 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9135350346476214000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.863999999999955 " " y[1] (analytic) = 1.9885290471573582 " " y[1] (numeric) = 1.9885290471573485 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9131606252710935000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.862999999999954 " " y[1] (analytic) = 1.9886795837351654 " " y[1] (numeric) = 1.9886795837351556 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9127887149881120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.861999999999954 " " y[1] (analytic) = 1.9888291316334716 " " y[1] (numeric) = 1.9888291316334616 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0240651962995640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.860999999999954 " " y[1] (analytic) = 1.9889776907027281 " " y[1] (numeric) = 1.9889776907027183 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9120523887070550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.859999999999953 " " y[1] (analytic) = 1.9891252607943768 " " y[1] (numeric) = 1.9891252607943668 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0233172432971870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.858999999999953 " " y[1] (analytic) = 1.9892718417608468 " " y[1] (numeric) = 1.9892718417608368 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0229470964520210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.857999999999953 " " y[1] (analytic) = 1.9894174334555577 " " y[1] (numeric) = 1.9894174334555474 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1341923795298930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.856999999999952 " " y[1] (analytic) = 1.9895620357329173 " " y[1] (numeric) = 1.9895620357329071 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1338192240830400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.855999999999952 " " y[1] (analytic) = 1.9897056484483238 " " y[1] (numeric) = 1.9897056484483135 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1334486759470620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.854999999999952 " " y[1] (analytic) = 1.9898482714581642 " " y[1] (numeric) = 1.989848271458154 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1330807343750720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.853999999999951 " " y[1] (analytic) = 1.989989904619816 " " y[1] (numeric) = 1.9899899046198055 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2442961681608480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.852999999999951 " " y[1] (analytic) = 1.9901305477916453 " " y[1] (numeric) = 1.990130547791635 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2439255520482910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.851999999999950 " " y[1] (analytic) = 1.9902702008330095 " " y[1] (numeric) = 1.990270200832999 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2435575969074640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.85099999999995 " " y[1] (analytic) = 1.9904088636042552 " " y[1] (numeric) = 1.990408863604245 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1316350189758090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.84999999999995 " " y[1] (analytic) = 1.99054653596672 " " y[1] (numeric) = 1.9905465359667096 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2428296665810550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.84899999999995 " " y[1] (analytic) = 1.9906832177827314 " " y[1] (numeric) = 1.990683217782721 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2424696899290870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.847999999999950 " " y[1] (analytic) = 1.9908189089156076 " " y[1] (numeric) = 1.990818908915597 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3536466770887550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.846999999999949 " " y[1] (analytic) = 1.9909536092296571 " " y[1] (numeric) = 1.9909536092296467 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2417577100223970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.845999999999949 " " y[1] (analytic) = 1.9910873185901803 " " y[1] (numeric) = 1.9910873185901699 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2414057053338630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.844999999999948 " " y[1] (analytic) = 1.9912200368634676 " " y[1] (numeric) = 1.991220036863457 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3525681939149260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.843999999999948 " " y[1] (analytic) = 1.9913517639168004 " " y[1] (numeric) = 1.9913517639167897 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3522141238562230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.842999999999948 " " y[1] (analytic) = 1.991482499618452 " " y[1] (numeric) = 1.9914824996184413 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3518627647712180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.841999999999947 " " y[1] (analytic) = 1.9916122438376864 " " y[1] (numeric) = 1.9916122438376758 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3515141159526470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.840999999999947 " " y[1] (analytic) = 1.9917409964447597 " " y[1] (numeric) = 1.991740996444749 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3511681766987730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.839999999999947 " " y[1] (analytic) = 1.9918687573109195 " " y[1] (numeric) = 1.9918687573109084 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.5737759857431060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.838999999999946 " " y[1] (analytic) = 1.9919955263084042 " " y[1] (numeric) = 1.9919955263083933 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 5.4619528496079790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.837999999999946 " " y[1] (analytic) = 1.9921213033104457 " " y[1] (numeric) = 1.9921213033104346 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.5730693847820520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.836999999999946 " " y[1] (analytic) = 1.992246088191266 " " y[1] (numeric) = 1.9922460881912551 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 5.4612659077697120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.835999999999945 " " y[1] (analytic) = 1.9923698808260812 " " y[1] (numeric) = 1.9923698808260701 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.5723740622139560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.834999999999945 " " y[1] (analytic) = 1.9924926810910981 " " y[1] (numeric) = 1.992492681091087 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.5720306285752240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.833999999999945 " " y[1] (analytic) = 1.9926144888635169 " " y[1] (numeric) = 1.9926144888635056 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6831238126926250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.832999999999944 " " y[1] (analytic) = 1.9927353040215294 " " y[1] (numeric) = 1.9927353040215179 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7942063016598630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.831999999999944 " " y[1] (analytic) = 1.9928551264443204 " " y[1] (numeric) = 1.992855126444309 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6824375745674620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.830999999999944 " " y[1] (analytic) = 1.9929739560120678 " " y[1] (numeric) = 1.9929739560120565 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6820987635164190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.829999999999943 " " y[1] (analytic) = 1.993091792605942 " " y[1] (numeric) = 1.9930917926059306 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6817628235628080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.828999999999943 " " y[1] (analytic) = 1.9932086361081063 " " y[1] (numeric) = 1.993208636108095 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6814297540312280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.827999999999943 " " y[1] (analytic) = 1.9933244864017174 " " y[1] (numeric) = 1.993324486401706 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7924936631590060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.826999999999942 " " y[1] (analytic) = 1.9934393433709248 " " y[1] (numeric) = 1.9934393433709132 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7921599142197590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.825999999999942 " " y[1] (analytic) = 1.9935532069008715 " " y[1] (numeric) = 1.99355320690086 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7918290899550410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.824999999999942 " " y[1] (analytic) = 1.9936660768776941 " " y[1] (numeric) = 1.9936660768776826 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7915011896999650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.823999999999941 " " y[1] (analytic) = 1.993777953188523 " " y[1] (numeric) = 1.9937779531885111 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 5.9025449861185700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.822999999999941 " " y[1] (analytic) = 1.993888835721481 " " y[1] (numeric) = 1.9938888357214692 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 5.9022167385617170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.821999999999940 " " y[1] (analytic) = 1.9939987243656865 " " y[1] (numeric) = 1.9939987243656745 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0132479120647250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.82099999999994 " " y[1] (analytic) = 1.9941076190112503 " " y[1] (numeric) = 1.9941076190112383 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0129195393661660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.81999999999994 " " y[1] (analytic) = 1.994215519549278 " " y[1] (numeric) = 1.994215519549266 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0125941997792190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.8189999999999396 " " y[1] (analytic) = 1.9943224258718688 " " y[1] (numeric) = 1.9943224258718568 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0122718926503460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.817999999999940 " " y[1] (analytic) = 1.9944283378721166 " " y[1] (numeric) = 1.9944283378721046 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0119526173321550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.816999999999939 " " y[1] (analytic) = 1.9945332554441095 " " y[1] (numeric) = 1.9945332554440975 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0116363731833910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.8159999999999386 " " y[1] (analytic) = 1.99463717848293 " " y[1] (numeric) = 1.9946371784829178 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1226439588202210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.814999999999938 " " y[1] (analytic) = 1.9947401068846546 " " y[1] (numeric) = 1.9947401068846424 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1223280309683490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.813999999999938 " " y[1] (analytic) = 1.9948420405463554 " " y[1] (numeric) = 1.9948420405463432 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1220151884967920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.8129999999999376 " " y[1] (analytic) = 1.9949429793660984 " " y[1] (numeric) = 1.9949429793660862 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1217054307774140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.811999999999937 " " y[1] (analytic) = 1.9950429232429454 " " y[1] (numeric) = 1.9950429232429328 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3439950756315330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.810999999999937 " " y[1] (analytic) = 1.9951418720769516 " " y[1] (numeric) = 1.9951418720769392 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2323878065159280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.8099999999999365 " " y[1] (analytic) = 1.9952398257691688 " " y[1] (numeric) = 1.9952398257691564 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2320818355799560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.808999999999936 " " y[1] (analytic) = 1.9953367842216432 " " y[1] (numeric) = 1.9953367842216307 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.231779002987860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.807999999999936 " " y[1] (analytic) = 1.9954327473374163 " " y[1] (numeric) = 1.9954327473374038 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2314793081318260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.8069999999999355 " " y[1] (analytic) = 1.995527715020525 " " y[1] (numeric) = 1.9955277150205124 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3424538709534310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.805999999999935 " " y[1] (analytic) = 1.9956216871760015 " " y[1] (numeric) = 1.995621687175989 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2308893292284140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.804999999999935 " " y[1] (analytic) = 1.995714663709874 " " y[1] (numeric) = 1.9957146637098615 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.230599043997110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.8039999999999345 " " y[1] (analytic) = 1.9958066445291656 " " y[1] (numeric) = 1.9958066445291531 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2303118941340120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.802999999999934 " " y[1] (analytic) = 1.9958976295418958 " " y[1] (numeric) = 1.9958976295418833 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2300278790629940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.801999999999934 " " y[1] (analytic) = 1.9959876186570793 " " y[1] (numeric) = 1.9959876186570669 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2297469982142520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.8009999999999335 " " y[1] (analytic) = 1.9960766117847273 " " y[1] (numeric) = 1.9960766117847148 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2294692510243130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.799999999999933 " " y[1] (analytic) = 1.9961646088358465 " " y[1] (numeric) = 1.996164608835834 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2291946369360250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.798999999999933 " " y[1] (analytic) = 1.9962516097224399 " " y[1] (numeric) = 1.9962516097224274 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2289231553985590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7979999999999325 " " y[1] (analytic) = 1.9963376143575065 " " y[1] (numeric) = 1.996337614357494 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2286548058674050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.796999999999932 " " y[1] (analytic) = 1.9964226226550417 " " y[1] (numeric) = 1.9964226226550292 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.228389587804369000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.795999999999932 " " y[1] (analytic) = 1.9965066345300375 " " y[1] (numeric) = 1.9965066345300249 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3393440631896710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7949999999999315 " " y[1] (analytic) = 1.9965896498984816 " " y[1] (numeric) = 1.996589649898469 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3390804822464730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.793999999999931 " " y[1] (analytic) = 1.996671668677359 " " y[1] (numeric) = 1.9966716686773462 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3388200870856090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.792999999999930 " " y[1] (analytic) = 1.9967526907846507 " " y[1] (numeric) = 1.996752690784638 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3385628771849690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7919999999999305 " " y[1] (analytic) = 1.9968327161393349 " " y[1] (numeric) = 1.996832716139322 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.449507252941650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.79099999999993 " " y[1] (analytic) = 1.9969117446613858 " " y[1] (numeric) = 1.996911744661373 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4492520113028950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.78999999999993 " " y[1] (analytic) = 1.996989776271775 " " y[1] (numeric) = 1.996989776271762 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4490000092514940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7889999999999295 " " y[1] (analytic) = 1.9970668108924712 " " y[1] (numeric) = 1.9970668108924583 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4487512462822860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.787999999999930 " " y[1] (analytic) = 1.9971428484464395 " " y[1] (numeric) = 1.9971428484464266 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4485057218966380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.786999999999929 " " y[1] (analytic) = 1.9972178888576426 " " y[1] (numeric) = 1.9972178888576295 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5594403913886790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7859999999999285 " " y[1] (analytic) = 1.9972919320510396 " " y[1] (numeric) = 1.9972919320510267 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4480243869140660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.784999999999928 " " y[1] (analytic) = 1.997364977952588 " " y[1] (numeric) = 1.997364977952575 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4477885753524610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.783999999999928 " " y[1] (analytic) = 1.9974370264892416 " " y[1] (numeric) = 1.9974370264892285 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5587207590734060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7829999999999275 " " y[1] (analytic) = 1.9975080775889515 " " y[1] (numeric) = 1.9975080775889384 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5584874662382730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.781999999999927 " " y[1] (analytic) = 1.997578131180667 " " y[1] (numeric) = 1.997578131180654 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5582574649201470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.780999999999927 " " y[1] (analytic) = 1.9976471871943349 " " y[1] (numeric) = 1.9976471871943215 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.669183818296450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7799999999999265 " " y[1] (analytic) = 1.9977152455608982 " " y[1] (numeric) = 1.997715245560885 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5578073349981290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.778999999999926 " " y[1] (analytic) = 1.9977823062122995 " " y[1] (numeric) = 1.9977823062122861 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.668732751348190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.777999999999926 " " y[1] (analytic) = 1.9978483690814774 " " y[1] (numeric) = 1.9978483690814641 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.668512236305030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7769999999999255 " " y[1] (analytic) = 1.9979134341023697 " " y[1] (numeric) = 1.9979134341023561 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7794333173961240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.775999999999925 " " y[1] (analytic) = 1.9979775012099106 " " y[1] (numeric) = 1.9979775012098973 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.668081240871880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.774999999999925 " " y[1] (analytic) = 1.998040570340034 " " y[1] (numeric) = 1.9980405703400204 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7790019389455240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7739999999999245 " " y[1] (analytic) = 1.9981026414296696 " " y[1] (numeric) = 1.9981026414296563 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6676636221096840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.772999999999924 " " y[1] (analytic) = 1.9981637144167474 " " y[1] (numeric) = 1.998163714416734 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7785841583959170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.771999999999924 " " y[1] (analytic) = 1.998223789240194 " " y[1] (numeric) = 1.9982237892401804 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7783803662837800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7709999999999235 " " y[1] (analytic) = 1.9982828658399343 " " y[1] (numeric) = 1.9982828658399208 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7781799724002960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.769999999999923 " " y[1] (analytic) = 1.998340944156892 " " y[1] (numeric) = 1.9983409441568785 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.777982976344150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.768999999999923 " " y[1] (analytic) = 1.9983980241329888 " " y[1] (numeric) = 1.9983980241329753 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7777893777208510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7679999999999225 " " y[1] (analytic) = 1.9984541057111447 " " y[1] (numeric) = 1.9984541057111311 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7775991761427290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.766999999999922 " " y[1] (analytic) = 1.998509188835278 " " y[1] (numeric) = 1.9985091888352644 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7774123712289310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.765999999999922 " " y[1] (analytic) = 1.9985632734503058 " " y[1] (numeric) = 1.998563273450292 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8883310767464930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7649999999999215 " " y[1] (analytic) = 1.9986163595021431 " " y[1] (numeric) = 1.9986163595021296 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7770489499049780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.763999999999921 " " y[1] (analytic) = 1.9986684469377045 " " y[1] (numeric) = 1.9986684469376907 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8879686005174780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.762999999999920 " " y[1] (analytic) = 1.9987195357049017 " " y[1] (numeric) = 1.9987195357048881 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7766991108384810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7619999999999205 " " y[1] (analytic) = 1.9987696257526468 " " y[1] (numeric) = 1.998769625752633 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8876199277683130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.76099999999992 " " y[1] (analytic) = 1.9988187170308493 " " y[1] (numeric) = 1.9988187170308356 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8874507668218250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.75999999999992 " " y[1] (analytic) = 1.9988668094904178 " " y[1] (numeric) = 1.9988668094904043 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7761998128729450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7589999999999195 " " y[1] (analytic) = 1.9989139030832606 " " y[1] (numeric) = 1.9989139030832468 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8871227940919060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.757999999999920 " " y[1] (analytic) = 1.998959997762283 " " y[1] (numeric) = 1.9989599977622694 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7758839174317740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.756999999999919 " " y[1] (analytic) = 1.999005093481391 " " y[1] (numeric) = 1.9990050934813774 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.775731059713279000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7559999999999185 " " y[1] (analytic) = 1.999049190195489 " " y[1] (numeric) = 1.9990491901954752 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8866567030327430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.754999999999918 " " y[1] (analytic) = 1.9990922878604798 " " y[1] (numeric) = 1.999092287860466 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8865082362384410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.753999999999918 " " y[1] (analytic) = 1.999134386433266 " " y[1] (numeric) = 1.9991343864332523 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8863632173891850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7529999999999175 " " y[1] (analytic) = 1.9991754858717492 " " y[1] (numeric) = 1.9991754858717354 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8862216461947470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.751999999999917 " " y[1] (analytic) = 1.9992155861348297 " " y[1] (numeric) = 1.999215586134816 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8860835223718050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.750999999999917 " " y[1] (analytic) = 1.9992546871824075 " " y[1] (numeric) = 1.9992546871823935 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 6.9970125367027160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7499999999999165 " " y[1] (analytic) = 1.999292788975381 " " y[1] (numeric) = 1.9992927889753673 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8858176157416550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.748999999999916 " " y[1] (analytic) = 1.9993298914756492 " " y[1] (numeric) = 1.9993298914756354 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8856898324023350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.747999999999916 " " y[1] (analytic) = 1.999365994646109 " " y[1] (numeric) = 1.9993659946460953 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8855654953702860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7469999999999155 " " y[1] (analytic) = 1.9994010984506574 " " y[1] (numeric) = 1.9994010984506438 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7743890462612830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.745999999999915 " " y[1] (analytic) = 1.9994352028541909 " " y[1] (numeric) = 1.999435202854177 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8853271592397210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.744999999999915 " " y[1] (analytic) = 1.9994683078226045 " " y[1] (numeric) = 1.9994683078225908 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8852131596643170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7439999999999145 " " y[1] (analytic) = 1.9995004133227936 " " y[1] (numeric) = 1.99950041332278 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7740525634191450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.742999999999914 " " y[1] (analytic) = 1.9995315193226528 " " y[1] (numeric) = 1.9995315193226393 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7739471818954990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.741999999999914 " " y[1] (analytic) = 1.9995616257910758 " " y[1] (numeric) = 1.9995616257910624 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.662798547272130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7409999999999135 " " y[1] (analytic) = 1.9995907326979565 " " y[1] (numeric) = 1.9995907326979432 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6627015606969730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.739999999999913 " " y[1] (analytic) = 1.9996188400141879 " " y[1] (numeric) = 1.9996188400141743 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7736513726440020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.738999999999913 " " y[1] (analytic) = 1.9996459477116624 " " y[1] (numeric) = 1.9996459477116488 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7735595473424180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7379999999999125 " " y[1] (analytic) = 1.9996720557632726 " " y[1] (numeric) = 1.999672055763259 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7734711106201380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.736999999999912 " " y[1] (analytic) = 1.9996971641429102 " " y[1] (numeric) = 1.9996971641428967 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7733860623002430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.735999999999912 " " y[1] (analytic) = 1.999721272825467 " " y[1] (numeric) = 1.9997212728254534 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7733044022125950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7349999999999115 " " y[1] (analytic) = 1.9997443817868343 " " y[1] (numeric) = 1.9997443817868208 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7732261301938390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.733999999999911 " " y[1] (analytic) = 1.999766491003903 " " y[1] (numeric) = 1.9997664910038897 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6621159797580960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.732999999999910 " " y[1] (analytic) = 1.9997876004545643 " " y[1] (numeric) = 1.9997876004545507 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7730797497434770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7319999999999105 " " y[1] (analytic) = 1.9998077101177083 " " y[1] (numeric) = 1.9998077101176948 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7730116410190610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.73099999999991 " " y[1] (analytic) = 1.9998268199732254 " " y[1] (numeric) = 1.9998268199732119 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.772946919777910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.72999999999991 " " y[1] (analytic) = 1.999844930002006 " " y[1] (numeric) = 1.9998449300019925 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7728855858905630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7289999999999095 " " y[1] (analytic) = 1.9998620401859397 " " y[1] (numeric) = 1.9998620401859264 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6617976779354170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.727999999999910 " " y[1] (analytic) = 1.9998781505079168 " " y[1] (numeric) = 1.9998781505079033 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7727730796933330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.726999999999909 " " y[1] (analytic) = 1.9998932609518265 " " y[1] (numeric) = 1.9998932609518132 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6616936791722080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7259999999999085 " " y[1] (analytic) = 1.9999073715025588 " " y[1] (numeric) = 1.9999073715025453 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7726741215272230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.724999999999908 " " y[1] (analytic) = 1.9999204821460028 " " y[1] (numeric) = 1.9999204821459893 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7726297227041890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.723999999999908 " " y[1] (analytic) = 1.999932592869048 " " y[1] (numeric) = 1.9999325928690344 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7725887106005060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7229999999999075 " " y[1] (analytic) = 1.9999437036595835 " " y[1] (numeric) = 1.99994370365957 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7725510851341430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.721999999999907 " " y[1] (analytic) = 1.999953814506499 " " y[1] (numeric) = 1.9999538145064852 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8835417125614850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.720999999999907 " " y[1] (analytic) = 1.9999629253996831 " " y[1] (numeric) = 1.9999629253996694 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8835103543735530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7199999999999065 " " y[1] (analytic) = 1.9999710363300252 " " y[1] (numeric) = 1.9999710363300114 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834824381327790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.718999999999906 " " y[1] (analytic) = 1.9999781472894143 " " y[1] (numeric) = 1.9999781472894005 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834579637833270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.717999999999906 " " y[1] (analytic) = 1.9999842582707394 " " y[1] (numeric) = 1.9999842582707257 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834369312762480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7169999999999055 " " y[1] (analytic) = 1.9999893692678894 " " y[1] (numeric) = 1.9999893692678758 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7723964479796470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.715999999999905 " " y[1] (analytic) = 1.9999934802757537 " " y[1] (numeric) = 1.99999348027574 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834051916278330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.714999999999905 " " y[1] (analytic) = 1.9999965912902211 " " y[1] (numeric) = 1.9999965912902073 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8833944844230170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7139999999999045 " " y[1] (analytic) = 1.9999987023081802 " " y[1] (numeric) = 1.9999987023081667 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7723648444346840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.712999999999904 " " y[1] (analytic) = 1.9999998133275207 " " y[1] (numeric) = 1.999999813327507 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8833833951450930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.711999999999904 " " y[1] (analytic) = 1.9999999243471311 " " y[1] (numeric) = 1.9999999243471174 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8833830130498070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7109999999999035 " " y[1] (analytic) = 1.9999990353669004 " " y[1] (numeric) = 1.9999990353668866 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8833860726469920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.709999999999903 " " y[1] (analytic) = 1.9999971463877178 " " y[1] (numeric) = 1.999997146387704 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8833925739427670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.708999999999903 " " y[1] (analytic) = 1.999994257411472 " " y[1] (numeric) = 1.9999942574114582 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834025169501340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7079999999999025 " " y[1] (analytic) = 1.9999903684410523 " " y[1] (numeric) = 1.9999903684410383 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 6.9944387388129960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.706999999999902 " " y[1] (analytic) = 1.999985479480347 " " y[1] (numeric) = 1.9999854794803333 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834327281860750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.705999999999902 " " y[1] (analytic) = 1.9999795905342461 " " y[1] (numeric) = 1.9999795905342324 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834529964750700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7049999999999015 " " y[1] (analytic) = 1.999972701608638 " " y[1] (numeric) = 1.9999727016086242 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.8834767065965050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.703999999999901 " " y[1] (analytic) = 1.9999648127104113 " " y[1] (numeric) = 1.9999648127103977 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7724796028139630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.702999999999900 " " y[1] (analytic) = 1.9999559238474554 " " y[1] (numeric) = 1.9999559238474418 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7725097032988510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7019999999999005 " " y[1] (analytic) = 1.9999460350286589 " " y[1] (numeric) = 1.9999460350286453 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7725431902630400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.7009999999999 " " y[1] (analytic) = 1.9999351462639108 " " y[1] (numeric) = 1.9999351462638972 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7725800637735050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6999999999999 " " y[1] (analytic) = 1.9999232575640997 " " y[1] (numeric) = 1.9999232575640862 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7726203239039970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6989999999998995 " " y[1] (analytic) = 1.9999103689411144 " " y[1] (numeric) = 1.9999103689411009 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7726639707350420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.697999999999900 " " y[1] (analytic) = 1.9998964804078434 " " y[1] (numeric) = 1.9998964804078299 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7727110043539380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.696999999999899 " " y[1] (analytic) = 1.9998815919781752 " " y[1] (numeric) = 1.9998815919781618 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6617325490374680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6959999999998985 " " y[1] (analytic) = 1.9998657036669987 " " y[1] (numeric) = 1.9998657036669851 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7728152323383540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.694999999999898 " " y[1] (analytic) = 1.9998488154902017 " " y[1] (numeric) = 1.9998488154901881 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7728724269123500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.693999999999898 " " y[1] (analytic) = 1.9998309274646724 " " y[1] (numeric) = 1.9998309274646588 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7729330086911480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6929999999998975 " " y[1] (analytic) = 1.999812039608299 " " y[1] (numeric) = 1.9998120396082855 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7729969777959220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.691999999999897 " " y[1] (analytic) = 1.9997921519399693 " " y[1] (numeric) = 1.9997921519399557 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7730643343546340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.690999999999897 " " y[1] (analytic) = 1.999771264479571 " " y[1] (numeric) = 1.9997712644795576 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7731350785020130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6899999999998965 " " y[1] (analytic) = 1.9997493772479915 " " y[1] (numeric) = 1.9997493772479782 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6621729938159720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.688999999999896 " " y[1] (analytic) = 1.9997264902671184 " " y[1] (numeric) = 1.9997264902671048 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.77328673013560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.687999999999896 " " y[1] (analytic) = 1.999702603559838 " " y[1] (numeric) = 1.9997026035598244 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7733676379251680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6869999999998955 " " y[1] (analytic) = 1.9996777171500373 " " y[1] (numeric) = 1.999677717150024 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6624117382722570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.685999999999895 " " y[1] (analytic) = 1.9996518310626028 " " y[1] (numeric) = 1.9996518310625895 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6624979851728940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.684999999999895 " " y[1] (analytic) = 1.9996249453234207 " " y[1] (numeric) = 1.9996249453234074 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6625875650631370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6839999999998945 " " y[1] (analytic) = 1.9995970599593766 " " y[1] (numeric) = 1.999597059959363 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7737251527575660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.682999999999894 " " y[1] (analytic) = 1.9995681749983558 " " y[1] (numeric) = 1.9995681749983423 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7738230032782190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.681999999999894 " " y[1] (analytic) = 1.9995382904692431 " " y[1] (numeric) = 1.9995382904692298 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6628763044969600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6809999999998935 " " y[1] (analytic) = 1.9995074064019234 " " y[1] (numeric) = 1.99950740640191 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6629792182044410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.679999999999893 " " y[1] (analytic) = 1.9994755228272805 " " y[1] (numeric) = 1.9994755228272671 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6630854658643010000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.678999999999893 " " y[1] (analytic) = 1.999442639777198 " " y[1] (numeric) = 1.9994426397771847 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6631950476891160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6779999999998925 " " y[1] (analytic) = 1.9994087572845594 " " y[1] (numeric) = 1.9994087572845458 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7743630966297710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.676999999999892 " " y[1] (analytic) = 1.9993738753832464 " " y[1] (numeric) = 1.9993738753832329 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.774481284962580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.675999999999892 " " y[1] (analytic) = 1.9993379941081413 " " y[1] (numeric) = 1.999337994108128 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6635438003791940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6749999999998915 " " y[1] (analytic) = 1.9993011134951257 " " y[1] (numeric) = 1.9993011134951122 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7747278331418440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.673999999999891 " " y[1] (analytic) = 1.9992632335810794 " " y[1] (numeric) = 1.999263233581066 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6637929771950570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.672999999999890 " " y[1] (analytic) = 1.9992243544038832 " " y[1] (numeric) = 1.9992243544038697 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7749879449950940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6719999999998905 " " y[1] (analytic) = 1.9991844760024158 " " y[1] (numeric) = 1.9991844760024022 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7751230879458580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.67099999999989 " " y[1] (analytic) = 1.9991435984165555 " " y[1] (numeric) = 1.999143598416542 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.775261622604379000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.66999999999989 " " y[1] (analytic) = 1.9991017216871803 " " y[1] (numeric) = 1.9991017216871667 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7754035492479000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6689999999998895 " " y[1] (analytic) = 1.9990588458561662 " " y[1] (numeric) = 1.999058845856153 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6644742965512760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.667999999999890 " " y[1] (analytic) = 1.9990149709663898 " " y[1] (numeric) = 1.9990149709663765 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6646205701307260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.666999999999889 " " y[1] (analytic) = 1.9989700970617257 " " y[1] (numeric) = 1.9989700970617124 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.664770180947079000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6659999999998885 " " y[1] (analytic) = 1.9989242241870477 " " y[1] (numeric) = 1.9989242241870344 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6649231292997820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.664999999999888 " " y[1] (analytic) = 1.998877352388229 " " y[1] (numeric) = 1.9988773523882155 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.776164072419890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.663999999999888 " " y[1] (analytic) = 1.998829481712141 " " y[1] (numeric) = 1.9988294817121275 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7763263571762430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6629999999998875 " " y[1] (analytic) = 1.9987806122066543 " " y[1] (numeric) = 1.998780612206641 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6654020026708380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.661999999999887 " " y[1] (analytic) = 1.998730743920639 " " y[1] (numeric) = 1.9987307439206254 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7766611093688730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.660999999999887 " " y[1] (analytic) = 1.9986798769039629 " " y[1] (numeric) = 1.9986798769039493 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7768335774752670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6599999999998865 " " y[1] (analytic) = 1.9986280112074928 " " y[1] (numeric) = 1.9986280112074795 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6659109252916150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.658999999999886 " " y[1] (analytic) = 1.998575146883095 " " y[1] (numeric) = 1.9985751468830817 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6660872453454840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.657999999999886 " " y[1] (analytic) = 1.9985212839836335 " " y[1] (numeric) = 1.9985212839836202 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6662669055722610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6569999999998855 " " y[1] (analytic) = 1.9984664225629714 " " y[1] (numeric) = 1.9984664225629578 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7775574047705160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.655999999999885 " " y[1] (analytic) = 1.9984105626759696 " " y[1] (numeric) = 1.998410562675956 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7777468521232520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.654999999999885 " " y[1] (analytic) = 1.9983537043784885 " " y[1] (numeric) = 1.998353704378475 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.7779396964360110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6539999999998845 " " y[1] (analytic) = 1.9982958477273862 " " y[1] (numeric) = 1.9982958477273727 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 6.778135938094950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.652999999999884 " " y[1] (analytic) = 1.9982369927805192 " " y[1] (numeric) = 1.998236992780506 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6672153221243080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.651999999999884 " " y[1] (analytic) = 1.9981771395967427 " " y[1] (numeric) = 1.9981771395967296 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5562914473241950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6509999999998834 " " y[1] (analytic) = 1.99811628823591 " " y[1] (numeric) = 1.9981162882358967 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6676180830617000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.649999999999883 " " y[1] (analytic) = 1.9980544387588721 " " y[1] (numeric) = 1.9980544387588588 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6678244781846400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.648999999999883 " " y[1] (analytic) = 1.9979915912274786 " " y[1] (numeric) = 1.9979915912274653 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6680342169593450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6479999999998824 " " y[1] (analytic) = 1.997927745704577 " " y[1] (numeric) = 1.9979277457045637 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6682472998059220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.646999999999882 " " y[1] (analytic) = 1.9978629022540129 " " y[1] (numeric) = 1.9978629022539995 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6684637271511850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.645999999999882 " " y[1] (analytic) = 1.9977970609406297 " " y[1] (numeric) = 1.9977970609406164 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.6686834994286740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.6449999999998814 " " y[1] (analytic) = 1.9977302218302686 " " y[1] (numeric) = 1.9977302218302555 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5577581734606730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.643999999999881 " " y[1] (analytic) = 1.997662384989769 " " y[1] (numeric) = 1.997662384989756 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5579808625389640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.642999999999880 " " y[1] (analytic) = 1.9975935504869673 " " y[1] (numeric) = 1.9975935504869544 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4470507939477040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.64199999999988 " " y[1] (analytic) = 1.9975237183906986 " " y[1] (numeric) = 1.9975237183906855 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5584361126541960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.64099999999988 " " y[1] (analytic) = 1.9974528887707943 " " y[1] (numeric) = 1.9974528887707814 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4475047987625510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.63999999999988 " " y[1] (analytic) = 1.9973810616980847 " " y[1] (numeric) = 1.9973810616980716 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.5589045284324830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.638999999999880 " " y[1] (analytic) = 1.9973082372443962 " " y[1] (numeric) = 1.9973082372443833 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4479717479260350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.637999999999879 " " y[1] (analytic) = 1.9972344154825536 " " y[1] (numeric) = 1.9972344154825408 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4482100778041160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.636999999999879 " " y[1] (analytic) = 1.9971595964863789 " " y[1] (numeric) = 1.997159596486366 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.4484516451811020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.635999999999878 " " y[1] (analytic) = 1.9970837803306905 " " y[1] (numeric) = 1.9970837803306778 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3375120289800910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.634999999999878 " " y[1] (analytic) = 1.9970069670913049 " " y[1] (numeric) = 1.9970069670912922 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3377557961960360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.633999999999878 " " y[1] (analytic) = 1.9969291568450354 " " y[1] (numeric) = 1.9969291568450227 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.338002746538570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.632999999999877 " " y[1] (analytic) = 1.996850349669692 " " y[1] (numeric) = 1.9968503496696794 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.3382528805027170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.631999999999877 " " y[1] (analytic) = 1.996770545644082 " " y[1] (numeric) = 1.9967705456440696 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2273043354567600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.630999999999877 " " y[1] (analytic) = 1.9966897448480097 " " y[1] (numeric) = 1.9966897448479972 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2275563381271750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.629999999999876 " " y[1] (analytic) = 1.9966079473622753 " " y[1] (numeric) = 1.9966079473622629 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2278114700630160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.628999999999876 " " y[1] (analytic) = 1.9965251532686767 " " y[1] (numeric) = 1.9965251532686643 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2280697317758340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.627999999999876 " " y[1] (analytic) = 1.996441362650008 " " y[1] (numeric) = 1.9964413626499955 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2283311237834840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.626999999999875 " " y[1] (analytic) = 1.9963565755900594 " " y[1] (numeric) = 1.996356575590047 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2285956466101310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.625999999999875 " " y[1] (analytic) = 1.9962707921736185 " " y[1] (numeric) = 1.996270792173606 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2288633007862530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.624999999999875 " " y[1] (analytic) = 1.9961840124864683 " " y[1] (numeric) = 1.9961840124864558 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2291340868486410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.623999999999874 " " y[1] (analytic) = 1.9960962366153887 " " y[1] (numeric) = 1.9960962366153763 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2294080053404020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.622999999999874 " " y[1] (analytic) = 1.9960074646481556 " " y[1] (numeric) = 1.9960074646481432 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2296850568109640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.621999999999874 " " y[1] (analytic) = 1.9959176966735406 " " y[1] (numeric) = 1.9959176966735284 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1187158624979290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.620999999999873 " " y[1] (analytic) = 1.9958269327813118 " " y[1] (numeric) = 1.9958269327812999 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0077396837421640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.619999999999873 " " y[1] (analytic) = 1.9957351730622337 " " y[1] (numeric) = 1.9957351730622215 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1192754608508860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.618999999999873 " " y[1] (analytic) = 1.9956424176080652 " " y[1] (numeric) = 1.9956424176080532 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0082951535591940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.617999999999872 " " y[1] (analytic) = 1.9955486665115623 " " y[1] (numeric) = 1.99554866651155 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1198473762233160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.616999999999872 " " y[1] (analytic) = 1.9954539198664754 " " y[1] (numeric) = 1.9954539198664634 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0088627186911050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.615999999999872 " " y[1] (analytic) = 1.995358177767552 " " y[1] (numeric) = 1.9953581777675398 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1204316132055380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.614999999999871 " " y[1] (analytic) = 1.9952614403105335 " " y[1] (numeric) = 1.9952614403105213 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1207283537620160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.613999999999871 " " y[1] (analytic) = 1.9951637075921578 " " y[1] (numeric) = 1.9951637075921456 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1210281764874290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.612999999999870 " " y[1] (analytic) = 1.9950649797101574 " " y[1] (numeric) = 1.9950649797101452 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1213310819835780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.61199999999987 " " y[1] (analytic) = 1.99496525676326 " " y[1] (numeric) = 1.994965256763248 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0103345786610740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.61099999999987 " " y[1] (analytic) = 1.9948645388511892 " " y[1] (numeric) = 1.994864538851177 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1219461437264710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.60999999999987 " " y[1] (analytic) = 1.9947628260746622 " " y[1] (numeric) = 1.99476282607465 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1222583012079960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.608999999999870 " " y[1] (analytic) = 1.994660118535392 " " y[1] (numeric) = 1.9946601185353798 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1225735439298260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.607999999999869 " " y[1] (analytic) = 1.9945564163360863 " " y[1] (numeric) = 1.994556416336074 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1228918725249550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.606999999999869 " " y[1] (analytic) = 1.994451719580447 " " y[1] (numeric) = 1.9944517195804348 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1232132876326210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.605999999999868 " " y[1] (analytic) = 1.994346028373171 " " y[1] (numeric) = 1.9943460283731589 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.123537789898310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.604999999999868 " " y[1] (analytic) = 1.9942393428199494 " " y[1] (numeric) = 1.9942393428199374 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0125223730651510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.603999999999868 " " y[1] (analytic) = 1.994131663027468 " " y[1] (numeric) = 1.994131663027456 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0128470392712130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.602999999999867 " " y[1] (analytic) = 1.9940229891034065 " " y[1] (numeric) = 1.9940229891033943 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1245298261921930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.601999999999867 " " y[1] (analytic) = 1.9939133211564384 " " y[1] (numeric) = 1.9939133211564264 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0135054712395630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.600999999999867 " " y[1] (analytic) = 1.9938026592962323 " " y[1] (numeric) = 1.9938026592962201 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1252066316269450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.599999999999866 " " y[1] (analytic) = 1.9936910036334494 " " y[1] (numeric) = 1.9936910036334374 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0141760403690880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.598999999999866 " " y[1] (analytic) = 1.9935783542797458 " " y[1] (numeric) = 1.9935783542797338 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0145158780496840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.597999999999866 " " y[1] (analytic) = 1.9934647113477708 " " y[1] (numeric) = 1.9934647113477588 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0148587520493600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.596999999999865 " " y[1] (analytic) = 1.9933500749511674 " " y[1] (numeric) = 1.9933500749511552 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.1265973420027080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.595999999999865 " " y[1] (analytic) = 1.9932344452045716 " " y[1] (numeric) = 1.9932344452045596 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0155536117684740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.594999999999865 " " y[1] (analytic) = 1.9931178222236134 " " y[1] (numeric) = 1.9931178222236015 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0159055988845870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.593999999999864 " " y[1] (analytic) = 1.9930002061249157 " " y[1] (numeric) = 1.993000206124904 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 5.9048483913147430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.592999999999864 " " y[1] (analytic) = 1.9928815970260945 " " y[1] (numeric) = 1.992881597026083 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7937809618653640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.591999999999864 " " y[1] (analytic) = 1.9927619950457593 " " y[1] (numeric) = 1.9927619950457476 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 5.905554245958220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.590999999999863 " " y[1] (analytic) = 1.9926414003035116 " " y[1] (numeric) = 1.9926414003035 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.794479355062550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.589999999999863 " " y[1] (analytic) = 1.9925198129199464 " " y[1] (numeric) = 1.9925198129199349 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7948329453151210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.588999999999863 " " y[1] (analytic) = 1.9923972330166508 " " y[1] (numeric) = 1.9923972330166395 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6837435143546790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.587999999999862 " " y[1] (analytic) = 1.9922736607162053 " " y[1] (numeric) = 1.9922736607161937 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7955489166838780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.586999999999862 " " y[1] (analytic) = 1.9921490961421815 " " y[1] (numeric) = 1.99214909614217 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.7959112992402030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.585999999999862 " " y[1] (analytic) = 1.9920235394191441 " " y[1] (numeric) = 1.9920235394191328 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6848097560527080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.584999999999861 " " y[1] (analytic) = 1.9918969906726502 " " y[1] (numeric) = 1.991896990672639 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6851709220929470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.583999999999861 " " y[1] (analytic) = 1.9917694500292482 " " y[1] (numeric) = 1.9917694500292369 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6855349654099300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.582999999999860 " " y[1] (analytic) = 1.9916409176164787 " " y[1] (numeric) = 1.9916409176164676 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.5744136144472770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.58199999999986 " " y[1] (analytic) = 1.9915113935628743 " " y[1] (numeric) = 1.9915113935628632 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.574776163539461000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.58099999999986 " " y[1] (analytic) = 1.9913808779979592 " " y[1] (numeric) = 1.991380877997948 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.5751415356630450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.57999999999986 " " y[1] (analytic) = 1.9912493710522483 " " y[1] (numeric) = 1.9912493710522374 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 5.4639995369224150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.578999999999860 " " y[1] (analytic) = 1.9911168728572493 " " y[1] (numeric) = 1.9911168728572384 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 5.4643631369129460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.577999999999859 " " y[1] (analytic) = 1.9909833835454598 " " y[1] (numeric) = 1.990983383545449 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 5.464729505653410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.576999999999859 " " y[1] (analytic) = 1.9908489032503693 " " y[1] (numeric) = 1.9908489032503587 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3535660184961490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.575999999999858 " " y[1] (analytic) = 1.9907134321064586 " " y[1] (numeric) = 1.9907134321064477 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 5.4654705523404980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.574999999999858 " " y[1] (analytic) = 1.9905769702491978 " " y[1] (numeric) = 1.9905769702491871 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3542973699063870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.573999999999858 " " y[1] (analytic) = 1.9904395178150494 " " y[1] (numeric) = 1.990439517815039 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2431115530364940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.572999999999857 " " y[1] (analytic) = 1.990301074941466 " " y[1] (numeric) = 1.9903010749414554 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3550395819963840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.571999999999857 " " y[1] (analytic) = 1.99016164176689 " " y[1] (numeric) = 1.9901616417668795 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2438436217729410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.570999999999857 " " y[1] (analytic) = 1.9900212184307546 " " y[1] (numeric) = 1.9900212184307442 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2442136469810750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.569999999999856 " " y[1] (analytic) = 1.9898798050734836 " " y[1] (numeric) = 1.989879805073473 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.3561732770125340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.568999999999856 " " y[1] (analytic) = 1.9897374018364897 " " y[1] (numeric) = 1.9897374018364793 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2449616828050540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.567999999999856 " " y[1] (analytic) = 1.9895940088621766 " " y[1] (numeric) = 1.9895940088621662 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2453396949283850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.566999999999855 " " y[1] (analytic) = 1.9894496262939372 " " y[1] (numeric) = 1.9894496262939267 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2457203708733460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.565999999999855 " " y[1] (analytic) = 1.9893042542761536 " " y[1] (numeric) = 1.9893042542761434 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1344844835050220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.564999999999855 " " y[1] (analytic) = 1.9891578929541984 " " y[1] (numeric) = 1.9891578929541882 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1348622765094020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.563999999999854 " " y[1] (analytic) = 1.9890105424744329 " " y[1] (numeric) = 1.9890105424744224 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2468783893389640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.562999999999854 " " y[1] (analytic) = 1.988862202984207 " " y[1] (numeric) = 1.9888622029841967 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1356256915263760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.561999999999854 " " y[1] (analytic) = 1.9887128746318607 " " y[1] (numeric) = 1.9887128746318503 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 5.2476637349714660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.560999999999853 " " y[1] (analytic) = 1.988562557566722 " " y[1] (numeric) = 1.9885625575667119 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1363995503615070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.559999999999853 " " y[1] (analytic) = 1.9884112519391082 " " y[1] (numeric) = 1.9884112519390982 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0251210416769440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.558999999999853 " " y[1] (analytic) = 1.988258957900325 " " y[1] (numeric) = 1.988258957900315 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0255059492745050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.557999999999852 " " y[1] (analytic) = 1.9881056756026658 " " y[1] (numeric) = 1.988105675602656 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9142068938260810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.556999999999852 " " y[1] (analytic) = 1.9879514051994138 " " y[1] (numeric) = 1.9879514051994038 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0262834370561980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.555999999999852 " " y[1] (analytic) = 1.9877961468448389 " " y[1] (numeric) = 1.9877961468448289 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0266760188092640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.554999999999851 " " y[1] (analytic) = 1.9876399006941992 " " y[1] (numeric) = 1.9876399006941894 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9153584677431456000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.553999999999851 " " y[1] (analytic) = 1.987482666903741 " " y[1] (numeric) = 1.9874826669037315 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8040258014681725000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.552999999999850 " " y[1] (analytic) = 1.9873244456306987 " " y[1] (numeric) = 1.987324445630689 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8044082750394650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = -4.55199999999985 " " y[1] (analytic) = 1.9871652370332926 " " y[1] (numeric) = 1.9871652370332833 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.6930538201112220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = cos ( x ) ;" Iterations = 449 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 1 Hours 4 Minutes 3 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 3 Minutes 50 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 6 Minutes 51 Seconds "Time to Timeout " Unknown Percent Done = 4.500000000001503 "%" (%o58) true (%o58) diffeq.max