(%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) display_alot(iter) := if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y1(ind_var), omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y1 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, 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_float(ALWAYS, "h ", 4, glob_h, 20, " "), analytic_val_y : exact_soln_y2(ind_var), omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y2 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 2 else array_last_rel_error : relerr, omniout_float(ALWAYS, 2 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%o3) display_alot(iter) := if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y1(ind_var), omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y1 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, 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_float(ALWAYS, "h ", 4, glob_h, 20, " "), analytic_val_y : exact_soln_y2(ind_var), omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y2 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 2 else array_last_rel_error : relerr, omniout_float(ALWAYS, 2 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%i4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), 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) 1 (%o4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), 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) 1 (%i5) prog_report(x_start, x_end) := (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, "%")) (%o5) prog_report(x_start, x_end) := (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, "%")) (%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y1_higher ! < glob_small_float) ! 1, m! or (!array_y1_higher ! < glob_small_float) ! 1, m - 1! or (!array_y1_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y1_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y1_higher 1, m - 1 array_y1_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y1_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(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 : glob_max_terms, m : - 1 - 1 + n, 1, 2 while (m >= 10) and ((!array_y2_higher ! < glob_small_float) ! 1, m! or (!array_y2_higher ! < glob_small_float) ! 1, m - 1! or (!array_y2_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y2_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y2_higher 1, m - 1 array_y2_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y2_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(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) 2, 1 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float)) 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 2, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_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 (!array_y1_higher ! >= glob_large_float) ! 1, m! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y1_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_y1_higher array_y1_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y1_higher array_y1_higher 1, m - 1 1, m - 2 array_y1_higher array_y1_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y1_higher array_y1_higher 1, m - 3 1, m - 4 array_y1_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y1_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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(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 abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) 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, 1, 1 array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0, 1, 2 while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! > glob_small_float ! 1, n! then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 elseif (!array_y2_higher ! >= glob_large_float) ! 1, m! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 array_y2_higher array_y2_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y2_higher array_y2_higher 1, m - 1 1, m - 2 array_y2_higher array_y2_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y2_higher array_y2_higher 1, m - 3 1, m - 4 array_y2_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y2_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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 2, 1 glob_large_float, array_complex_pole : glob_large_float) 2, 2 else (if abs(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 abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) 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, 2, 1 array_complex_pole : ord_no), found : false, 2, 2 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 glob_display_flag 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 glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), found : false, if (not found) and ((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 2, 1 2, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 2, 1 2, 2 then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 2, 2 2, 2 2 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) 2, 1 2, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 2, 1 2, 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))) 2, 1 2, 2 2, 1 2, 2 then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 2, 1 2, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 found : true, array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 2, 1 2, 1 and (array_real_pole > 0.0) and (array_real_pole > 2, 1 2, 2 0.0)) then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 2, 1 and (array_complex_pole # glob_large_float) 2, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 2, 1 2, 2 0.0)) then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 2, 2 2, 2 2 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, 2, 1 2, 2 array_type_pole : 3, if glob_display_flag 2 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 array_pole > array_poles then (array_pole : array_poles , 1 2, 1 1 2, 1 array_pole : array_poles ), display_pole()) 2 2, 2 (%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y1_higher ! < glob_small_float) ! 1, m! or (!array_y1_higher ! < glob_small_float) ! 1, m - 1! or (!array_y1_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y1_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y1_higher 1, m - 1 array_y1_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y1_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(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 : glob_max_terms, m : - 1 - 1 + n, 1, 2 while (m >= 10) and ((!array_y2_higher ! < glob_small_float) ! 1, m! or (!array_y2_higher ! < glob_small_float) ! 1, m - 1! or (!array_y2_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y2_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y2_higher 1, m - 1 array_y2_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y2_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(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) 2, 1 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float)) 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 2, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_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 (!array_y1_higher ! >= glob_large_float) ! 1, m! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y1_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_y1_higher array_y1_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y1_higher array_y1_higher 1, m - 1 1, m - 2 array_y1_higher array_y1_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y1_higher array_y1_higher 1, m - 3 1, m - 4 array_y1_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y1_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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(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 abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) 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, 1, 1 array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0, 1, 2 while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! > glob_small_float ! 1, n! then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 elseif (!array_y2_higher ! >= glob_large_float) ! 1, m! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 array_y2_higher array_y2_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y2_higher array_y2_higher 1, m - 1 1, m - 2 array_y2_higher array_y2_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y2_higher array_y2_higher 1, m - 3 1, m - 4 array_y2_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y2_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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 2, 1 glob_large_float, array_complex_pole : glob_large_float) 2, 2 else (if abs(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 abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) 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, 2, 1 array_complex_pole : ord_no), found : false, 2, 2 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 glob_display_flag 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 glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), found : false, if (not found) and ((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 2, 1 2, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 2, 1 2, 2 then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 2, 2 2, 2 2 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) 2, 1 2, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 2, 1 2, 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))) 2, 1 2, 2 2, 1 2, 2 then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 2, 1 2, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 found : true, array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 2, 1 2, 1 and (array_real_pole > 0.0) and (array_real_pole > 2, 1 2, 2 0.0)) then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 2, 1 and (array_complex_pole # glob_large_float) 2, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 2, 1 2, 2 0.0)) then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 2, 2 2, 2 2 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, 2, 1 2, 2 array_type_pole : 3, if glob_display_flag 2 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 array_pole > array_poles then (array_pole : array_poles , 1 2, 1 1 2, 1 array_pole : array_poles ), display_pole()) 2 2, 2 (%i7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_y1 ! > array_norms ! iii! iii then array_norms : !array_y1 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_y2 ! > array_norms ! iii! iii then array_norms : !array_y2 !, iii : 1 + iii)) iii ! iii! (%o7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_y1 ! > array_norms ! iii! iii then array_norms : !array_y1 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_y2 ! > array_norms ! iii! iii then array_norms : !array_y2 !, iii : 1 + iii)) iii ! iii! (%i8) atomall() := (array_tmp1 : array_m1 array_y2 , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : array_const_1D0 + array_tmp2 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp3 glob_h factorial_3(0, 1), 1 array_y1 : temporary, array_y1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp5 : array_y1 - array_const_1D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp5 glob_h factorial_3(0, 1), 1 array_y2 : temporary, array_y2_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : ats(2, array_m1, array_y2, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 array_tmp3 : array_const_1D0 + array_tmp2 , 2 2 2 if not array_y1_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp3 glob_h factorial_3(1, 2), 2 array_y1 : temporary, array_y1_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp5 : array_y1 - array_const_1D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp5 glob_h factorial_3(1, 2), 2 array_y2 : temporary, array_y2_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_m1, array_y2, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 array_tmp3 : array_const_1D0 + array_tmp2 , 3 3 3 if not array_y1_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp3 glob_h factorial_3(2, 3), 3 array_y1 : temporary, array_y1_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp5 : array_y1 - array_const_1D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp5 glob_h factorial_3(2, 3), 3 array_y2 : temporary, array_y2_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_m1, array_y2, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 array_tmp3 : array_const_1D0 + array_tmp2 , 4 4 4 if not array_y1_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp3 glob_h factorial_3(3, 4), 4 array_y1 : temporary, array_y1_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp5 : array_y1 - array_const_1D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp5 glob_h factorial_3(3, 4), 4 array_y2 : temporary, array_y2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_m1, array_y2, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 array_tmp3 : array_const_1D0 + array_tmp2 , 5 5 5 if not array_y1_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp3 glob_h factorial_3(4, 5), 5 array_y1 : temporary, array_y1_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 6, glob_h 2, 5 array_tmp5 : array_y1 - array_const_1D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp5 glob_h factorial_3(4, 5), 5 array_y2 : temporary, array_y2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_m1, array_y2, 1), array_tmp2 : kkk array_tmp1 + array_const_0D0 , array_tmp3 : kkk kkk kkk array_const_1D0 + array_tmp2 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 1, order_d + kkk order_d array_tmp3 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y1 : temporary, array_y1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), array_tmp5 : kkk array_y1 - array_const_1D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 2, order_d + kkk order_d array_tmp5 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y2 : temporary, array_y2_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y2_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) (%o8) atomall() := (array_tmp1 : array_m1 array_y2 , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : array_const_1D0 + array_tmp2 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp3 glob_h factorial_3(0, 1), 1 array_y1 : temporary, array_y1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp5 : array_y1 - array_const_1D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp5 glob_h factorial_3(0, 1), 1 array_y2 : temporary, array_y2_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : ats(2, array_m1, array_y2, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 array_tmp3 : array_const_1D0 + array_tmp2 , 2 2 2 if not array_y1_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp3 glob_h factorial_3(1, 2), 2 array_y1 : temporary, array_y1_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp5 : array_y1 - array_const_1D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp5 glob_h factorial_3(1, 2), 2 array_y2 : temporary, array_y2_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_m1, array_y2, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 array_tmp3 : array_const_1D0 + array_tmp2 , 3 3 3 if not array_y1_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp3 glob_h factorial_3(2, 3), 3 array_y1 : temporary, array_y1_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp5 : array_y1 - array_const_1D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp5 glob_h factorial_3(2, 3), 3 array_y2 : temporary, array_y2_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_m1, array_y2, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 array_tmp3 : array_const_1D0 + array_tmp2 , 4 4 4 if not array_y1_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp3 glob_h factorial_3(3, 4), 4 array_y1 : temporary, array_y1_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp5 : array_y1 - array_const_1D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp5 glob_h factorial_3(3, 4), 4 array_y2 : temporary, array_y2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_m1, array_y2, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 array_tmp3 : array_const_1D0 + array_tmp2 , 5 5 5 if not array_y1_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp3 glob_h factorial_3(4, 5), 5 array_y1 : temporary, array_y1_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 6, glob_h 2, 5 array_tmp5 : array_y1 - array_const_1D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp5 glob_h factorial_3(4, 5), 5 array_y2 : temporary, array_y2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_m1, array_y2, 1), array_tmp2 : kkk array_tmp1 + array_const_0D0 , array_tmp3 : kkk kkk kkk array_const_1D0 + array_tmp2 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 1, order_d + kkk order_d array_tmp3 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y1 : temporary, array_y1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), array_tmp5 : kkk array_y1 - array_const_1D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 2, order_d + kkk order_d array_tmp5 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y2 : temporary, array_y2_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y2_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) log(x) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) 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)) (%o13) 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)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) := 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 (%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) := 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 (%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := 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 (%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := 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 (%i18) 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)) (%o18) 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)) (%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min 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_min, 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, "")) (%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min 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_min, 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, "")) (%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) 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_min), 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~%")) (%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) 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_min), 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~%")) (%i21) mode_declare(ats, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o21) [ats] (%i22) ats(mmm_ats, array_a, array_b, jjj_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) := (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) mode_declare(att, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o23) [att] (%i24) att(mmm_att, array_aa, array_bb, jjj_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) (%o24) att(mmm_att, array_aa, array_bb, jjj_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) (%i25) 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 (%o25) 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 (%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str), 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) chk_data() := (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()) (%o34) chk_data() := (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()) (%i35) mode_declare(comp_expect_sec, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o35) [comp_expect_sec] (%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(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_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i37) mode_declare(comp_percent, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o37) [comp_percent] (%i38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i39) mode_declare(factorial_1, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o39) [factorial_1] (%i40) factorial_1(nnn) := nnn! (%o40) factorial_1(nnn) := nnn! (%i41) mode_declare(factorial_3, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o41) [factorial_3] mmm2! (%i42) factorial_3(mmm2, nnn2) := ----- nnn2! mmm2! (%o42) factorial_3(mmm2, nnn2) := ----- nnn2! (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) exact_soln_y1(x) := cos(x) + 1.0 (%o49) exact_soln_y1(x) := cos(x) + 1.0 (%i50) exact_soln_y2(x) := sin(x) + 1.0 (%o50) exact_soln_y2(x) := sin(x) + 1.0 (%i51) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_clock_sec, 0.0, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(hours_in_day, 24.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_almost_1, 0.999, float), define_variable(days_in_year, 365.0, float), define_variable(min_in_hour, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_h, 0.1, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(years_in_century, 100.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_max_opt_iter, 10, fixnum), 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 : 2, 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/mtest2postode.ode#################"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"), omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 10.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS, "/* # testing comment */"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 1000,"), omniout_str(ALWAYS, "glob_max_minutes : 15,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y1 (x) := ("), omniout_str(ALWAYS, "1.0 + cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 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_y2_init, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_x, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_real_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y2_higher_work, 1 + 2, 1 + max_terms), array(array_y2_higher, 1 + 2, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1_init : 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_norms : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 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_y2_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_y1_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term term : 1 + 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_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : 0.1, x_end : 10.0, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 10, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15, 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_log10_abserr glob_log10_relerr glob_abserr : 10.0 , glob_relerr : 10.0 , chk_data(), array_y1_set_initial : true, array_y1_set_initial : false, 1, 1 1, 2 array_y1_set_initial : false, array_y1_set_initial : false, 1, 3 1, 4 array_y1_set_initial : false, array_y1_set_initial : false, 1, 5 1, 6 array_y1_set_initial : false, array_y1_set_initial : false, 1, 7 1, 8 array_y1_set_initial : false, array_y1_set_initial : false, 1, 9 1, 10 array_y1_set_initial : false, array_y1_set_initial : false, 1, 11 1, 12 array_y1_set_initial : false, array_y1_set_initial : false, 1, 13 1, 14 array_y1_set_initial : false, array_y1_set_initial : false, 1, 15 1, 16 array_y1_set_initial : false, array_y1_set_initial : false, 1, 17 1, 18 array_y1_set_initial : false, array_y1_set_initial : false, 1, 19 1, 20 array_y1_set_initial : false, array_y1_set_initial : false, 1, 21 1, 22 array_y1_set_initial : false, array_y1_set_initial : false, 1, 23 1, 24 array_y1_set_initial : false, array_y1_set_initial : false, 1, 25 1, 26 array_y1_set_initial : false, array_y1_set_initial : false, 1, 27 1, 28 array_y1_set_initial : false, array_y1_set_initial : false, 1, 29 1, 30 array_y2_set_initial : true, array_y2_set_initial : false, 2, 1 2, 2 array_y2_set_initial : false, array_y2_set_initial : false, 2, 3 2, 4 array_y2_set_initial : false, array_y2_set_initial : false, 2, 5 2, 6 array_y2_set_initial : false, array_y2_set_initial : false, 2, 7 2, 8 array_y2_set_initial : false, array_y2_set_initial : false, 2, 9 2, 10 array_y2_set_initial : false, array_y2_set_initial : false, 2, 11 2, 12 array_y2_set_initial : false, array_y2_set_initial : false, 2, 13 2, 14 array_y2_set_initial : false, array_y2_set_initial : false, 2, 15 2, 16 array_y2_set_initial : false, array_y2_set_initial : false, 2, 17 2, 18 array_y2_set_initial : false, array_y2_set_initial : false, 2, 19 2, 20 array_y2_set_initial : false, array_y2_set_initial : false, 2, 21 2, 22 array_y2_set_initial : false, array_y2_set_initial : false, 2, 23 2, 24 array_y2_set_initial : false, array_y2_set_initial : false, 2, 25 2, 26 array_y2_set_initial : false, array_y2_set_initial : false, 2, 27 2, 28 array_y2_set_initial : false, array_y2_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y1 : term_no term_no - 1 array_y1_init glob_h 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, term_no - 1 array_y1_init glob_h it array_y1_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y2 : term_no term_no - 1 array_y2_init glob_h 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, term_no - 1 array_y2_init glob_h it array_y2_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(), start_array_y1(), if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), start_array_y2(), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_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 (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (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, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(), subiter : 1 + subiter)), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_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 ( y1 , x , 1 ) = m1 * y2 + 1.0;"), omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-13T14:22:12-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest2"), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), 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, " 090 "), logitem_str(html_log_file, "mtest2 diffeq.max"), logitem_str(html_log_file, "\ mtest2 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 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), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o51) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_clock_sec, 0.0, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(hours_in_day, 24.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_almost_1, 0.999, float), define_variable(days_in_year, 365.0, float), define_variable(min_in_hour, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_h, 0.1, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(years_in_century, 100.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_max_opt_iter, 10, fixnum), 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 : 2, 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/mtest2postode.ode#################"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"), omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 10.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS, "/* # testing comment */"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 1000,"), omniout_str(ALWAYS, "glob_max_minutes : 15,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y1 (x) := ("), omniout_str(ALWAYS, "1.0 + cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 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_y2_init, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_x, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_real_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y2_higher_work, 1 + 2, 1 + max_terms), array(array_y2_higher, 1 + 2, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1_init : 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_norms : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 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_y2_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_y1_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term term : 1 + 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_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : 0.1, x_end : 10.0, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 10, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15, 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_log10_abserr glob_log10_relerr glob_abserr : 10.0 , glob_relerr : 10.0 , chk_data(), array_y1_set_initial : true, array_y1_set_initial : false, 1, 1 1, 2 array_y1_set_initial : false, array_y1_set_initial : false, 1, 3 1, 4 array_y1_set_initial : false, array_y1_set_initial : false, 1, 5 1, 6 array_y1_set_initial : false, array_y1_set_initial : false, 1, 7 1, 8 array_y1_set_initial : false, array_y1_set_initial : false, 1, 9 1, 10 array_y1_set_initial : false, array_y1_set_initial : false, 1, 11 1, 12 array_y1_set_initial : false, array_y1_set_initial : false, 1, 13 1, 14 array_y1_set_initial : false, array_y1_set_initial : false, 1, 15 1, 16 array_y1_set_initial : false, array_y1_set_initial : false, 1, 17 1, 18 array_y1_set_initial : false, array_y1_set_initial : false, 1, 19 1, 20 array_y1_set_initial : false, array_y1_set_initial : false, 1, 21 1, 22 array_y1_set_initial : false, array_y1_set_initial : false, 1, 23 1, 24 array_y1_set_initial : false, array_y1_set_initial : false, 1, 25 1, 26 array_y1_set_initial : false, array_y1_set_initial : false, 1, 27 1, 28 array_y1_set_initial : false, array_y1_set_initial : false, 1, 29 1, 30 array_y2_set_initial : true, array_y2_set_initial : false, 2, 1 2, 2 array_y2_set_initial : false, array_y2_set_initial : false, 2, 3 2, 4 array_y2_set_initial : false, array_y2_set_initial : false, 2, 5 2, 6 array_y2_set_initial : false, array_y2_set_initial : false, 2, 7 2, 8 array_y2_set_initial : false, array_y2_set_initial : false, 2, 9 2, 10 array_y2_set_initial : false, array_y2_set_initial : false, 2, 11 2, 12 array_y2_set_initial : false, array_y2_set_initial : false, 2, 13 2, 14 array_y2_set_initial : false, array_y2_set_initial : false, 2, 15 2, 16 array_y2_set_initial : false, array_y2_set_initial : false, 2, 17 2, 18 array_y2_set_initial : false, array_y2_set_initial : false, 2, 19 2, 20 array_y2_set_initial : false, array_y2_set_initial : false, 2, 21 2, 22 array_y2_set_initial : false, array_y2_set_initial : false, 2, 23 2, 24 array_y2_set_initial : false, array_y2_set_initial : false, 2, 25 2, 26 array_y2_set_initial : false, array_y2_set_initial : false, 2, 27 2, 28 array_y2_set_initial : false, array_y2_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y1 : term_no term_no - 1 array_y1_init glob_h 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, term_no - 1 array_y1_init glob_h it array_y1_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y2 : term_no term_no - 1 array_y2_init glob_h 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, term_no - 1 array_y2_init glob_h it array_y2_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(), start_array_y1(), if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), start_array_y2(), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_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 (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (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, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(), subiter : 1 + subiter)), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, 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_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_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 ( y1 , x , 1 ) = m1 * y2 + 1.0;"), omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-13T14:22:12-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest2"), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), 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, " 090 "), logitem_str(html_log_file, "mtest2 diffeq.max"), logitem_str(html_log_file, "\ mtest2 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 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), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i52) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/mtest2postode.ode#################" "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;" "diff ( y2 , x , 1 ) = y1 - 1.0;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.1," "x_end : 10.0," "array_y1_init[0 + 1] : exact_soln_y1(x_start)," "array_y2_init[0 + 1] : exact_soln_y2(x_start)," "/* # testing comment */" "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.0001 ," "glob_look_poles : true," "glob_max_iter : 1000," "glob_max_minutes : 15," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y1 (x) := (" "1.0 + cos(x) " ");" "exact_soln_y2 (x) := (" "1.0 + sin(x) " ");" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.1 " " y1[1] (analytic) = 1.9950041652780257 " " y1[1] (numeric) = 1.9950041652780257 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.0998334166468282 " " y2[1] (numeric) = 1.0998334166468282 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " x[1] = 0.1 " " y1[1] (analytic) = 1.9950041652780257 " " y1[1] (numeric) = 1.9950041652780257 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.0998334166468282 " " y2[1] (numeric) = 1.0998334166468282 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10010000000000001 " " y1[1] (analytic) = 1.9949941769613568 " " y1[1] (numeric) = 1.9949941769613568 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.099932916564023 " " y2[1] (numeric) = 1.099932916564023 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10020000000000001 " " y1[1] (analytic) = 1.9949841786947462 " " y1[1] (numeric) = 1.9949841786947462 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1000324154818888 " " y2[1] (numeric) = 1.1000324154818888 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10030000000000001 " " y1[1] (analytic) = 1.9949741704782937 " " y1[1] (numeric) = 1.9949741704782937 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1001319133994303 " " y2[1] (numeric) = 1.1001319133994303 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10040000000000002 " " y1[1] (analytic) = 1.9949641523120998 " " y1[1] (numeric) = 1.9949641523120996 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113025538166631800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1002314103156527 " " y2[1] (numeric) = 1.1002314103156527 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10050000000000002 " " y1[1] (analytic) = 1.9949541241962643 " " y1[1] (numeric) = 1.9949541241962638 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226062266113408600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1003309062295612 " " y2[1] (numeric) = 1.100330906229561 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.017980260918948400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10060000000000002 " " y1[1] (analytic) = 1.9949440861308871 " " y1[1] (numeric) = 1.994944086130887 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113036733554160800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1004304011401604 " " y2[1] (numeric) = 1.1004304011401602 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.017797806158117800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10070000000000003 " " y1[1] (analytic) = 1.9949340381160696 " " y1[1] (numeric) = 1.9949340381160692 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22608467931822700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1005298950464557 " " y2[1] (numeric) = 1.1005298950464555 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.017615386228634500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10080000000000003 " " y1[1] (analytic) = 1.9949239801519116 " " y1[1] (numeric) = 1.9949239801519112 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226095902743350000000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.100629387947452 " " y2[1] (numeric) = 1.1006293879474518 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01743300112237700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10090000000000003 " " y1[1] (analytic) = 1.9949139122385136 " " y1[1] (numeric) = 1.9949139122385133 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11305356869195800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1007288798421544 " " y2[1] (numeric) = 1.1007288798421542 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.017250650831226600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10100000000000003 " " y1[1] (analytic) = 1.9949038343759766 " " y1[1] (numeric) = 1.9949038343759764 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113059191620075200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.100828370729568 " " y2[1] (numeric) = 1.1008283707295679 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.017068335347066100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10110000000000004 " " y1[1] (analytic) = 1.9948937465644012 " " y1[1] (numeric) = 1.994893746564401 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113064820156139800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.100927860608698 " " y2[1] (numeric) = 1.1009278606086979 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.016886054661781700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10120000000000004 " " y1[1] (analytic) = 1.9948836488038886 " " y1[1] (numeric) = 1.9948836488038881 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226140908600528500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1010273494785492 " " y2[1] (numeric) = 1.1010273494785492 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10130000000000004 " " y1[1] (analytic) = 1.9948735410945393 " " y1[1] (numeric) = 1.9948735410945388 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226152188105124400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.101126837338127 " " y2[1] (numeric) = 1.101126837338127 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10140000000000005 " " y1[1] (analytic) = 1.9948634234364546 " " y1[1] (numeric) = 1.9948634234364542 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22616347882629300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1012263241864366 " " y2[1] (numeric) = 1.1012263241864366 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10150000000000005 " " y1[1] (analytic) = 1.9948532958297358 " " y1[1] (numeric) = 1.9948532958297354 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226174780764261200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1013258100224828 " " y2[1] (numeric) = 1.1013258100224828 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10160000000000005 " " y1[1] (analytic) = 1.9948431582744839 " " y1[1] (numeric) = 1.9948431582744834 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226186093919256300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.101425294845271 " " y2[1] (numeric) = 1.101425294845271 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10170000000000005 " " y1[1] (analytic) = 1.9948330107708006 " " y1[1] (numeric) = 1.9948330107708 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22619741829150480000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.101524778653806 " " y2[1] (numeric) = 1.101524778653806 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10180000000000006 " " y1[1] (analytic) = 1.9948228533187868 " " y1[1] (numeric) = 1.9948228533187866 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113104376940617600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1016242614470935 " " y2[1] (numeric) = 1.1016242614470935 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10190000000000006 " " y1[1] (analytic) = 1.994812685918545 " " y1[1] (numeric) = 1.9948126859185447 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226220100688673400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1017237432241382 " " y2[1] (numeric) = 1.1017237432241382 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10200000000000006 " " y1[1] (analytic) = 1.9948025085701762 " " y1[1] (numeric) = 1.9948025085701757 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226231458714048300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1018232239839456 " " y2[1] (numeric) = 1.1018232239839456 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10210000000000007 " " y1[1] (analytic) = 1.9947923212737821 " " y1[1] (numeric) = 1.9947923212737817 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22624282795758800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1019227037255206 " " y2[1] (numeric) = 1.1019227037255208 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.015065159963713000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10220000000000007 " " y1[1] (analytic) = 1.994782124029465 " " y1[1] (numeric) = 1.9947821240294645 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226254208419520500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1020221824478686 " " y2[1] (numeric) = 1.1020221824478689 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.014883261531218400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10230000000000007 " " y1[1] (analytic) = 1.9947719168373266 " " y1[1] (numeric) = 1.9947719168373261 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226265600100074000000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.102121660149995 " " y2[1] (numeric) = 1.102121660149995 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10240000000000007 " " y1[1] (analytic) = 1.9947616996974689 " " y1[1] (numeric) = 1.9947616996974686 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113138501499739100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1022211368309045 " " y2[1] (numeric) = 1.1022211368309047 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01451956876323200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10250000000000008 " " y1[1] (analytic) = 1.9947514726099944 " " y1[1] (numeric) = 1.9947514726099942 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113144208558980400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1023206124896028 " " y2[1] (numeric) = 1.102320612489603 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.014337774411577300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10260000000000008 " " y1[1] (analytic) = 1.9947412355750052 " " y1[1] (numeric) = 1.994741235575005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113149921227876100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.102420087125095 " " y2[1] (numeric) = 1.102420087125095 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10270000000000008 " " y1[1] (analytic) = 1.9947309885926034 " " y1[1] (numeric) = 1.9947309885926032 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113155639506540500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1025195607363862 " " y2[1] (numeric) = 1.1025195607363865 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01397428973255580000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10280000000000009 " " y1[1] (analytic) = 1.994720731662892 " " y1[1] (numeric) = 1.9947207316628917 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226322726790176400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.102619033322482 " " y2[1] (numeric) = 1.1026190333224821 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.013792599389041500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10290000000000009 " " y1[1] (analytic) = 1.9947104647859732 " " y1[1] (numeric) = 1.9947104647859728 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226334185787269500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1027185048823873 " " y2[1] (numeric) = 1.1027185048823875 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01361094369876310000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10300000000000009 " " y1[1] (analytic) = 1.99470018796195 " " y1[1] (numeric) = 1.9947001879619493 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33951848400688500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1028179754151077 " " y2[1] (numeric) = 1.1028179754151077 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1031000000000001 " " y1[1] (analytic) = 1.9946899011909245 " " y1[1] (numeric) = 1.994689901190924 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226357137442367700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1029174449196482 " " y2[1] (numeric) = 1.1029174449196482 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1032000000000001 " " y1[1] (analytic) = 1.9946796044730002 " " y1[1] (numeric) = 1.9946796044729997 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226368630100833700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1030169133950143 " " y2[1] (numeric) = 1.1030169133950143 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1033000000000001 " " y1[1] (analytic) = 1.9946692978082798 " " y1[1] (numeric) = 1.9946692978082794 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226380133980218300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1031163808402111 " " y2[1] (numeric) = 1.1031163808402111 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1034000000000001 " " y1[1] (analytic) = 1.9946589811968667 " " y1[1] (numeric) = 1.994658981196866 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.339587473621129500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1032158472542444 " " y2[1] (numeric) = 1.1032158472542444 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1035000000000001 " " y1[1] (analytic) = 1.9946486546388633 " " y1[1] (numeric) = 1.9946486546388629 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226403175402668600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.103315312636119 " " y2[1] (numeric) = 1.103315312636119 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10360000000000011 " " y1[1] (analytic) = 1.9946383181343736 " " y1[1] (numeric) = 1.9946383181343732 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226414712946196700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1034147769848406 " " y2[1] (numeric) = 1.1034147769848406 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10370000000000011 " " y1[1] (analytic) = 1.994627971683501 " " y1[1] (numeric) = 1.9946279716835003 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33963939256735340000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1035142402994143 " " y2[1] (numeric) = 1.1035142402994145 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01215894472539320000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10380000000000011 " " y1[1] (analytic) = 1.9946176152863484 " " y1[1] (numeric) = 1.9946176152863477 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33965673254852600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1036137025788457 " " y2[1] (numeric) = 1.103613702578846 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01197760055147300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10390000000000012 " " y1[1] (analytic) = 1.9946072489430198 " " y1[1] (numeric) = 1.994607248943019 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33967408936316100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.10371316382214 " " y2[1] (numeric) = 1.1037131638221402 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.011796290950219300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10400000000000012 " " y1[1] (analytic) = 1.9945968726536185 " " y1[1] (numeric) = 1.9945968726536178 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33969146301160760000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1038126240283028 " " y2[1] (numeric) = 1.103812624028303 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.011615015913587600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10410000000000012 " " y1[1] (analytic) = 1.9945864864182488 " " y1[1] (numeric) = 1.9945864864182479 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.45294513799228300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1039120831963394 " " y2[1] (numeric) = 1.1039120831963396 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.011433775433536500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10420000000000013 " " y1[1] (analytic) = 1.9945760902370138 " " y1[1] (numeric) = 1.994576090237013 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33972626081132760000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.104011541325255 " " y2[1] (numeric) = 1.1040115413252551 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.011252569502027500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10430000000000013 " " y1[1] (analytic) = 1.9945656841100181 " " y1[1] (numeric) = 1.9945656841100174 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33974368496330100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1041109984140551 " " y2[1] (numeric) = 1.1041109984140554 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.011071398111024500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10440000000000013 " " y1[1] (analytic) = 1.9945552680373657 " " y1[1] (numeric) = 1.994555268037365 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33976112595048300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1042104544617455 " " y2[1] (numeric) = 1.1042104544617457 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01089026125249300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10450000000000013 " " y1[1] (analytic) = 1.9945448420191605 " " y1[1] (numeric) = 1.9945448420191598 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.339778583773223600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1043099094673312 " " y2[1] (numeric) = 1.1043099094673314 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.01070915891840100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10460000000000014 " " y1[1] (analytic) = 1.994534406055507 " " y1[1] (numeric) = 1.9945344060555064 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33979605843187300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1044093634298178 " " y2[1] (numeric) = 1.104409363429818 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.010528091100720300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10470000000000014 " " y1[1] (analytic) = 1.9945239601465095 " " y1[1] (numeric) = 1.9945239601465088 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33981354992678300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1045088163482106 " " y2[1] (numeric) = 1.104508816348211 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.020694115582847400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10480000000000014 " " y1[1] (analytic) = 1.9945135042922724 " " y1[1] (numeric) = 1.9945135042922717 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.339831058258304600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1046082682215155 " " y2[1] (numeric) = 1.104608268221516 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.02033211796497260000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10490000000000015 " " y1[1] (analytic) = 1.9945030384929 " " y1[1] (numeric) = 1.9945030384928994 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226565722284526100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1047077190487378 " " y2[1] (numeric) = 1.104707719048738 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00998509466588680000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10500000000000015 " " y1[1] (analytic) = 1.9944925627484973 " " y1[1] (numeric) = 1.9944925627484968 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226577416955059800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1048071688288825 " " y2[1] (numeric) = 1.104807168828883 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01960832966721200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10510000000000015 " " y1[1] (analytic) = 1.9944820770591694 " " y1[1] (numeric) = 1.9944820770591687 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.33988368427605600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1049066175609559 " " y2[1] (numeric) = 1.1049066175609563 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01924653895525230000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10520000000000015 " " y1[1] (analytic) = 1.9944715814250202 " " y1[1] (numeric) = 1.9944715814250198 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226600839971695500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.105006065243963 " " y2[1] (numeric) = 1.1050060652439635 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01888481717986470000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10530000000000016 " " y1[1] (analytic) = 1.9944610758461554 " " y1[1] (numeric) = 1.994461075846155 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22661256831826910000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1051055118769093 " " y2[1] (numeric) = 1.10510551187691 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.0277847464875400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10540000000000016 " " y1[1] (analytic) = 1.9944505603226799 " " y1[1] (numeric) = 1.9944505603226794 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.2266243078906600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1052049574588008 " " y2[1] (numeric) = 1.1052049574588012 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.018161580374716000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10550000000000016 " " y1[1] (analytic) = 1.9944400348546987 " " y1[1] (numeric) = 1.9944400348546982 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226636058689104300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1053044019886424 " " y2[1] (numeric) = 1.1053044019886429 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01780006531292100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10560000000000017 " " y1[1] (analytic) = 1.994429499442317 " " y1[1] (numeric) = 1.9944294994423168 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11332391035691900000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1054038454654402 " " y2[1] (numeric) = 1.1054038454654407 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01743861912362800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10570000000000017 " " y1[1] (analytic) = 1.9944189540856407 " " y1[1] (numeric) = 1.9944189540856403 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22665959396509700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1055032878881994 " " y2[1] (numeric) = 1.1055032878881998 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.017077241790833500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10580000000000017 " " y1[1] (analytic) = 1.9944083987847747 " " y1[1] (numeric) = 1.9944083987847743 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22667137844311800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1056027292559258 " " y2[1] (numeric) = 1.1056027292559263 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01671593329853700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10590000000000017 " " y1[1] (analytic) = 1.994397833539825 " " y1[1] (numeric) = 1.9943978335398242 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34002476122220600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.105702169567625 " " y2[1] (numeric) = 1.1057021695676255 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01635469363074260000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10600000000000018 " " y1[1] (analytic) = 1.9943872583508964 " " y1[1] (numeric) = 1.994387258350896 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22669498108039300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1058016088223024 " " y2[1] (numeric) = 1.1058016088223028 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.0159935227714600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10610000000000018 " " y1[1] (analytic) = 1.9943766732180954 " " y1[1] (numeric) = 1.994376673218095 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22670679924012100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1059010470189636 " " y2[1] (numeric) = 1.105901047018964 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01563242070470300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10620000000000018 " " y1[1] (analytic) = 1.994366078141528 " " y1[1] (numeric) = 1.9943660781415273 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.340077942941338500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1060004841566144 " " y2[1] (numeric) = 1.106000484156615 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01527138741448900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10630000000000019 " " y1[1] (analytic) = 1.9943554731212996 " " y1[1] (numeric) = 1.994355473121299 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34009570386441700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1060999202342605 " " y2[1] (numeric) = 1.106099920234261 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01491042288484300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10640000000000019 " " y1[1] (analytic) = 1.9943448581575165 " " y1[1] (numeric) = 1.9943448581575158 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34011348162977340000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1061993552509073 " " y2[1] (numeric) = 1.1061993552509077 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01454952709979330000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10650000000000019 " " y1[1] (analytic) = 1.9943342332502847 " " y1[1] (numeric) = 1.9943342332502842 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226754184158510600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1062987892055607 " " y2[1] (numeric) = 1.106298789205561 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00709435002168620000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1066000000000002 " " y1[1] (analytic) = 1.9943235983997107 " " y1[1] (numeric) = 1.9943235983997103 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226766058459166700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.106398222097226 " " y2[1] (numeric) = 1.1063982220972262 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.006913970849809600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1067000000000002 " " y1[1] (analytic) = 1.9943129536059008 " " y1[1] (numeric) = 1.9943129536059003 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226777943988723600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1064976539249092 " " y2[1] (numeric) = 1.1064976539249094 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.006733626026287500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1068000000000002 " " y1[1] (analytic) = 1.9943022988689614 " " y1[1] (numeric) = 1.994302298868961 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22678984074741900000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1065970846876156 " " y2[1] (numeric) = 1.106597084687616 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01310663108628900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1069000000000002 " " y1[1] (analytic) = 1.9942916341889987 " " y1[1] (numeric) = 1.9942916341889985 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113400874367746500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1066965143843515 " " y2[1] (numeric) = 1.106696514384352 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.012746078784812400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1070000000000002 " " y1[1] (analytic) = 1.9942809595661202 " " y1[1] (numeric) = 1.9942809595661197 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226813667953183300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.106795943014122 " " y2[1] (numeric) = 1.1067959430141225 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01238559513220300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10710000000000021 " " y1[1] (analytic) = 1.9942702750004315 " " y1[1] (numeric) = 1.9942702750004313 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113412799200365500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1068953705759332 " " y2[1] (numeric) = 1.1068953705759337 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01202518011252300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10720000000000021 " " y1[1] (analytic) = 1.9942595804920404 " " y1[1] (numeric) = 1.9942595804920402 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113418770039187200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1069947970687908 " " y2[1] (numeric) = 1.1069947970687912 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01166483370983760000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10730000000000021 " " y1[1] (analytic) = 1.9942488760410535 " " y1[1] (numeric) = 1.9942488760410533 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11342474649317710000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1070942224917002 " " y2[1] (numeric) = 1.1070942224917006 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.01130455590822050000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10740000000000022 " " y1[1] (analytic) = 1.9942381616475777 " " y1[1] (numeric) = 1.9942381616475775 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113430728562454800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1071936468436676 " " y2[1] (numeric) = 1.1071936468436678 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00547217334587300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10750000000000022 " " y1[1] (analytic) = 1.9942274373117206 " " y1[1] (numeric) = 1.9942274373117201 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226873432494281500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1072930701236983 " " y2[1] (numeric) = 1.1072930701236987 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.010584206044497400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10760000000000022 " " y1[1] (analytic) = 1.9942167030335889 " " y1[1] (numeric) = 1.9942167030335884 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22688541909471100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1073924923307985 " " y2[1] (numeric) = 1.1073924923307987 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00511206697527900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10770000000000023 " " y1[1] (analytic) = 1.99420595881329 " " y1[1] (numeric) = 1.9942059588132897 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22689741692643800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1074919134639738 " " y2[1] (numeric) = 1.107491913463974 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.0049320651970098000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10780000000000023 " " y1[1] (analytic) = 1.994195204650932 " " y1[1] (numeric) = 1.9941952046509315 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226909425989703800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1075913335222298 " " y2[1] (numeric) = 1.10759133352223 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00475209767948910000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10790000000000023 " " y1[1] (analytic) = 1.9941844405466216 " " y1[1] (numeric) = 1.9941844405466211 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226921446284749200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1076907525045725 " " y2[1] (numeric) = 1.1076907525045727 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00457216441476700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10800000000000023 " " y1[1] (analytic) = 1.9941736665004668 " " y1[1] (numeric) = 1.9941736665004663 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226933477811816600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1077901704100077 " " y2[1] (numeric) = 1.107790170410008 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00439226539489600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10810000000000024 " " y1[1] (analytic) = 1.9941628825125755 " " y1[1] (numeric) = 1.994162882512575 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22694552057114700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1078895872375412 " " y2[1] (numeric) = 1.1078895872375414 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.004212400611930200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10820000000000024 " " y1[1] (analytic) = 1.9941520885830553 " " y1[1] (numeric) = 1.9941520885830548 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.226957574562982200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1079890029861788 " " y2[1] (numeric) = 1.107989002986179 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00403257005792800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10830000000000024 " " y1[1] (analytic) = 1.9941412847120144 " " y1[1] (numeric) = 1.9941412847120137 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34045445968134740000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1080884176549264 " " y2[1] (numeric) = 1.1080884176549266 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00385277372494800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10840000000000025 " " y1[1] (analytic) = 1.9941304708995604 " " y1[1] (numeric) = 1.9941304708995597 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34047257436770550000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1081878312427897 " " y2[1] (numeric) = 1.10818783124279 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.003673011605053300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10850000000000025 " " y1[1] (analytic) = 1.9941196471458018 " " y1[1] (numeric) = 1.9941196471458011 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34049070590391240000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.108287243748775 " " y2[1] (numeric) = 1.1082872437487752 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.003493283690307400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10860000000000025 " " y1[1] (analytic) = 1.9941088134508467 " " y1[1] (numeric) = 1.994108813450846 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34050885429033100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1083866551718877 " " y2[1] (numeric) = 1.108386655171888 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.00331358997277720000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10870000000000025 " " y1[1] (analytic) = 1.9940979698148036 " " y1[1] (numeric) = 1.994097969814803 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34052701952732730000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1084860655111337 " " y2[1] (numeric) = 1.1084860655111342 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.00626786088906560000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10880000000000026 " " y1[1] (analytic) = 1.9940871162377807 " " y1[1] (numeric) = 1.99408711623778 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34054520161526540000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1085854747655193 " " y2[1] (numeric) = 1.1085854747655197 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.00590861019528900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10890000000000026 " " y1[1] (analytic) = 1.9940762527198865 " " y1[1] (numeric) = 1.994076252719886 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227042267036340500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1086848829340499 " " y2[1] (numeric) = 1.1086848829340505 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00832414177256300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10900000000000026 " " y1[1] (analytic) = 1.99406537926123 " " y1[1] (numeric) = 1.9940653792612295 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22705441089695200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1087842900157319 " " y2[1] (numeric) = 1.1087842900157325 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00778547074871100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10910000000000027 " " y1[1] (analytic) = 1.9940544958619197 " " y1[1] (numeric) = 1.994054495861919 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34059984898838500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.108883696009571 " " y2[1] (numeric) = 1.1088836960095716 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00724690219761700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10920000000000027 " " y1[1] (analytic) = 1.9940436025220645 " " y1[1] (numeric) = 1.9940436025220638 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34061809848374700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.108983100914573 " " y2[1] (numeric) = 1.1089831009145736 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00670843609552500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10930000000000027 " " y1[1] (analytic) = 1.9940326992417732 " " y1[1] (numeric) = 1.9940326992417725 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.3406363648318800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.109082504729744 " " y2[1] (numeric) = 1.1090825047297446 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00617007241868200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10940000000000027 " " y1[1] (analytic) = 1.9940217860211549 " " y1[1] (numeric) = 1.9940217860211542 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.340654648033153000000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1091819074540898 " " y2[1] (numeric) = 1.1091819074540905 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00563181114334800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10950000000000028 " " y1[1] (analytic) = 1.9940108628603186 " " y1[1] (numeric) = 1.9940108628603181 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227115298725287400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.109281309086617 " " y2[1] (numeric) = 1.1092813090866174 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.00339576816385700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10960000000000028 " " y1[1] (analytic) = 1.993999929759374 " " y1[1] (numeric) = 1.9939999297593733 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.340691264996582500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1093807096263306 " " y2[1] (numeric) = 1.1093807096263313 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.0045555957022700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10970000000000028 " " y1[1] (analytic) = 1.99398898671843 " " y1[1] (numeric) = 1.9939889867184293 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34070959875947600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1094801090722375 " " y2[1] (numeric) = 1.109480109072238 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.00267842765938500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10980000000000029 " " y1[1] (analytic) = 1.993978033737596 " " y1[1] (numeric) = 1.9939780337375954 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.340727949376978700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.109579507423343 " " y2[1] (numeric) = 1.1095795074233437 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00347978958249500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10990000000000029 " " y1[1] (analytic) = 1.9939670708169817 " " y1[1] (numeric) = 1.9939670708169812 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22716421123297400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1096789046786535 " " y2[1] (numeric) = 1.1096789046786542 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00294203995881500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11000000000000029 " " y1[1] (analytic) = 1.9939560979566968 " " y1[1] (numeric) = 1.9939560979566964 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227176467451526500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.109778300837175 " " y2[1] (numeric) = 1.1097783008371758 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00240439259433600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1101000000000003 " " y1[1] (analytic) = 1.9939451151568508 " " y1[1] (numeric) = 1.9939451151568504 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227188734907224200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1098776958979135 " " y2[1] (numeric) = 1.1098776958979142 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.0018668474653700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1102000000000003 " " y1[1] (analytic) = 1.9939341224175537 " " y1[1] (numeric) = 1.9939341224175533 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22720101360031300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.109977089859875 " " y2[1] (numeric) = 1.1099770898598758 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00132940454822800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1103000000000003 " " y1[1] (analytic) = 1.9939231197389156 " " y1[1] (numeric) = 1.9939231197389151 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227213303531039300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1100764827220657 " " y2[1] (numeric) = 1.1100764827220664 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.00079206381923100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1104000000000003 " " y1[1] (analytic) = 1.9939121071210462 " " y1[1] (numeric) = 1.9939121071210457 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227225604699650500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1101758744834918 " " y2[1] (numeric) = 1.1101758744834922 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.000169883503140000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1105000000000003 " " y1[1] (analytic) = 1.9939010845640555 " " y1[1] (numeric) = 1.9939010845640552 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113618958553196800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1102752651431587 " " y2[1] (numeric) = 1.1102752651431593 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99971768883100100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11060000000000031 " " y1[1] (analytic) = 1.9938900520680543 " " y1[1] (numeric) = 1.9938900520680538 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22725024075151600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1103746547000732 " " y2[1] (numeric) = 1.1103746547000737 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.99945376968296300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11070000000000031 " " y1[1] (analytic) = 1.9938790096331522 " " y1[1] (numeric) = 1.993879009633152 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113631287817632600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.110474043153241 " " y2[1] (numeric) = 1.1104740431532416 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99864372231139300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11080000000000031 " " y1[1] (analytic) = 1.9938679572594604 " " y1[1] (numeric) = 1.99386795725946 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227274921757888800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1105734305016686 " " y2[1] (numeric) = 1.110573430501669 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.99873792811213300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11090000000000032 " " y1[1] (analytic) = 1.993856894947089 " " y1[1] (numeric) = 1.9938568949470885 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227287279119635200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1106728167443616 " " y2[1] (numeric) = 1.1106728167443622 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99757016407123300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11100000000000032 " " y1[1] (analytic) = 1.9938458226961484 " " y1[1] (numeric) = 1.993845822696148 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22729964772075300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1107722018803265 " " y2[1] (numeric) = 1.1107722018803272 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99703353799686200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11110000000000032 " " y1[1] (analytic) = 1.9938347405067498 " " y1[1] (numeric) = 1.9938347405067494 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.2273120275614902000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1108715859085696 " " y2[1] (numeric) = 1.1108715859085703 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99649701392146500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11120000000000033 " " y1[1] (analytic) = 1.9938236483790037 " " y1[1] (numeric) = 1.9938236483790033 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227324418642095400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1109709688280966 " " y2[1] (numeric) = 1.1109709688280973 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99596059182142800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11130000000000033 " " y1[1] (analytic) = 1.9938125463130212 " " y1[1] (numeric) = 1.9938125463130207 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227336820962818300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.111070350637914 " " y2[1] (numeric) = 1.1110703506379147 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99542427167314300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11140000000000033 " " y1[1] (analytic) = 1.9938014343089132 " " y1[1] (numeric) = 1.9938014343089128 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227349234523907400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1111697313370281 " " y2[1] (numeric) = 1.1111697313370286 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.996592035635339600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11150000000000033 " " y1[1] (analytic) = 1.9937903123667908 " " y1[1] (numeric) = 1.9937903123667904 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227361659325612400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1112691109244446 " " y2[1] (numeric) = 1.1112691109244452 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99435193713743400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11160000000000034 " " y1[1] (analytic) = 1.9937791804867655 " " y1[1] (numeric) = 1.9937791804867648 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34106114305227400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1113684893991702 " " y2[1] (numeric) = 1.1113684893991707 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.99587728180188800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11170000000000034 " " y1[1] (analytic) = 1.9937680386689483 " " y1[1] (numeric) = 1.9937680386689476 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34107981397780300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1114678667602107 " " y2[1] (numeric) = 1.1114678667602114 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99328001012562200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11180000000000034 " " y1[1] (analytic) = 1.9937568869134505 " " y1[1] (numeric) = 1.9937568869134499 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34109850176538100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1115672430065726 " " y2[1] (numeric) = 1.1115672430065733 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99274419938223300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11190000000000035 " " y1[1] (analytic) = 1.9937457252203838 " " y1[1] (numeric) = 1.9937457252203834 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22741147094358800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1116666181372623 " " y2[1] (numeric) = 1.1116666181372628 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.99480566029939900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11200000000000035 " " y1[1] (analytic) = 1.99373455358986 " " y1[1] (numeric) = 1.9937345535898596 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22742395195212220000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1117659921512855 " " y2[1] (numeric) = 1.1117659921512861 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99167288330266300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11210000000000035 " " y1[1] (analytic) = 1.9937233720219911 " " y1[1] (numeric) = 1.9937233720219905 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34115466630415900000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1118653650476489 " " y2[1] (numeric) = 1.1118653650476495 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99113737791937400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11220000000000036 " " y1[1] (analytic) = 1.993712180516888 " " y1[1] (numeric) = 1.9937121805168876 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227448947695792300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1119647368253587 " " y2[1] (numeric) = 1.1119647368253593 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99060197427568800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11230000000000036 " " y1[1] (analytic) = 1.9937009790746631 " " y1[1] (numeric) = 1.9937009790746627 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227461462431431800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.112064107483421 " " y2[1] (numeric) = 1.1120641074834217 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.99006667234806800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11240000000000036 " " y1[1] (analytic) = 1.9936897676954286 " " y1[1] (numeric) = 1.9936897676954282 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227473988409941500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1121634770208424 " " y2[1] (numeric) = 1.112163477020843 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98953147211298200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11250000000000036 " " y1[1] (analytic) = 1.9936785463792965 " " y1[1] (numeric) = 1.9936785463792959 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.34122978844736100000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.112262845436629 " " y2[1] (numeric) = 1.1122628454366297 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.9889963735469110000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11260000000000037 " " y1[1] (analytic) = 1.9936673151263786 " " y1[1] (numeric) = 1.9936673151263782 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227499074096581700000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.112362212729787 " " y2[1] (numeric) = 1.1123622127297879 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.98461516883511600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11270000000000037 " " y1[1] (analytic) = 1.993656073936788 " " y1[1] (numeric) = 1.9936560739367875 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227511633805215600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.112461578899323 " " y2[1] (numeric) = 1.1124615788993237 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98792648132775200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11280000000000037 " " y1[1] (analytic) = 1.9936448228106363 " " y1[1] (numeric) = 1.9936448228106358 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22752420475772900000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1125609439442432 " " y2[1] (numeric) = 1.1125609439442439 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98739168762765600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11290000000000038 " " y1[1] (analytic) = 1.9936335617480365 " " y1[1] (numeric) = 1.993633561748036 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227536786954374000000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.112660307863554 " " y2[1] (numeric) = 1.1126603078635546 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98685699550255100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11300000000000038 " " y1[1] (analytic) = 1.9936222907491012 " " y1[1] (numeric) = 1.9936222907491008 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.22754938039540400000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1127596706562617 " " y2[1] (numeric) = 1.1127596706562624 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.9863224049289500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11310000000000038 " " y1[1] (analytic) = 1.993611009813943 " " y1[1] (numeric) = 1.9936110098139426 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.227561985081071600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1128590323213725 " " y2[1] (numeric) = 1.1128590323213734 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.98105055451116900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11320000000000038 " " y1[1] (analytic) = 1.9935997189426744 " " y1[1] (numeric) = 1.9935997189426742 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113787300505815000000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1129583928578932 " " y2[1] (numeric) = 1.112958392857894 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.98033803778980400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11330000000000039 " " y1[1] (analytic) = 1.9935884181354089 " " y1[1] (numeric) = 1.9935884181354087 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113793614093666800000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.11305775226483 " " y2[1] (numeric) = 1.1130577522648308 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.97962565637655100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11340000000000039 " " y1[1] (analytic) = 1.9935771073922592 " " y1[1] (numeric) = 1.993577107392259 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113799933304217600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.113157110541189 " " y2[1] (numeric) = 1.11315711054119 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.97891341024013400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11350000000000039 " " y1[1] (analytic) = 1.9935657867133385 " " y1[1] (numeric) = 1.9935657867133383 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113806258137594500000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.113256467685977 " " y2[1] (numeric) = 1.113256467685978 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.9782012993492800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1136000000000004 " " y1[1] (analytic) = 1.9935544560987597 " " y1[1] (numeric) = 1.9935544560987597 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1133558236982006 " " y2[1] (numeric) = 1.1133558236982013 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98311699275454600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1137000000000004 " " y1[1] (analytic) = 1.9935431155486367 " " y1[1] (numeric) = 1.9935431155486365 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113818924673335200000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1134551785768658 " " y2[1] (numeric) = 1.1134551785768665 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98258311238442300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1138000000000004 " " y1[1] (analytic) = 1.9935317650630822 " " y1[1] (numeric) = 1.9935317650630822 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.113554532320979 " " y2[1] (numeric) = 1.11355453232098 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.97606577783754400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1139000000000004 " " y1[1] (analytic) = 1.9935204046422101 " " y1[1] (numeric) = 1.9935204046422101 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1136538849295472 " " y2[1] (numeric) = 1.1136538849295479 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98151565571232500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1140000000000004 " " y1[1] (analytic) = 1.9935090342861344 " " y1[1] (numeric) = 1.9935090342861341 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113837966651324300000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1137532364015763 " " y2[1] (numeric) = 1.113753236401577 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.9809820793635090000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11410000000000041 " " y1[1] (analytic) = 1.993497653994968 " " y1[1] (numeric) = 1.9934976539949678 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113844325224331600000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1138525867360731 " " y2[1] (numeric) = 1.1138525867360738 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98044860430830000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11420000000000041 " " y1[1] (analytic) = 1.9934862637688249 " " y1[1] (numeric) = 1.9934862637688249 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1139519359320442 " " y2[1] (numeric) = 1.1139519359320447 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.986610153682195000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11430000000000042 " " y1[1] (analytic) = 1.9934748636078194 " " y1[1] (numeric) = 1.9934748636078194 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1140512839884957 " " y2[1] (numeric) = 1.1140512839884964 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.97938195798509400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11440000000000042 " " y1[1] (analytic) = 1.9934634535120654 " " y1[1] (numeric) = 1.9934634535120652 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113863434686174900000000000000E-14 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1141506309044347 " " y2[1] (numeric) = 1.1141506309044351 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.9858991911135400000000000000E-14 "%" h = 1.0000E-4 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;" "diff ( y2 , x , 1 ) = y1 - 1.0;" Iterations = 144 "Total Elapsed Time "= 15 Minutes 9 Seconds "Elapsed Time(since restart) "= 15 Minutes 9 Seconds "Expected Time Remaining "= 7 Days 4 Hours 17 Minutes 39 Seconds "Optimized Time Remaining "= 7 Days 4 Hours 10 Minutes 6 Seconds "Time to Timeout " Unknown Percent Done = 0.14646464646465066 "%" (%o52) true (%o52) diffeq.max