(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac (%i3) reached_interval() := block([ret], if (((array_x >= glob_next_display) and (not glob_neg_h)) 1 or ((array_x <= glob_next_display) and glob_neg_h)) 1 or (glob_next_display = 0.0) then ret : true else ret : false, return(ret)) (%o3) reached_interval() := block([ret], if (((array_x >= glob_next_display) and (not glob_neg_h)) 1 or ((array_x <= glob_next_display) and glob_neg_h)) 1 or (glob_next_display = 0.0) then ret : true else ret : false, return(ret)) (%i4) 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) relerr if relerr # 0.0 then glob_good_digits : - floor(log10(------)) 100.0 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, " ")))) (%o4) 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) relerr if relerr # 0.0 then glob_good_digits : - floor(log10(------)) 100.0 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, " ")))) (%i5) 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 (%o5) 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 (%i6) 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)), 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, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o6) 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)), 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, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i7) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < 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 - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > 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 : false, if (not found) 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 : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 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 : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) 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 : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) 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, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if reached_interval() then display_pole()) (%o7) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < 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 - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > 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 : false, if (not found) 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 : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 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 : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) 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 : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) 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, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if reached_interval() then display_pole()) (%i8) 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 (%o8) 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 (%i9) atomall() := block([kkk, order_d, adj2, 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 2.0 temporary : -------------, array_y_higher : temporary)), 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)), 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 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary)), 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 2.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary)), 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 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary)), 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 array_tmp2 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) (%o9) atomall() := block([kkk, order_d, adj2, 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 2.0 temporary : -------------, array_y_higher : temporary)), 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)), 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 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary)), 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 2.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary)), 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 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary)), 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 array_tmp2 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) log(x) (%i10) log10(x) := --------- log(10.0) log(x) (%o10) log10(x) := --------- log(10.0) (%i11) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o11) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i12) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o12) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i13) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o13) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i14) 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)) (%o14) 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)) (%i15) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o15) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i16) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o16) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i17) dump_series(iolevel, dump_label, series_name, array_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 (%o17) dump_series(iolevel, dump_label, series_name, array_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 (%i18) dump_series_2(iolevel, dump_label, series_name, 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 (%o18) dump_series_2(iolevel, dump_label, series_name, 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 (%i19) 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)) (%o19) 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)) (%i20) logitem_time(fd, secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_minute min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, "")) (%o20) logitem_time(fd, secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_minute min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, "")) (%i21) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%")) (%o21) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%")) (%i22) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o22) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i23) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o23) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i24) 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 (%o24) 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 (%i25) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o25) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i26) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o26) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i27) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o27) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i28) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 rel_error then (good_digits : - floor(log10(---------)), 100.0 printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o28) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 rel_error then (good_digits : - floor(log10(---------)), 100.0 printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i29) log_revs(file, revs) := printf(file, revs) (%o29) log_revs(file, revs) := printf(file, revs) (%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i31) 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, "")) (%o31) 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, "")) (%i32) logstart(file) := printf(file, "") (%o32) logstart(file) := printf(file, "") (%i33) logend(file) := printf(file, "~%") (%o33) logend(file) := printf(file, "~%") (%i34) not_reached_end(x, x_end) := block([ret], if (glob_neg_h and (x > x_end)) or ((not glob_neg_h) and (x < x_end)) then ret : true else ret : false, ret) (%o34) not_reached_end(x, x_end) := block([ret], if (glob_neg_h and (x > x_end)) or ((not glob_neg_h) and (x < x_end)) then ret : true else ret : false, ret) (%i35) 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()) (%o35) 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()) (%i36) 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 (%o36) 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 (%i37) 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 (%o37) 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 (%i38) factorial_2(nnn) := block([ret], ret : nnn!) (%o38) factorial_2(nnn) := block([ret], ret : nnn!) (%i39) 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 (%o39) 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 (%i40) 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) (%o40) 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) (%i41) convfp(mmm) := mmm (%o41) convfp(mmm) := mmm (%i42) convfloat(mmm) := mmm (%o42) convfloat(mmm) := mmm (%i43) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o43) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i44) arcsin(x) := asin(x) (%o44) arcsin(x) := asin(x) (%i45) arccos(x) := acos(x) (%o45) arccos(x) := acos(x) (%i46) arctan(x) := atan(x) (%o46) arctan(x) := atan(x) (%i47) omniabs(x) := abs(x) (%o47) omniabs(x) := abs(x) y (%i48) expt(x, y) := x y (%o48) expt(x, y) := x (%i49) exact_soln_y(x) := sin(x) + 1.0 (%o49) exact_soln_y(x) := sin(x) + 1.0 (%i50) 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, log10norm, max_terms, opt_iter, tmp, subiter], define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_h, 0.1, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(years_in_century, 100, fixnum), define_variable(djd_debug2, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_hmax, 1.0, float), define_variable(hours_in_day, 24, fixnum), define_variable(glob_html_log, true, boolean), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_clock_sec, 0.0, float), define_variable(min_in_hour, 60, fixnum), define_variable(djd_debug, true, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_display_interval, 0.0, float), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_next_display, 0.0, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(centuries_in_millinium, 10, fixnum), define_variable(days_in_year, 365, fixnum), define_variable(glob_percent_done, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(sec_in_minute, 60, fixnum), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_dump, false, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_almost_1, 0.999, 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 : 1.6,"), omniout_str(ALWAYS, "x_end : 10.0 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.005 ,"), omniout_str(ALWAYS, "glob_display_interval : 0.1,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10000,"), omniout_str(ALWAYS, "glob_max_minutes : 10,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), 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, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), array(array_poles, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_y_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 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_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 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_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1_g : 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_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 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_work : 0.0, term : 1 + term), ord, 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, term ord : 1 + ord), 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 <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 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_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), 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_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 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_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term 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_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_const_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.6, iiif, jjjf x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 100, glob_h : 0.005, glob_display_interval : 0.1, glob_look_poles : true, glob_max_iter : 10000, glob_max_minutes : 10, 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), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), 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, if glob_html_log 1, 30 then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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 not_reached_end(array_x , x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 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(), 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 : 1, 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 display_alot(current_iter)), 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, "2012-09-20T21:26:11-05:00"), 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_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 130 "), logitem_str(html_log_file, "cos diffeq.max"), logitem_str(html_log_file, "cos maxima results"), logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o50) 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, log10norm, max_terms, opt_iter, tmp, subiter], define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_h, 0.1, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(years_in_century, 100, fixnum), define_variable(djd_debug2, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_hmax, 1.0, float), define_variable(hours_in_day, 24, fixnum), define_variable(glob_html_log, true, boolean), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_clock_sec, 0.0, float), define_variable(min_in_hour, 60, fixnum), define_variable(djd_debug, true, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_display_interval, 0.0, float), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_next_display, 0.0, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(centuries_in_millinium, 10, fixnum), define_variable(days_in_year, 365, fixnum), define_variable(glob_percent_done, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(sec_in_minute, 60, fixnum), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_dump, false, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_almost_1, 0.999, 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 : 1.6,"), omniout_str(ALWAYS, "x_end : 10.0 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.005 ,"), omniout_str(ALWAYS, "glob_display_interval : 0.1,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10000,"), omniout_str(ALWAYS, "glob_max_minutes : 10,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), 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, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), array(array_poles, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_y_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 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_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 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_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1_g : 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_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 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_work : 0.0, term : 1 + term), ord, 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, term ord : 1 + ord), 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 <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 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_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), 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_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 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_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term 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_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_const_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.6, iiif, jjjf x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 100, glob_h : 0.005, glob_display_interval : 0.1, glob_look_poles : true, glob_max_iter : 10000, glob_max_minutes : 10, 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), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), 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, if glob_html_log 1, 30 then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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 not_reached_end(array_x , x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 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(), 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 : 1, 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 display_alot(current_iter)), 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, "2012-09-20T21:26:11-05:00"), 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_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 130 "), logitem_str(html_log_file, "cos diffeq.max"), logitem_str(html_log_file, "cos maxima results"), logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i51) 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 : 1.6," "x_end : 10.0 ," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 100," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.005 ," "glob_display_interval : 0.1," "glob_look_poles : true," "glob_max_iter : 10000," "glob_max_minutes : 10," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (" " (1.0 + sin(x)) " ");" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 1.6 " " y[1] (analytic) = 1.999573603041505 " " y[1] (numeric) = 1.999573603041505 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.7049999999999979 " " y[1] (analytic) = 1.9910081948809422 " " y[1] (numeric) = 1.9910081948809262 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 8.029706555556520000000000000E-13 "%" Correct digits = 15 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.8049999999999957 " " y[1] (analytic) = 1.9726994520680763 " " y[1] (numeric) = 1.9726994520680452 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 1.5758226453054047000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.9049999999999936 " " y[1] (analytic) = 1.944671817861837 " " y[1] (numeric) = 1.9446718178617903 " " absolute error = 4.662936703425657500000000000000E-14 " " relative error = 2.397801346528767000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.0049999999999915 " " y[1] (analytic) = 1.9072053351185088 " " y[1] (numeric) = 1.9072053351184468 " " absolute error = 6.19504447740837300000000000000E-14 " " relative error = 3.2482315162061090000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.1049999999999893 " " y[1] (analytic) = 1.8606743565488904 " " y[1] (numeric) = 1.8606743565488137 " " absolute error = 7.6605388699135800000000000000E-14 " " relative error = 4.117076608785034000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.204999999999987 " " y[1] (analytic) = 1.8055438043097525 " " y[1] (numeric) = 1.805543804309662 " " absolute error = 9.03721542044877400000000000000E-14 " " relative error = 5.005259578237506000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.304999999999985 " " y[1] (analytic) = 1.7423645246553314 " " y[1] (numeric) = 1.7423645246552277 " " absolute error = 1.03694830499989620000000000000E-13 " " relative error = 5.951385547206441000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.404999999999983 " " y[1] (analytic) = 1.6717677840636405 " " y[1] (numeric) = 1.6717677840635246 " " absolute error = 1.15907283770866340000000000000E-13 " " relative error = 6.9332167347504060000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.504999999999981 " " y[1] (analytic) = 1.5944589618304923 " " y[1] (numeric) = 1.5944589618303642 " " absolute error = 1.28119737041743060000000000000E-13 " " relative error = 8.03531104335587900000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.6049999999999787 " " y[1] (analytic) = 1.5112105021527413 " " y[1] (numeric) = 1.5112105021526032 " " absolute error = 1.38111744263369470000000000000E-13 " " relative error = 9.139146668622755000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.7049999999999765 " " y[1] (analytic) = 1.4228541961212053 " " y[1] (numeric) = 1.422854196121058 " " absolute error = 1.4743761767022080000000000000E-13 " " relative error = 1.03621030230747100000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.8049999999999744 " " y[1] (analytic) = 1.33027287073904 " " y[1] (numeric) = 1.3302728707388856 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 1.161739432767388400000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.9049999999999723 " " y[1] (analytic) = 1.2343915680061464 " " y[1] (numeric) = 1.2343915680059852 " " absolute error = 1.61204383175572730000000000000E-13 " " relative error = 1.305942031311494400000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.00499999999997 " " y[1] (analytic) = 1.1361683022052866 " " y[1] (numeric) = 1.13616830220512 " " absolute error = 1.66533453693773480000000000000E-13 " " relative error = 1.46574634559452500000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.104999999999968 " " y[1] (analytic) = 1.036584487740048 " " y[1] (numeric) = 1.0365844877398784 " " absolute error = 1.69642078162723920000000000000E-13 " " relative error = 1.63654849333676600000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.204999999999966 " " y[1] (analytic) = 0.9366351331665349 " " y[1] (numeric) = 0.936635133166363 " " absolute error = 1.71862524211974230000000000000E-13 " " relative error = 1.834892992225787600000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.3049999999999637 " " y[1] (analytic) = 0.8373188993967814 " " y[1] (numeric) = 0.8373188993966091 " " absolute error = 1.7230661342182430000000000000E-13 " " relative error = 2.05783738484771900000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.4049999999999616 " " y[1] (analytic) = 0.7396281214090329 " " y[1] (numeric) = 0.7396281214088618 " " absolute error = 1.71085368094736620000000000000E-13 " " relative error = 2.313126869335490300000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.5049999999999595 " " y[1] (analytic) = 0.6445388931646652 " " y[1] (numeric) = 0.6445388931644965 " " absolute error = 1.68642877440561280000000000000E-13 " " relative error = 2.616488767846579000000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.6049999999999573 " " y[1] (analytic) = 0.5530013147999759 " " y[1] (numeric) = 0.5530013147998114 " " absolute error = 1.6453505224944820000000000000E-13 " " relative error = 2.975310326503682300000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.704999999999955 " " y[1] (analytic) = 0.4659299995396847 " " y[1] (numeric) = 0.4659299995395259 " " absolute error = 1.58817403672628640000000000000E-13 " " relative error = 3.408610817709359400000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.804999999999953 " " y[1] (analytic) = 0.3841949351839222 " " y[1] (numeric) = 0.38419493518377035 " " absolute error = 1.51878509768721410000000000000E-13 " " relative error = 3.953162727041520400000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.904999999999951 " " y[1] (analytic) = 0.3086127914777109 " " y[1] (numeric) = 0.3086127914775673 " " absolute error = 1.436073482352640000000000000E-13 " " relative error = 4.65331808016246240000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.004999999999950 " " y[1] (analytic) = 0.23993876021682803 " " y[1] (numeric) = 0.23993876021669433 " " absolute error = 1.33698607740484480000000000000E-13 " " relative error = 5.57219715646040800000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.104999999999947 " " y[1] (analytic) = 0.1788590096210163 " " y[1] (numeric) = 0.17885900962089327 " " absolute error = 1.23040466704082970000000000000E-13 " " relative error = 6.87918752120974900000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.204999999999945 " " y[1] (analytic) = 0.12598382836794741 " " y[1] (numeric) = 0.12598382836783617 " " absolute error = 1.11244347067440690000000000000E-13 " " relative error = 8.83004973801409600000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.304999999999943 " " y[1] (analytic) = 8.18415277904910300E-2 " " y[1] (numeric) = 8.1841527790392400E-2 " " absolute error = 9.86294379501373400000000000000E-14 " " relative error = 1.2051270377383749000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.404999999999940 " " y[1] (analytic) = 4.68731631645122900E-2 " " y[1] (numeric) = 4.68731631644272340E-2 " " absolute error = 8.5056961474094800000000000000E-14 " " relative error = 1.814619618811890000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.504999999999939 " " y[1] (analytic) = 2.14281268303496700E-2 " " y[1] (numeric) = 2.14281268302787100E-2 " " absolute error = 7.09605985083072700000000000000E-14 " " relative error = 3.3115633050949850000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.6049999999999365 " " y[1] (analytic) = 5.7606571800432600000E-3 " " y[1] (numeric) = 5.7606571799869110000E-3 " " absolute error = 5.634989003189261000000000000000E-14 " " relative error = 9.781850971293079000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.704999999999934 " " y[1] (analytic) = 2.729839136184075700000E-5 " " y[1] (numeric) = 2.729839132062971700000E-5 " " absolute error = 4.121103957220595400000000000000E-14 " " relative error = 1.50965084447478050000000E-7 "%" Correct digits = 9 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.804999999999932 " " y[1] (analytic) = 4.28533629012572970E-3 " " y[1] (numeric) = 4.285336290099778000E-3 " " absolute error = 2.595146320061303400000000000000E-14 " " relative error = 6.0558755354650660000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.90499999999993 " " y[1] (analytic) = 1.84922259691705500E-2 " " y[1] (numeric) = 1.84922259691599500E-2 " " absolute error = 1.059916043821829100000000000000E-14 " " relative error = 5.731684468862083000000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.004999999999928 " " y[1] (analytic) = 4.25060168829967100E-2 " " y[1] (numeric) = 4.250601688300134600E-2 " " absolute error = 4.6351811278100286000000000000000E-15 " " relative error = 1.09047647079446710000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.104999999999926 " " y[1] (analytic) = 7.60867711706970700E-2 " " y[1] (numeric) = 7.60867711707167700E-2 " " absolute error = 1.97064586870965290000000000000E-14 " " relative error = 2.589998022505912700000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.204999999999924 " " y[1] (analytic) = 0.1188989610357506 " " y[1] (numeric) = 0.11889896103578493 " " absolute error = 3.433364703653296600000000000000E-14 " " relative error = 2.887632216248678000000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.304999999999922 " " y[1] (analytic) = 0.17051482122885409 " " y[1] (numeric) = 0.17051482122890252 " " absolute error = 4.843347944927245400000000000000E-14 " " relative error = 2.840426368818000400000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.404999999999920 " " y[1] (analytic) = 0.23041862313689299 " " y[1] (numeric) = 0.2304186231369549 " " absolute error = 6.1922689198468110000000000000E-14 " " relative error = 2.687399497291479400000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.504999999999917 " " y[1] (analytic) = 0.29801182777276647 " " y[1] (numeric) = 0.29801182777284113 " " absolute error = 7.46624984060417800000000000000E-14 " " relative error = 2.505353527879833300000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.604999999999915 " " y[1] (analytic) = 0.3726190661790958 " " y[1] (numeric) = 0.37261906617918206 " " absolute error = 8.62643290133746600000000000000E-14 " " relative error = 2.31508091891123290000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.704999999999913 " " y[1] (analytic) = 0.45349488749159894 " " y[1] (numeric) = 0.453494887491696 " " absolute error = 9.70334923522386800000000000000E-14 " " relative error = 2.139682166847718700000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.804999999999911 " " y[1] (analytic) = 0.5398312072377137 " " y[1] (numeric) = 0.5398312072378202 " " absolute error = 1.06470388061552510000000000000E-13 " " relative error = 1.972290349910587300000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.904999999999909 " " y[1] (analytic) = 0.6307653814495299 " " y[1] (numeric) = 0.6307653814496447 " " absolute error = 1.14797060746241190000000000000E-13 " " relative error = 1.819964508553591000000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.004999999999907 " " y[1] (analytic) = 0.7253888259171646 " " y[1] (numeric) = 0.7253888259172864 " " absolute error = 1.21791465801379670000000000000E-13 " " relative error = 1.67898182946765700000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.1049999999999045 " " y[1] (analytic) = 0.8227560944618495 " " y[1] (numeric) = 0.8227560944619766 " " absolute error = 1.27120536319580420000000000000E-13 " " relative error = 1.545057364816334300000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.204999999999902 " " y[1] (analytic) = 0.9218943255216259 " " y[1] (numeric) = 0.9218943255217572 " " absolute error = 1.31339383813156020000000000000E-13 " " relative error = 1.424668534962959300000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.3049999999999 " " y[1] (analytic) = 1.0218129626624868 " " y[1] (numeric) = 1.021812962662621 " " absolute error = 1.3411494137471890000000000000E-13 " " relative error = 1.31251947543572300000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.404999999999898 " " y[1] (analytic) = 1.121513651890831 " " y[1] (numeric) = 1.121513651890966 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 1.203758149237048600000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.504999999999896 " " y[1] (analytic) = 1.2200002168765551 " " y[1] (numeric) = 1.22000021687669 " " absolute error = 1.347810751894940000000000000E-13 " " relative error = 1.104762714998203500000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.604999999999894 " " y[1] (analytic) = 1.3162886124176516 " " y[1] (numeric) = 1.3162886124177844 " " absolute error = 1.32782673745168720000000000000E-13 " " relative error = 1.008765649816603100000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.704999999999892 " " y[1] (analytic) = 1.409416756694586 " " y[1] (numeric) = 1.4094167566947153 " " absolute error = 1.29229960066368220000000000000E-13 " " relative error = 9.169038146633284000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.80499999999989 " " y[1] (analytic) = 1.4984541440738148 " " y[1] (numeric) = 1.4984541440739394 " " absolute error = 1.24567023362942560000000000000E-13 " " relative error = 8.313035394215328000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.9049999999998875 " " y[1] (analytic) = 1.5825111424124922 " " y[1] (numeric) = 1.58251114241261 " " absolute error = 1.1768364061026660000000000000E-13 " " relative error = 7.436512606847198000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.004999999999885 " " y[1] (analytic) = 1.660747881968767 " " y[1] (numeric) = 1.6607478819688777 " " absolute error = 1.10578213252665590000000000000E-13 " " relative error = 6.65833835787154000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.104999999999883 " " y[1] (analytic) = 1.7323826471026216 " " y[1] (numeric) = 1.732382647102723 " " absolute error = 1.01474384450739310000000000000E-13 " " relative error = 5.85750409243901000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.204999999999881 " " y[1] (analytic) = 1.7966996869201428 " " y[1] (numeric) = 1.7966996869202339 " " absolute error = 9.10382880192628400000000000000E-14 " " relative error = 5.066972999551104000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.304999999999879 " " y[1] (analytic) = 1.8530563668198612 " " y[1] (numeric) = 1.853056366819941 " " absolute error = 7.97140131680862400000000000000E-14 " " relative error = 4.301758683406276000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.404999999999877 " " y[1] (analytic) = 1.9008895894852602 " " y[1] (numeric) = 1.9008895894853277 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 3.5510510589669860000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.504999999999875 " " y[1] (analytic) = 1.9397214211670284 " " y[1] (numeric) = 1.9397214211670835 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 2.838916012397121000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.6049999999998725 " " y[1] (analytic) = 1.9691638670390987 " " y[1] (numeric) = 1.9691638670391394 " " absolute error = 4.06341627012807300000000000000E-14 " " relative error = 2.063523680351683000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.70499999999987 " " y[1] (analytic) = 1.9889227479146956 " " y[1] (numeric) = 1.9889227479147218 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 1.3173595308628577000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.804999999999868 " " y[1] (analytic) = 1.9988006395875284 " " y[1] (numeric) = 1.9988006395875397 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 5.6655349347464020000000000000E-13 "%" Correct digits = 15 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.904999999999866 " " y[1] (analytic) = 1.9986988454291987 " " y[1] (numeric) = 1.9986988454291952 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.77751324914464270000000000000E-13 "%" Correct digits = 15 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.004999999999864 " " y[1] (analytic) = 1.988618382533288 " " y[1] (numeric) = 1.988618382533269 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 9.4909066437294320000000000000E-13 "%" Correct digits = 15 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.10499999999988 " " y[1] (analytic) = 1.9686599715528894 " " y[1] (numeric) = 1.9686599715528583 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 1.5790560654810992000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.204999999999895 " " y[1] (analytic) = 1.9390230303331468 " " y[1] (numeric) = 1.9390230303331057 " " absolute error = 4.10782519111307900000000000000E-14 " " relative error = 2.1185025277432146000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.304999999999911 " " y[1] (analytic) = 1.900003681394058 " " y[1] (numeric) = 1.9000036813940089 " " absolute error = 4.90718576884319200000000000000E-14 " " relative error = 2.5827243477984860000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.404999999999927 " " y[1] (analytic) = 1.85199179317214 " " y[1] (numeric) = 1.851991793172085 " " absolute error = 5.48450174164827300000000000000E-14 " " relative error = 2.9614071519476204000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.504999999999942 " " y[1] (analytic) = 1.7954670845838863 " " y[1] (numeric) = 1.7954670845838283 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 3.2277752336999477000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.604999999999958 " " y[1] (analytic) = 1.7309943318329268 " " y[1] (numeric) = 1.7309943318328669 " " absolute error = 5.99520433297584500000000000000E-14 " " relative error = 3.4634453866914766000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.704999999999973 " " y[1] (analytic) = 1.6592177253528901 " " y[1] (numeric) = 1.659217725352831 " " absolute error = 5.90638649100583300000000000000E-14 " " relative error = 3.559741678717683000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.799999999999988 " " y[1] (analytic) = 1.5849171928917718 " " y[1] (numeric) = 1.5849171928917154 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 3.5585032394061017000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.900000000000004 " " y[1] (analytic) = 1.5010208564578815 " " y[1] (numeric) = 1.50102085645783 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 3.4319542011009196000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.00000000000002 " " y[1] (analytic) = 1.4121184852417388 " " y[1] (numeric) = 1.4121184852416937 " " absolute error = 4.507505479978135600000000000000E-14 " " relative error = 3.192016482389225000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.100000000000035 " " y[1] (analytic) = 1.3190983623493184 " " y[1] (numeric) = 1.3190983623492822 " " absolute error = 3.619327060278010300000000000000E-14 " " relative error = 2.7437886086311086000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.20000000000005 " " y[1] (analytic) = 1.2228899141001974 " " y[1] (numeric) = 1.2228899141001721 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 2.069939793401513200000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.300000000000066 " " y[1] (analytic) = 1.1244544235069964 " " y[1] (numeric) = 1.1244544235069838 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 1.1255718521034422000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.400000000000082 " " y[1] (analytic) = 1.0247754254532762 " " y[1] (numeric) = 1.0247754254532773 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.08338178009497590000000000000E-13 "%" Correct digits = 15 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.500000000000098 " " y[1] (analytic) = 0.9248488795380932 " " y[1] (numeric) = 0.9248488795381105 " " absolute error = 1.720845688168992600000000000000E-14 " " relative error = 1.860677702316569000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.600000000000113 " " y[1] (analytic) = 0.8256732187769085 " " y[1] (numeric) = 0.8256732187769429 " " absolute error = 3.44169137633798500000000000000E-14 " " relative error = 4.1683456579059860000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.700000000000129 " " y[1] (analytic) = 0.7282393735889328 " " y[1] (numeric) = 0.7282393735889859 " " absolute error = 5.317968287954500000000000000E-14 " " relative error = 7.30250036021304000000000000E-12 "%" Correct digits = 14 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.800000000000145 " " y[1] (analytic) = 0.6335208707479377 " " y[1] (numeric) = 0.6335208707480103 " " absolute error = 7.26085858104852400000000000000E-14 " " relative error = 1.146111977727950800000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.90000000000016 " " y[1] (analytic) = 0.5424641062245366 " " y[1] (numeric) = 0.5424641062246293 " " absolute error = 9.27036225562005700000000000000E-14 " " relative error = 1.708935605000724600000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 10.000000000000176 " " y[1] (analytic) = 0.4559788891104827 " " y[1] (numeric) = 0.45597888911059675 " " absolute error = 1.14075415780234830000000000000E-13 " " relative error = 2.501769676284172000000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " "Finished!" "diff ( y , x , 1 ) = cos ( x ) ;" Iterations = 1680 "Total Elapsed Time "= 9 Minutes 53 Seconds "Elapsed Time(since restart) "= 9 Minutes 53 Seconds "Time to Timeout "= 6 Seconds Percent Done = 100.05952380952591 "%" (%o51) true (%o51) diffeq.max