(%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_y2_higher , 1 6, 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp2 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_tmp4 : array_y1 - array_const_2D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 2 6, 2 2 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(1, 2), array_y1 : temporary, 2 3 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 3 glob_h array_y1_higher : temporary)), kkk : 3, 2, 2 array_tmp4 : array_y1 - array_const_2D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 3 6, 3 3 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(2, 3), array_y1 : temporary, 3 4 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 4 glob_h array_y1_higher : temporary)), kkk : 4, 2, 3 array_tmp4 : array_y1 - array_const_2D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 4 6, 4 4 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(3, 4), array_y1 : temporary, 4 5 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 5 glob_h array_y1_higher : temporary)), kkk : 5, 2, 4 array_tmp4 : array_y1 - array_const_2D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 5 6, 5 5 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(4, 5), array_y1 : temporary, 5 6 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 6 glob_h array_y1_higher : temporary)), kkk : 6, 2, 5 array_tmp4 : array_y1 - array_const_2D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp4 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 : array_y2_higher , kkk 6, kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 1, order_d + kkk order_d array_tmp2 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_tmp4 : kkk array_y1 - array_const_2D0 , 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_tmp4 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_y2_higher , 1 6, 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp2 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_tmp4 : array_y1 - array_const_2D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 2 6, 2 2 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(1, 2), array_y1 : temporary, 2 3 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 3 glob_h array_y1_higher : temporary)), kkk : 3, 2, 2 array_tmp4 : array_y1 - array_const_2D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 3 6, 3 3 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(2, 3), array_y1 : temporary, 3 4 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 4 glob_h array_y1_higher : temporary)), kkk : 4, 2, 3 array_tmp4 : array_y1 - array_const_2D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 4 6, 4 4 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(3, 4), array_y1 : temporary, 4 5 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 5 glob_h array_y1_higher : temporary)), kkk : 5, 2, 4 array_tmp4 : array_y1 - array_const_2D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp4 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 : array_y2_higher , array_tmp2 : 5 6, 5 5 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(4, 5), array_y1 : temporary, 5 6 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 6 glob_h array_y1_higher : temporary)), kkk : 6, 2, 5 array_tmp4 : array_y1 - array_const_2D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp4 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 : array_y2_higher , kkk 6, kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 1, order_d + kkk order_d array_tmp2 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_tmp4 : kkk array_y1 - array_const_2D0 , 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_tmp4 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) factorial_1(nnn) := (if nnn <= glob_max_terms then (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret) nnn nnn else ret : array_fact_1 ) else ret : nnn!, ret) nnn (%o39) factorial_1(nnn) := (if nnn <= glob_max_terms then (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret) nnn nnn else ret : array_fact_1 ) else ret : nnn!, ret) nnn (%i40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then (if array_fact_2 = 0 mmm, nnn factorial_1(mmm) then (ret : ----------------, array_fact_2 : ret) factorial_1(nnn) mmm, nnn mmm! else ret : array_fact_2 ) else ret : ----, ret) mmm, nnn nnn! (%o40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then (if array_fact_2 = 0 mmm, nnn factorial_1(mmm) then (ret : ----------------, array_fact_2 : ret) factorial_1(nnn) mmm, nnn mmm! else ret : array_fact_2 ) else ret : ----, ret) mmm, nnn nnn! (%i41) convfp(mmm) := mmm (%o41) convfp(mmm) := mmm (%i42) convfloat(mmm) := mmm (%o42) convfloat(mmm) := mmm (%i43) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o43) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i44) arcsin(x) := asin(x) (%o44) arcsin(x) := asin(x) (%i45) arccos(x) := acos(x) (%o45) arccos(x) := acos(x) (%i46) arctan(x) := atan(x) (%o46) arctan(x) := atan(x) (%i47) exact_soln_y1(x) := sin(x) + 2.0 (%o47) exact_soln_y1(x) := sin(x) + 2.0 (%i48) exact_soln_y2(x) := 2.0 - cos(x) (%o48) exact_soln_y2(x) := 2.0 - cos(x) (%i49) exact_soln_y2p(x) := sin(x) (%o49) exact_soln_y2p(x) := sin(x) (%i50) exact_soln_y2pp(x) := cos(x) (%o50) exact_soln_y2pp(x) := cos(x) (%i51) exact_soln_y2ppp(x) := - sin(x) (%o51) exact_soln_y2ppp(x) := - sin(x) (%i52) exact_soln_y2pppp(x) := - cos(x) (%o52) exact_soln_y2pppp(x) := - cos(x) (%i53) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(hours_in_day, 24.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_look_poles, false, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_start, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), define_variable(years_in_century, 100.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(min_in_hour, 60.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_hours, 0.0, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_almost_1, 0.999, float), define_variable(days_in_year, 365.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), 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/mtest9postode.ode#################"), omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"), omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.5,"), 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, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"), omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "glob_subiter_method : 3,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.001 ,"), 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, "2.0 + sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2p (x) := ("), omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("), omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("), omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("), omniout_str(ALWAYS, "-cos(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_last_rel_error, 1 + max_terms), array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_m1, 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_y1, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2_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), term : 1, term while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term 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 <= 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 <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 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 <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 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_y1_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 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_y1_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), 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_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_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 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_const_2D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_5, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term), term array_const_5 : 5, 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_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.5, iiif, jjjf x_end : 10.0, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 10, glob_subiter_method : 3, glob_h : 0.001, 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 : true, 2, 1 2, 2 array_y2_set_initial : true, array_y2_set_initial : true, 2, 3 2, 4 array_y2_set_initial : true, 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 : 5, 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 factorial_1(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 factorial_1(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 factorial_1(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 : 5, ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 6, iii array_y2_higher 6, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 6, 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 : 5, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, 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 : 5, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, 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 : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, 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 : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 5, 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 : 5, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, 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 : 4, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, 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 : 3, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, 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 : 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 : 2, ord, calc_term factorial_1(calc_term - 1)! 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 factorial_1(calc_term - 1)! calc_term : 6, 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 : 6, 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 factorial_1(calc_term - 1)! calc_term : 5, 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 : 5, 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 factorial_1(calc_term - 1)! calc_term : 4, 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 : 4, 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 factorial_1(calc_term - 1)! calc_term : 3, 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 : 3, 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 factorial_1(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 factorial_1(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 factorial_1(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) = diff(y2,x,5);"), omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-17T23:50:46-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest9"), logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"), 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, " 092 "), logitem_str(html_log_file, "mtest9 diffeq.max"), logitem_str(html_log_file, "\ mtest9 maxima results"), logitem_str(html_log_file, "Mostly affecting speed of factorials"), 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 - 2.0;"), 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)) (%o53) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(hours_in_day, 24.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_look_poles, false, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_start, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), define_variable(years_in_century, 100.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(min_in_hour, 60.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_hours, 0.0, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_almost_1, 0.999, float), define_variable(days_in_year, 365.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), 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/mtest9postode.ode#################"), omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"), omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.5,"), 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, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"), omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "glob_subiter_method : 3,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.001 ,"), 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, "2.0 + sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2p (x) := ("), omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("), omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("), omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("), omniout_str(ALWAYS, "-cos(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_last_rel_error, 1 + max_terms), array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_m1, 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_y1, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2_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), term : 1, term while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term 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 <= 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 <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 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 <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 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_y1_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 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_y1_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), 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_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_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 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_const_2D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_5, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term), term array_const_5 : 5, 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_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.5, iiif, jjjf x_end : 10.0, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 10, glob_subiter_method : 3, glob_h : 0.001, 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 : true, 2, 1 2, 2 array_y2_set_initial : true, array_y2_set_initial : true, 2, 3 2, 4 array_y2_set_initial : true, 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 : 5, 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 factorial_1(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 factorial_1(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 factorial_1(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 : 5, ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 6, iii array_y2_higher 6, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 6, 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 : 5, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, 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 : 5, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, 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 : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, 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 : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 5, 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 : 5, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, 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 : 4, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, 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 : 3, 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 : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, 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 : 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 : 2, ord, calc_term factorial_1(calc_term - 1)! 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 factorial_1(calc_term - 1)! calc_term : 6, 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 : 6, 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 factorial_1(calc_term - 1)! calc_term : 5, 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 : 5, 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 factorial_1(calc_term - 1)! calc_term : 4, 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 : 4, 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 factorial_1(calc_term - 1)! calc_term : 3, 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 : 3, 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 factorial_1(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 factorial_1(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 factorial_1(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) = diff(y2,x,5);"), omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-17T23:50:46-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest9"), logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"), 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, " 092 "), logitem_str(html_log_file, "mtest9 diffeq.max"), logitem_str(html_log_file, "\ mtest9 maxima results"), logitem_str(html_log_file, "Mostly affecting speed of factorials"), 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 - 2.0;"), 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)) (%i54) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/mtest9postode.ode#################" "diff(y1,x,1) = diff(y2,x,5);" "diff(y2,x,1) = y1 - 2.0;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.5," "x_end : 10.0," "array_y1_init[0 + 1] : exact_soln_y1(x_start)," "array_y2_init[0 + 1] : exact_soln_y2(x_start)," "array_y2_init[1 + 1] : exact_soln_y2p(x_start)," "array_y2_init[2 + 1] : exact_soln_y2pp(x_start)," "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start)," "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 10," "glob_subiter_method : 3," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.001 ," "glob_look_poles : true," "glob_max_iter : 1000," "glob_max_minutes : 15," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y1 (x) := (" "2.0 + sin(x) " ");" "exact_soln_y2 (x) := (" "2.0 - cos(x) " ");" "exact_soln_y2p (x) := (" "sin(x) " ");" "exact_soln_y2pp (x) := (" "cos(x) " ");" "exact_soln_y2ppp (x) := (" "-sin(x) " ");" "exact_soln_y2pppp (x) := (" "-cos(x) " ");" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.5 " " y1[1] (analytic) = 2.479425538604203 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1224174381096272 " " y2[1] (numeric) = 1.1224174381096272 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " x[1] = 0.5 " " y1[1] (analytic) = 2.479425538604203 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1224174381096272 " " y2[1] (numeric) = 1.1224174381096272 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.501 " " y1[1] (analytic) = 2.48030288130708 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.7734270287720410000E-4 " " relative error = 3.537240187435731000E-2 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1228973023595716 " " y2[1] (numeric) = 1.1228973023595716 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.502 " " y1[1] (analytic) = 2.4811797437071164 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.7542051029133532000E-3 " " relative error = 7.07004443093028700E-2 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1233780437121403 " " y2[1] (numeric) = 1.1233780437915604 " " absolute error = 7.9420026111165500000000000E-11 " " relative error = 7.069750611176843000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.503 " " y1[1] (analytic) = 2.482056124927449 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.630586323245865000E-3 " " relative error = 0.1059841595371965 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1238596616865926 " " y2[1] (numeric) = 1.1238596623229056 " " absolute error = 6.3631300228905730000000000E-10 " " relative error = 5.661854624572370000000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.504 " " y1[1] (analytic) = 2.4829320240916966 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.506485487493549000E-3 " " relative error = 0.14122357976257074 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.12434215580131 " " y2[1] (numeric) = 1.124342157952918 " " absolute error = 2.15160800287605980000000E-9 " " relative error = 1.91365946013349030000000E-7 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.505 " " y1[1] (analytic) = 2.48380744032396 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.381901719757053000E-3 " " relative error = 0.1764187371620695 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1248255255737987 " " y2[1] (numeric) = 1.124825530681592 " " absolute error = 5.107793299430341000000000E-9 " " relative error = 4.54096496149902160000000E-7 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.506 " " y1[1] (analytic) = 2.484682372748824 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.256834144621081000E-3 " " relative error = 0.21156966388445872 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1253097705206887 " " y2[1] (numeric) = 1.1253097805089274 " " absolute error = 9.988238680591621000000000E-9 " " relative error = 8.8759903648308270000000E-7 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.507 " " y1[1] (analytic) = 2.4855568204913556 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.131281887152618000E-3 " " relative error = 0.24667639205047662 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1257948901577355 " " y2[1] (numeric) = 1.125794907434924 " " absolute error = 1.72771885686984200000000E-8 " " relative error = 1.5346657477080670000000E-6 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.508 " " y1[1] (analytic) = 2.4864307826771066 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.005244072903594000E-3 " " relative error = 0.2817389537528626 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1262808839998193 " " y2[1] (numeric) = 1.1262809114595822 " " absolute error = 2.74597629079664800000000E-8 " " relative error = 2.438091891469134000000E-6 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.509 " " y1[1] (analytic) = 2.487304258432116 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.878719827913105000E-3 " " relative error = 0.31675738105636875 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.126767751560946 " " y2[1] (numeric) = 1.1267677925829018 " " absolute error = 4.102195583222112400000000E-8 " " relative error = 3.6406753543835585000000E-6 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.51 " " y1[1] (analytic) = 2.4881772468829073 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.751708278704307000E-3 " " relative error = 0.35173170599755743 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1272554923542488 " " y2[1] (numeric) = 1.1272555508048827 " " absolute error = 5.84506338885404400000000E-8 " " relative error = 5.185216154189459000000E-6 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.511 " " y1[1] (analytic) = 2.4890497471564927 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.624208552289737000E-3 " " relative error = 0.386661960584938 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1277441058919861 " " y2[1] (numeric) = 1.127744186125525 " " absolute error = 8.02335389238351100000000E-8 " " relative error = 7.114516360994377000000E-6 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.512 " " y1[1] (analytic) = 2.4899217583803717 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.049621977616865800E-2 " " relative error = 0.4215481767987831 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1282335916855453 " " y2[1] (numeric) = 1.128233698544829 " " absolute error = 1.06859283643956360000000E-7 " " relative error = 9.471379369613695000000E-6 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.513 " " y1[1] (analytic) = 2.4907932796825327 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.136774107832971800E-2 " " relative error = 0.45639038659115894 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1287239492454397 " " y2[1] (numeric) = 1.128724088062794 " " absolute error = 1.38817354278231160000000E-7 " " relative error = 1.229860980366648400000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.514 " " y1[1] (analytic) = 2.4916643101914553 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.223877158725228400E-2 " " relative error = 0.49118862188590234 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1292151780813124 " " y2[1] (numeric) = 1.1292153546794206 " " absolute error = 1.76598108136971630000000E-7 " " relative error = 1.563901296801867600000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.515 " " y1[1] (analytic) = 2.4925348490361086 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.310931043190555200E-2 " " relative error = 0.5259429145785092 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1297072777019346 " " y2[1] (numeric) = 1.1297074983947086 " " absolute error = 2.2069277405556420000000E-7 " " relative error = 1.953539455853558500000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.516 " " y1[1] (analytic) = 2.4934048953459538 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.39793567417507700E-2 " " relative error = 0.5606532965361476 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1302002476152064 " " y2[1] (numeric) = 1.130200519208658 " " absolute error = 2.7159345150629120000000E-7 " " relative error = 2.403056025508492300000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.517 " " y1[1] (analytic) = 2.494274448250945 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.484890964674212600E-2 " " relative error = 0.5953197995976183 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1306940873281581 " " y2[1] (numeric) = 1.1306944171212687 " " absolute error = 3.29793110598330940000000E-7 " " relative error = 2.916731539453217300000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.518 " " y1[1] (analytic) = 2.495143506881529 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.571796827732585600E-2 " " relative error = 0.6299424555732439 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.13118879634695 " " y2[1] (numeric) = 1.131189192132541 " " absolute error = 3.9578559096753450000000E-7 " " relative error = 3.49884645468272500000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.519 " " y1[1] (analytic) = 2.4960120703686473 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.658653176444424600E-2 " " relative error = 0.6645212962449539 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1316843741768734 " " y2[1] (numeric) = 1.1316848442424745 " " absolute error = 4.70065601110292160000000E-7 " " relative error = 4.15368111318310600000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.52 " " y1[1] (analytic) = 2.496880137843737 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.745459923953385200E-2 " " relative error = 0.699056353366139 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.13218082032235 " " y2[1] (numeric) = 1.1321813734510695 " " absolute error = 5.5312871949375620000000E-7 " " relative error = 4.88551571944375150000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.521 " " y1[1] (analytic) = 2.4977477084387294 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.83221698345263920E-2 " " relative error = 0.733547658661613 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1326781342869343 " " y2[1] (numeric) = 1.1326787797583258 " " absolute error = 6.4547139144721650000000E-7 " " relative error = 5.69863028082171200000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.522 " " y1[1] (analytic) = 2.4986147812860557 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.918924268185273600E-2 " " relative error = 0.7679952438276976 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1331763155733117 " " y2[1] (numeric) = 1.1331770631642435 " " absolute error = 7.475909318266360000000E-7 " " relative error = 6.59730459905001600000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.523 " " y1[1] (analytic) = 2.499481355518642 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.005581691443891800E-2 " " relative error = 0.80239914053199 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1336753636833015 " " y2[1] (numeric) = 1.1336762236688227 " " absolute error = 8.5998552123989210000000E-7 " " relative error = 7.58581820500894200000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.524 " " y1[1] (analytic) = 2.500347430269914 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.092189166571101200E-2 " " relative error = 0.8367593804134844 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1341752781178553 " " y2[1] (numeric) = 1.1341762612720632 " " absolute error = 9.8315420782313370000000E-7 " " relative error = 8.66845034265480900000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.525 " " y1[1] (analytic) = 2.501213004673798 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.17874660695951400E-2 " " relative error = 0.8710759950824982 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1346760583770588 " " y2[1] (numeric) = 1.1346771759739651 " " absolute error = 1.1175969063526026000000E-6 " " relative error = 9.84947992955024800000E-5 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.526 " " y1[1] (analytic) = 2.5020780778647187 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.26525392605156920E-2 " " relative error = 0.9053490161205296 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1351777039601316 " " y2[1] (numeric) = 1.1351789677745285 " " absolute error = 1.263814396912366000000E-6 " " relative error = 1.11331855136290820000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.527 " " y1[1] (analytic) = 2.5029426489776037 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.35171103734006510E-2 " " relative error = 0.9395784750803966 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1356802143654288 " " y2[1] (numeric) = 1.1356816366737532 " " absolute error = 1.4223083244502277000000E-6 " " relative error = 1.25238452379392300000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.528 " " y1[1] (analytic) = 2.5038067171478815 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.438117854367849400E-2 " " relative error = 0.973764403486041 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1361835890904395 " " y2[1] (numeric) = 1.1361851826716394 " " absolute error = 1.5935811998879500000000E-6 " " relative error = 1.4025736819202570000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.529 " " y1[1] (analytic) = 2.504670281511484 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.524474290728085000E-2 " " relative error = 1.0079068328325635 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.136687827631789 " " y2[1] (numeric) = 1.136689605768187 " " absolute error = 1.7781363979008090000000E-6 " " relative error = 1.56431374971739950000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.53 " " y1[1] (analytic) = 2.505533341204847 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.610780260064382600E-2 " " relative error = 1.0420057945862038 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.137192929485239 " " y2[1] (numeric) = 1.137194905963396 " " absolute error = 1.9764781569175938000000E-6 " " relative error = 1.73803240037050280000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.531 " " y1[1] (analytic) = 2.506395895364911 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.697035676070802500E-2 " " relative error = 1.0760613201842704 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1376988941456876 " " y2[1] (numeric) = 1.1377010832572663 " " absolute error = 2.189111578676517000000E-6 " " relative error = 1.92415725280312260000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.532 " " y1[1] (analytic) = 2.507257943129122 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.783240452491897400E-2 " " relative error = 1.1100734410350863 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.13820572110717 " " y2[1] (numeric) = 1.1382081376497981 " " absolute error = 2.416542628003171000000E-6 " " relative error = 2.12311586841482440000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.533 " " y1[1] (analytic) = 2.508119483635432 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.869394503122890700E-2 " " relative error = 1.14404218851799 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1387134098628597 " " y2[1] (numeric) = 1.1387160691409912 " " absolute error = 2.65927813147826000000E-6 " " relative error = 2.33533574685708540000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.534 " " y1[1] (analytic) = 2.5089805160223007 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.95549774180976500E-2 " " relative error = 1.1779675939832988 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.139221959905068 " " y2[1] (numeric) = 1.1392248777308458 " " absolute error = 2.9178257778816885000000E-6 " " relative error = 2.5612443233843846000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.535 " " y1[1] (analytic) = 2.5098410394286956 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.041550082449262500E-2 " " relative error = 1.2118496887522396 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1397313707252443 " " y2[1] (numeric) = 1.1397345634193619 " " absolute error = 3.192694117526429000000E-6 " " relative error = 2.80126896524294500000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.536 " " y1[1] (analytic) = 2.510701052994094 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.12755143898910700E-2 " " relative error = 1.245688504116967 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1402416418139782 " " y2[1] (numeric) = 1.1402451262065392 " " absolute error = 3.4843925609262527000000E-6 " " relative error = 3.0558369674896550000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.537 " " y1[1] (analytic) = 2.5115605558584817 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.2135017254278697E-2 " " relative error = 1.2794840713404403 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1407527726609987 " " y2[1] (numeric) = 1.140756566092378 " " absolute error = 3.79343137923982000000E-6 " " relative error = 3.32537555038415530000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.538 " " y1[1] (analytic) = 2.5124195471623563 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.299400855815326500E-2 " " relative error = 1.3132364216564958 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.141264762755175 " " y2[1] (numeric) = 1.141268883076878 " " absolute error = 4.120321702938412000000E-6 " " relative error = 3.6103118552362650000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.539 " " y1[1] (analytic) = 2.5132780260467262 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.38524874425232270E-2 " " relative error = 1.3469455862697242 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.141777611584517 " " y2[1] (numeric) = 1.1417820771600395 " " absolute error = 4.465575522472065000000E-6 " " relative error = 3.91107294201968400000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.54 " " y1[1] (analytic) = 2.514135991653113 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.47104530489099600E-2 " " relative error = 1.3806115963554897 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1422913186361758 " " y2[1] (numeric) = 1.1422961483418625 " " absolute error = 4.829705686715257700000E-6 " " relative error = 4.2280857850531710000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.541 " " y1[1] (analytic) = 2.514993443123551 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.556790451934821500E-2 " " relative error = 1.4142344830598794 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1428058833964445 " " y2[1] (numeric) = 1.1428110966223468 " " absolute error = 5.213225902300778000000E-6 " " relative error = 4.5617772694755070000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.542 " " y1[1] (analytic) = 2.5158503796005887 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.642484099638565500E-2 " " relative error = 1.4478142774996179 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1433213053507585 " " y2[1] (numeric) = 1.1433269220014926 " " absolute error = 5.6166507340638100000000E-6 " " relative error = 4.912574188706020000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.543 " " y1[1] (analytic) = 2.51670680022729 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.72812616230868700E-2 " " relative error = 1.481351010762156 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1438375839836956 " " y2[1] (numeric) = 1.1438436244792998 " " absolute error = 6.040495604153762000000E-6 " " relative error = 5.2809032407522850000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.544 " " y1[1] (analytic) = 2.517562704147234 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.81371655430311500E-2 " " relative error = 1.5148447139055163 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1443547187789775 " " y2[1] (numeric) = 1.1443612040557682 " " absolute error = 6.485276790701988000000E-6 " " relative error = 5.6671910241448180000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.545 " " y1[1] (analytic) = 2.5184180905045173 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.899255190031425400E-2 " " relative error = 1.548295417958296 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1448727092194693 " " y2[1] (numeric) = 1.1448796607308982 " " absolute error = 6.951511428932022000000E-6 " " relative error = 6.0718640360213480000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.546 " " y1[1] (analytic) = 2.5192729584437528 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.98474198395497600E-2 " " relative error = 1.5817031539196518 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1453915547871805 " " y2[1] (numeric) = 1.1453989945046896 " " absolute error = 7.43971750916117000000E-6 " " relative error = 6.4953486675074250000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.547 " " y1[1] (analytic) = 2.520127307110073 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.07017685058699300E-2 " " relative error = 1.6150679527592682 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1459112549632657 " " y2[1] (numeric) = 1.1459192053771423 " " absolute error = 7.950413876578466000000E-6 " " relative error = 6.9380712006649510000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.548 " " y1[1] (analytic) = 2.52098113564913 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.15555970449270600E-2 " " relative error = 1.6483898454173425 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1464318092280248 " " y2[1] (numeric) = 1.1464402933482565 " " absolute error = 8.484120231688763000000E-6 " " relative error = 7.4004578060353480000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.549 " " y1[1] (analytic) = 2.5218344432070943 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.24089046028912600E-2 " " relative error = 1.6816688628044336 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1469532170609038 " " y2[1] (numeric) = 1.1469622584180321 " " absolute error = 9.041357128314331000000E-6 " " relative error = 7.8829345380651480000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.55 " " y1[1] (analytic) = 2.522687228930659 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.326169032645621500E-2 " " relative error = 1.71490503580162 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1474754779404943 " " y2[1] (numeric) = 1.147485100586469 " " absolute error = 9.62264597470508000000E-6 " " relative error = 8.3859273332585240000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.551 " " y1[1] (analytic) = 2.5235394919670386 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.411395336283563400E-2 " " relative error = 1.7480983952602962 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1479985913445359 " " y2[1] (numeric) = 1.1480088198535674 " " absolute error = 1.022850903154015600000E-5 " " relative error = 8.9098620056323650000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.552 " " y1[1] (analytic) = 2.52439123146397 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.496569285976681500E-2 " " relative error = 1.7812489720022466 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1485225567499153 " " y2[1] (numeric) = 1.1485334162193273 " " absolute error = 1.085946941192794700000E-5 " " relative error = 9.4551642439292020000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.553 " " y1[1] (analytic) = 2.525242446569713 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.58169079655101900E-2 " " relative error = 1.814356796819562 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1490473736326667 " " y2[1] (numeric) = 1.1490588896837484 " " absolute error = 1.15160510816281200000E-5 " " relative error = 1.0022259609036477000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.554 " " y1[1] (analytic) = 2.5260931364330537 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.66675978288506600E-2 " " relative error = 1.8474219004746282 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1495730414679737 " " y2[1] (numeric) = 1.149585240246831 " " absolute error = 1.219877885727527200000E-5 " " relative error = 1.0611573529679995000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.555 " " y1[1] (analytic) = 2.5269433002033015 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.751776159909848500E-2 " " relative error = 1.8804443137000941 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1500995597301684 " " y2[1] (numeric) = 1.1501124679085748 " " absolute error = 1.290817840637892300000E-5 " " relative error = 1.1223531299679296000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.556 " " y1[1] (analytic) = 2.527792937030293 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.83673984260901700E-2 " " relative error = 1.9134240671988447 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1506269278927328 " " y2[1] (numeric) = 1.1506405726689801 " " absolute error = 1.36447762473235200000E-5 " " relative error = 1.1858558075216154000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.557 " " y1[1] (analytic) = 2.5286420460643915 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.92165074601884630E-2 " " relative error = 1.9463611916439347 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.151155145428298 " " y2[1] (numeric) = 1.151169554528047 " " absolute error = 1.440909974892434800000E-5 " " relative error = 1.2517078871730455000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.558 " " y1[1] (analytic) = 2.529490626456488 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.00650878522850300E-2 " " relative error = 1.9792557176786296 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1516842118086474 " " y2[1] (numeric) = 1.151699413485775 " " absolute error = 1.520167712754094700000E-5 " " relative error = 1.3199518558709486000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.559 " " y1[1] (analytic) = 2.530338677358002 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.0913138753799100E-2 " " relative error = 2.012107675916291 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.152214126504714 " " y2[1] (numeric) = 1.1522301495421645 " " absolute error = 1.602303745040778400000E-5 " " relative error = 1.3906301859893253000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.56 " " y1[1] (analytic) = 2.531186197920883 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.17606593166801700E-2 " " relative error = 2.0449170969404142 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.152744888986584 " " y2[1] (numeric) = 1.1527617626972155 " " absolute error = 1.68737106316374500000E-5 " " relative error = 1.4637853347128424000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.561 " " y1[1] (analytic) = 2.532033187297611 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.26076486934079500E-2 " " relative error = 2.07768401130457 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.153276498723494 " " y2[1] (numeric) = 1.1532942529509278 " " absolute error = 1.775422743377497200000E-5 " " relative error = 1.5394597439058427000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.562 " " y1[1] (analytic) = 2.5328796446411954 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.34541060369924100E-2 " " relative error = 2.1104084495323367 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1538089551838349 " " y2[1] (numeric) = 1.1538276203033015 " " absolute error = 1.866511946668758500000E-5 " " relative error = 1.6176958397513647000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5630000000000001 " " y1[1] (analytic) = 2.5337255691051794 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.430003050097643000E-2 " " relative error = 2.143090442117346 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1543422578351499 " " y2[1] (numeric) = 1.1543618647543368 " " absolute error = 1.960691918689860800000E-5 " " relative error = 1.6985360324302230000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5640000000000001 " " y1[1] (analytic) = 2.5345709598436392 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.51454212394362200E-2 " " relative error = 2.1757300195232334 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1548764061441366 " " y2[1] (numeric) = 1.1548969863040333 " " absolute error = 2.058015989669925700000E-5 " " relative error = 1.7820227157823423000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5650000000000001 " " y1[1] (analytic) = 2.5354158160111835 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.59902774069804800E-2 " " relative error = 2.2083272121835464 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1554113995766468 " " y2[1] (numeric) = 1.1554329849523912 " " absolute error = 2.158537574437069400000E-5 " " relative error = 1.8681982670657196000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5660000000000001 " " y1[1] (analytic) = 2.536260136762956 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.683459815875302000E-2 " " relative error = 2.240882050501782 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1559472375976871 " " y2[1] (numeric) = 1.1559698606994107 " " absolute error = 2.26231017235178900000E-5 " " relative error = 1.957105046639816800E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5670000000000001 " " y1[1] (analytic) = 2.537103921254637 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.767838265043412000E-2 " " relative error = 2.2733945648513787 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1564839196714192 " " y2[1] (numeric) = 1.1565076135450914 " " absolute error = 2.369387367218145400000E-5 " " relative error = 2.0487853976312417000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5680000000000001 " " y1[1] (analytic) = 2.5379471686424413 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.85216300382382900E-2 " " relative error = 2.3058647855755705 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1570214452611616 " " y2[1] (numeric) = 1.1570462434894335 " " absolute error = 2.47982282719494400000E-5 " " relative error = 2.1432816456009607000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5690000000000001 " " y1[1] (analytic) = 2.538789878083122 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.93643394789191700E-2 " " relative error = 2.338292742987513 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1575598138293886 " " y2[1] (numeric) = 1.1575857505324372 " " absolute error = 2.5936703048623500000E-5 " " relative error = 2.240636098347336000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5700000000000001 " " y1[1] (analytic) = 2.5396320487339694 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.02065101297664100E-2 " " relative error = 2.370678467370103 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1580990248377314 " " y2[1] (numeric) = 1.158126134674102 " " absolute error = 2.710983637066455300000E-5 " " relative error = 2.340891045518588800E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5710000000000001 " " y1[1] (analytic) = 2.5404736797528127 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.10481411486096800E-2 " " relative error = 2.4030219889760733 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.158639077746979 " " y2[1] (numeric) = 1.1586673959144285 " " absolute error = 2.831816744941484400000E-5 " " relative error = 2.444088758380277800E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5720000000000001 " " y1[1] (analytic) = 2.5413147702980217 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.18892316938186600E-2 " " relative error = 2.435323338027932 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.159179972017079 " " y2[1] (numeric) = 1.159209534253416 " " absolute error = 2.956223633709953400000E-5 " " relative error = 2.5502714893925005000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5730000000000001 " " y1[1] (analytic) = 2.542155319528505 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.27297809243021500E-2 " " relative error = 2.4675825447178683 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1597217071071368 " " y2[1] (numeric) = 1.1597525496910652 " " absolute error = 3.08425839283810200000E-5 " " relative error = 2.6594814720952475000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5740000000000001 " " y1[1] (analytic) = 2.5429953266037146 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.35697879995116300E-2 " " relative error = 2.4997996392078297 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1602642824754175 " " y2[1] (numeric) = 1.1602964422273758 " " absolute error = 3.215975195836051600000E-5 " " relative error = 2.7717609206885060000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5750000000000001 " " y1[1] (analytic) = 2.5438347906836425 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.44092520794394800E-2 " " relative error = 2.531974651629394 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.160807697579346 " " y2[1] (numeric) = 1.1608412118623477 " " absolute error = 3.351428300168990400000E-5 " " relative error = 2.887152029709819000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5760000000000001 " " y1[1] (analytic) = 2.544673710928825 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.5248172324622100E-2 " " relative error = 2.5641076120838306 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1613519518755067 " " y2[1] (numeric) = 1.161386858595981 " " absolute error = 3.49067204743480630000E-5 " " relative error = 3.0056969739428274000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5770000000000001 " " y1[1] (analytic) = 2.5455120865003424 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.60865478961394400E-2 " " relative error = 2.596198550642024 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1618970448196455 " " y2[1] (numeric) = 1.1619333824282758 " " absolute error = 3.633760863031021400000E-5 " " relative error = 3.127437907887156000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5780000000000001 " " y1[1] (analytic) = 2.5463499165598185 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.69243779556154500E-2 " " relative error = 2.628247497344432 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1624429758666701 " " y2[1] (numeric) = 1.1624807833592319 " " absolute error = 3.78074925617699600000E-5 " " relative error = 3.252416965536072000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5790000000000001 " " y1[1] (analytic) = 2.5471872002694234 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.77616616652203500E-2 " " relative error = 2.660254482201112 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1629897444706487 " " y2[1] (numeric) = 1.1630290613888494 " " absolute error = 3.93169182006936070000E-5 " " relative error = 3.38067626026997000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5800000000000001 " " y1[1] (analytic) = 2.5480239367918736 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.85983981876705500E-2 " " relative error = 2.6922195351916653 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.163537350084813 " " y2[1] (numeric) = 1.1635782165171284 " " absolute error = 4.086643231548947600000E-5 " " relative error = 3.5122578843309693000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5810000000000001 " " y1[1] (analytic) = 2.5488601252904326 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.9434586686229590E-2 " " relative error = 2.72414268626521 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1640857921615577 " " y2[1] (numeric) = 1.1641282487440687 " " absolute error = 4.24565825110079230000E-5 " " relative error = 3.6472039085857670000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5820000000000001 " " y1[1] (analytic) = 2.5496957649289125 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.02702263247094700E-2 " " relative error = 2.756023965340377 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1646350701524406 " " y2[1] (numeric) = 1.1646791580696705 " " absolute error = 4.4087917229873597000E-5 " " relative error = 3.7855563824042215000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5830000000000001 " " y1[1] (analytic) = 2.550530854871673 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.11053162674701900E-2 " " relative error = 2.7878634023052333 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1651851835081837 " " y2[1] (numeric) = 1.1652309444939337 " " absolute error = 4.57609857500429500000E-5 " " relative error = 3.927357333214969000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5840000000000001 " " y1[1] (analytic) = 2.5513653942836245 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.19398556794215200E-2 " " relative error = 2.8196610270172955 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1657361316786736 " " y2[1] (numeric) = 1.1657836080168582 " " absolute error = 4.74763381845821900000E-5 " " relative error = 4.0726487662534494000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5850000000000001 " " y1[1] (analytic) = 2.552199382330228 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.2773843726024800E-2 " " relative error = 2.8514168693035375 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1662879141129625 " " y2[1] (numeric) = 1.1663371486384442 " " absolute error = 4.92345254816672900000E-5 " " relative error = 4.2214726643303460000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5860000000000001 " " y1[1] (analytic) = 2.5530328181774946 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.3607279573291610E-2 " " relative error = 2.883130958960286 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1668405302592677 " " y2[1] (numeric) = 1.1668915663586916 " " absolute error = 5.10360994239178500000E-5 " " relative error = 4.373870987544271600E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5870000000000001 " " y1[1] (analytic) = 2.5538657009919894 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.44401623877863900E-2 " " relative error = 2.914803325753263 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1673939795649733 " " y2[1] (numeric) = 1.1674468611776003 " " absolute error = 5.28816126270648100000E-5 " " relative error = 4.529885672938884000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5880000000000001 " " y1[1] (analytic) = 2.5546980299408295 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.5272491336626500E-2 " " relative error = 2.9464339994175326 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1679482614766297 " " y2[1] (numeric) = 1.1680030330951705 " " absolute error = 5.477161854083867000000E-5 " " relative error = 4.68955863435177000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5890000000000001 " " y1[1] (analytic) = 2.5555298041916856 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.61042655874826200E-2 " " relative error = 2.9780230096574596 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1685033754399554 " " y2[1] (numeric) = 1.168560082111402 " " absolute error = 5.67066714465269700000E-5 " " relative error = 4.852931761979398000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5900000000000001 " " y1[1] (analytic) = 2.556361022912784 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.69354843085809900E-2 " " relative error = 3.0095703861467387 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1690593208998366 " " y2[1] (numeric) = 1.1691180082262949 " " absolute error = 5.868732645830654000000E-5 " " relative error = 5.020046922266898000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5910000000000001 " " y1[1] (analytic) = 2.5571916852729055 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.77661466687025200E-2 " " relative error = 3.041076158528306 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1696160973003273 " " y2[1] (numeric) = 1.1696768114398493 " " absolute error = 6.07141395219112900000E-5 " " relative error = 5.190945957571023000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5920000000000001 " " y1[1] (analytic) = 2.5580217904413884 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.85962518371854400E-2 " " relative error = 3.072540356414384 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1701737040846518 " " y2[1] (numeric) = 1.170236491752065 " " absolute error = 6.27876674130778400000E-5 " " relative error = 5.3656706858057800000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5930000000000001 " " y1[1] (analytic) = 2.5588513375881274 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.94257989839244300E-2 " " relative error = 3.1039630093863937 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.170732140695203 " " y2[1] (numeric) = 1.170797049162942 " " absolute error = 6.49084677390998600000E-5 " " relative error = 5.544262900355327000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5940000000000001 " " y1[1] (analytic) = 2.5596803258835754 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.02547872793724100E-2 " " relative error = 3.135344146994968 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1712914065735442 " " y2[1] (numeric) = 1.1713584836724806 " " absolute error = 6.70770989363855800000E-5 " " relative error = 5.726764369646544000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5950000000000001 " " y1[1] (analytic) = 2.5605087544987444 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.10832158945413700E-2 " " relative error = 3.166683798759929 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.17185150116041 " " y2[1] (numeric) = 1.1719207952806805 " " absolute error = 6.92941202704577800000E-5 " " relative error = 5.913216836932002000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5960000000000001 " " y1[1] (analytic) = 2.5613366226052054 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.19110840010024400E-2 " " relative error = 3.1979819941702328 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1724124238957057 " " y2[1] (numeric) = 1.1724839839875418 " " absolute error = 7.15600918361758400000E-5 " " relative error = 6.1036620200931620000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5970000000000001 " " y1[1] (analytic) = 2.5621639293750906 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.27383907708876300E-2 " " relative error = 3.229238762683988 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1729741742185082 " " y2[1] (numeric) = 1.1730480497930647 " " absolute error = 7.38755745564034800000E-5 " " relative error = 6.298141611312367000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5980000000000001 " " y1[1] (analytic) = 2.562990673981093 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.35651353768898100E-2 " " relative error = 3.2604541337283957 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1735367515670676 " " y2[1] (numeric) = 1.1736129926972487 " " absolute error = 7.62411301811205500000E-5 " " relative error = 6.496697276784295000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5990000000000001 " " y1[1] (analytic) = 2.5638168555964684 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.43913169922654300E-2 " " relative error = 3.2916281366997997 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1741001553788069 " " y2[1] (numeric) = 1.1741788127000943 " " absolute error = 7.86573212874230900000E-5 " " relative error = 6.699370656504633000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6000000000000001 " " y1[1] (analytic) = 2.5646424733950353 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.52169347908322500E-2 " " relative error = 3.3227608009635494 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1746643850903218 " " y2[1] (numeric) = 1.1747455098016013 " " absolute error = 8.11247112795232500000E-5 " " relative error = 6.906203364060063000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6010000000000001 " " y1[1] (analytic) = 2.565467526551176 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.60419879469729300E-2 " " relative error = 3.353852155854079 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1752294401373828 " " y2[1] (numeric) = 1.1753130840017696 " " absolute error = 8.36438643867509800000E-5 " " relative error = 7.11723698624952000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6020000000000001 " " y1[1] (analytic) = 2.566292014239837 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.6866475635634100E-2 " " relative error = 3.384902230674823 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.175795319954935 " " y2[1] (numeric) = 1.1758815353005994 " " absolute error = 8.62153456644421100000E-5 " " relative error = 7.332513082952781000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6030000000000001 " " y1[1] (analytic) = 2.567115935636531 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.76903970323281700E-2 " " relative error = 3.4159110546982303 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1763620239770984 " " y2[1] (numeric) = 1.1764508636980906 " " absolute error = 8.88397209921620900000E-5 " " relative error = 7.552073186773635000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6040000000000001 " " y1[1] (analytic) = 2.567939289917337 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.85137513131342100E-2 " " relative error = 3.4468786571657426 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1769295516371694 " " y2[1] (numeric) = 1.177021069194243 " " absolute error = 9.1517557073705900000E-5 " " relative error = 7.775958802835760000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6050000000000001 " " y1[1] (analytic) = 2.5687620762589 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.93365376546970700E-2 " " relative error = 3.477805067287712 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.17749790236762 " " y2[1] (numeric) = 1.177592151789057 " " absolute error = 9.42494214370981400000E-5 " " relative error = 8.004211408579907000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6060000000000001 " " y1[1] (analytic) = 2.5695842938384343 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.01587552342313400E-2 " " relative error = 3.508690314243498 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1780670756001 " " y2[1] (numeric) = 1.1781641114825323 " " absolute error = 9.70358824323724900000E-5 " " relative error = 8.236872453373933000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6070000000000001 " " y1[1] (analytic) = 2.570405941833722 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.09804032295191700E-2 " " relative error = 3.5395344271813323 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1786370707654354 " " y2[1] (numeric) = 1.178736948274669 " " absolute error = 9.9877509233570190000E-5 " " relative error = 8.473983358482635000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6080000000000001 " " y1[1] (analytic) = 2.571227019423116 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.18014808189129300E-2 " " relative error = 3.5703374352183666 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1792078872936318 " " y2[1] (numeric) = 1.1793106621654672 " " absolute error = 1.02774871835409340000E-4 " " relative error = 8.715585516586491000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6090000000000001 " " y1[1] (analytic) = 2.5720475257855377 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.26219871813347400E-2 " " relative error = 3.6010993674406055 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1797795246138727 " " y2[1] (numeric) = 1.1798852531549266 " " absolute error = 1.05728541053951020000E-4 " " relative error = 8.961720291641326000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6100000000000001 " " y1[1] (analytic) = 2.5728674601004813 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.34419214962782800E-2 " " relative error = 3.631820252902922 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1803519821545205 " " y2[1] (numeric) = 1.1804607212430476 " " absolute error = 1.08739088527043390000E-4 " " relative error = 9.212429018720307000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6110000000000001 " " y1[1] (analytic) = 2.5736868215480126 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.42612829438096400E-2 " " relative error = 3.662500120629039 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1809252593431179 " " y2[1] (numeric) = 1.18103706642983 " " absolute error = 1.11807086712101270000E-4 " " relative error = 9.467753003631513000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6120000000000001 " " y1[1] (analytic) = 2.5745056093087704 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.50800707045673700E-2 " " relative error = 3.69313899961148 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1814993556063875 " " y2[1] (numeric) = 1.1816142887152736 " " absolute error = 1.14933108886106080000E-4 " " relative error = 9.72773352272531000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6130000000000001 " " y1[1] (analytic) = 2.5753238225639663 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.5898283959763300E-2 " " relative error = 3.723736918811551 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1820742703702336 " " y2[1] (numeric) = 1.1821923880993788 " " absolute error = 1.18117729145161830000E-4 " " relative error = 9.992411822665472000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6140000000000001 " " y1[1] (analytic) = 2.576141460495388 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.67159218911848300E-2 " " relative error = 3.754293907159373 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.182650003059741 " " y2[1] (numeric) = 1.1827713645821454 " " absolute error = 1.213615224042730000E-4 " " relative error = 1.026182912022048800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6150000000000001 " " y1[1] (analytic) = 2.576958522285397 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.75329836811940100E-2 " " relative error = 3.784809993553799 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1832265530991772 " " y2[1] (numeric) = 1.1833512181635732 " " absolute error = 1.24665064396012330000E-4 " " relative error = 1.053602660196242100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6160000000000001 " " y1[1] (analytic) = 2.577775007116932 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.83494685127288500E-2 " " relative error = 3.8152852068624146 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1838039199119923 " " y2[1] (numeric) = 1.1839319488436626 " " absolute error = 1.28028931670298720000E-4 " " relative error = 1.081504542406117300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6170000000000001 " " y1[1] (analytic) = 2.5785909141735077 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.91653755693047100E-2 " " relative error = 3.8457195759215375 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1843821029208192 " " y2[1] (numeric) = 1.1845135566224134 " " absolute error = 1.31453701594175240000E-4 " " relative error = 1.109892671208013400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6180000000000001 " " y1[1] (analytic) = 2.5794062426392177 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.99807040350146900E-2 " " relative error = 3.8761131295361846 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1849611015474757 " " y2[1] (numeric) = 1.1850960414998255 " " absolute error = 1.3493995234981070000E-4 " " relative error = 1.138771156062326800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6190000000000001 " " y1[1] (analytic) = 2.580220991698733 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10079545309453009 " " relative error = 3.90646589648004 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1855409152129623 " " y2[1] (numeric) = 1.185679403475899 " " absolute error = 1.38488262936720120000E-4 " " relative error = 1.168144103333987900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6200000000000001 " " y1[1] (analytic) = 2.581035160537305 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10160962193310219 " " relative error = 3.936777905495471 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.186121543337466 " " y2[1] (numeric) = 1.186263642550634 " " absolute error = 1.4209921316798990000E-4 " " relative error = 1.198015616242465700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6210000000000001 " " y1[1] (analytic) = 2.5818487483407653 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10242320973656227 " " relative error = 3.9670491852934813 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1867029853403586 " " y2[1] (numeric) = 1.1868487587240304 " " absolute error = 1.45773383671832240000E-4 " " relative error = 1.22838979485690710E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6220000000000001 " " y1[1] (analytic) = 2.5826617542955255 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10323621569132246 " " relative error = 3.997279764553693 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1872852406401981 " " y2[1] (numeric) = 1.1874347519960882 " " absolute error = 1.49511355890030730000E-4 " " relative error = 1.259270736065180600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6230000000000001 " " y1[1] (analytic) = 2.58347417758858 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1040486389843771 " " relative error = 4.027469671924350 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1878683086547293 " " y2[1] (numeric) = 1.1880216223668072 " " absolute error = 1.53313712077940420000E-4 " " relative error = 1.290662533556177500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6240000000000001 " " y1[1] (analytic) = 2.5842860174075053 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10486047880330229 " " relative error = 4.057618936022254 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1884521888008839 " " y2[1] (numeric) = 1.1886093698361877 " " absolute error = 1.57181035303821660000E-4 " " relative error = 1.322569277796636400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6250000000000001 " " y1[1] (analytic) = 2.5850972729404624 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10567173433625943 " " relative error = 4.087727585432843 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1890368804947822 " " y2[1] (numeric) = 1.1891979944042297 " " absolute error = 1.6111390944750780000E-4 " " relative error = 1.354995056002511000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6260000000000001 " " y1[1] (analytic) = 2.5859079433761947 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10648240477199167 " " relative error = 4.117795648710018 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1896223831517325 " " y2[1] (numeric) = 1.189787496070933 " " absolute error = 1.65112919200405270000E-4 " " relative error = 1.387943952121701600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6270000000000001 " " y1[1] (analytic) = 2.586718027904033 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10729248929983015 " " relative error = 4.147823154376326 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.190208696186232 " " y2[1] (numeric) = 1.1903778748362976 " " absolute error = 1.69178650065715530000E-4 " " relative error = 1.42142004681878200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6280000000000001 " " y1[1] (analytic) = 2.587527525713892 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1081019871096891 " " relative error = 4.177810130922725 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1907958190119676 " " y2[1] (numeric) = 1.1909691307003238 " " absolute error = 1.7331168835621470000E-4 " " relative error = 1.455427417439335800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6290000000000001 " " y1[1] (analytic) = 2.588336435996274 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.10891089739207116 " " relative error = 4.207756606808743 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1913837510418173 " " y2[1] (numeric) = 1.1915612636630113 " " absolute error = 1.77512621194031440000E-4 " " relative error = 1.48997013799125400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6300000000000001 " " y1[1] (analytic) = 2.5891447579422695 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1097192193380665 " " relative error = 4.237662610462390 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1919724916878482 " " y2[1] (numeric) = 1.1921542737243602 " " absolute error = 1.81782036511979330000E-4 " " relative error = 1.525052279139207700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6310000000000001 " " y1[1] (analytic) = 2.5899524907435563 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11052695213935326 " " relative error = 4.267528170280134 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1925620403613202 " " y2[1] (numeric) = 1.1927481608843706 " " absolute error = 1.86120523050448130000E-4 " " relative error = 1.560677908161974300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6320000000000001 " " y1[1] (analytic) = 2.590759633592401 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11133409498819802 " " relative error = 4.2973533146268705 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1931523964726845 " " y2[1] (numeric) = 1.1933429251430423 " " absolute error = 1.90528670357847930000E-4 " " relative error = 1.596851088939750500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6330000000000001 " " y1[1] (analytic) = 2.5915661856816614 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11214064707745841 " " relative error = 4.327138071835969 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.193743559431585 " " y2[1] (numeric) = 1.1939385665003754 " " absolute error = 1.9500706879038710000E-4 " " relative error = 1.633575881935999700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6340000000000001 " " y1[1] (analytic) = 2.5923721462047857 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11294660760058273 " " relative error = 4.356882470209215 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.194335528646859 " " y2[1] (numeric) = 1.19453508495637 " " absolute error = 1.99556309510962040000E-4 " " relative error = 1.67085634417199700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6350000000000001 " " y1[1] (analytic) = 2.593177514355813 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11375197575160989 " " relative error = 4.386586538016767 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1949283035265372 " " y2[1] (numeric) = 1.195132480511026 " " absolute error = 2.04176984488713130000E-4 " " relative error = 1.708696529207107400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6360000000000001 " " y1[1] (analytic) = 2.593982289329375 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11455675072517213 " " relative error = 4.4162503034972 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.195521883477845 " " y2[1] (numeric) = 1.1957307531643433 " " absolute error = 2.08869686498358580000E-4 " " relative error = 1.747100487117342600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6370000000000001 " " y1[1] (analytic) = 2.594786470320698 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11536093171649497 " " relative error = 4.4458737948574685 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.196116267907202 " " y2[1] (numeric) = 1.1963299029163221 " " absolute error = 2.1363500912019440000E-4 " " relative error = 1.786072264479633400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6380000000000001 " " y1[1] (analytic) = 2.5955900565256 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11616451792139681 " " relative error = 4.475457040272842 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1967114562202241 " " y2[1] (numeric) = 1.1969299297669622 " " absolute error = 2.18473546738096050000E-4 " " relative error = 1.825615904339530400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6390000000000001 " " y1[1] (analytic) = 2.5963930471404946 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11696750853629156 " " relative error = 4.505000067886959 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1973074478217232 " " y2[1] (numeric) = 1.1975308337162638 " " absolute error = 2.23385894540628630000E-4 " " relative error = 1.86573544620504520E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6400000000000001 " " y1[1] (analytic) = 2.597195441362392 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1177699027581891 " " relative error = 4.534502905811793 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1979042421157073 " " y2[1] (numeric) = 1.1981326147642268 " " absolute error = 2.28372648519492570000E-4 " " relative error = 1.906434926018349700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6410000000000001 " " y1[1] (analytic) = 2.5979972383888983 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11857169978469528 " " relative error = 4.563965582127617 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1985018385053827 " " y2[1] (numeric) = 1.1987352729108511 " " absolute error = 2.33434405468413430000E-4 " " relative error = 1.94771837613134400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6420000000000001 " " y1[1] (analytic) = 2.5987984374182154 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.11937289881401236 " " relative error = 4.593388124882965 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1991002363931529 " " y2[1] (numeric) = 1.199338808156137 " " absolute error = 2.38571762984030040000E-4 " " relative error = 1.989589825298047600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6430000000000001 " " y1[1] (analytic) = 2.599599037649145 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12017349904494212 " " relative error = 4.622770562094712 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.1996994351806198 " " y2[1] (numeric) = 1.199943220500084 " " absolute error = 2.4378531946411820000E-4 " " relative error = 2.032053298644883600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6440000000000001 " " y1[1] (analytic) = 2.600399038281087 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12097349967688409 " " relative error = 4.652112921747959 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2002994342685849 " " y2[1] (numeric) = 1.2005485099426925 " " absolute error = 2.49075674107590570000E-4 " " relative error = 2.07511281765593300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6450000000000001 " " y1[1] (analytic) = 2.601198438514041 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1217728999098382 " " relative error = 4.681415231796083 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.200900233057049 " " y2[1] (numeric) = 1.2011546764839625 " " absolute error = 2.5444342691338660000E-4 " " relative error = 2.11877240014907400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6460000000000001 " " y1[1] (analytic) = 2.6019972375486065 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12257169894440345 " " relative error = 4.710677520160655 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2015018309452135 " " y2[1] (numeric) = 1.2017617201238937 " " absolute error = 2.5988917868025040000E-4 " " relative error = 2.163036060259661300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6470000000000001 " " y1[1] (analytic) = 2.6027954345859845 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1233698959817815 " " relative error = 4.739899814731518 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2021042273314804 " " y2[1] (numeric) = 1.2023696408624864 " " absolute error = 2.6541353100606460000E-4 " " relative error = 2.207907808420648300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6480000000000001 " " y1[1] (analytic) = 2.6035930288279783 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12416749022377527 " " relative error = 4.769082143366697 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2027074216134537 " " y2[1] (numeric) = 1.2029784386997406 " " absolute error = 2.7101708628696210000E-4 " " relative error = 2.253391651341003500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6490000000000001 " " y1[1] (analytic) = 2.604390019476994 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12496448087279077 " " relative error = 4.798224533892423 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2033114131879388 " " y2[1] (numeric) = 1.203588113635656 " " absolute error = 2.76700447717326270000E-4 " " relative error = 2.29949159199165610E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6500000000000001 " " y1[1] (analytic) = 2.6051864057360397 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12576086713183665 " " relative error = 4.82732701410307 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2039162014509444 " " y2[1] (numeric) = 1.204198665670233 " " absolute error = 2.8246421928868060000E-4 " " relative error = 2.346211629582344300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6510000000000001 " " y1[1] (analytic) = 2.6059821868087303 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12655664820452728 " " relative error = 4.856389611761228 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.204521785797682 " " y2[1] (numeric) = 1.2048100948034715 " " absolute error = 2.8830900578946660000E-4 " " relative error = 2.393555759545992800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6520000000000001 " " y1[1] (analytic) = 2.606777361899285 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12735182329508188 " " relative error = 4.885412354597632 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2051281656225676 " " y2[1] (numeric) = 1.2054224010353711 " " absolute error = 2.94235412803489640000E-4 " " relative error = 2.441527973512161700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6530000000000001 " " y1[1] (analytic) = 2.607571930212528 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12814639160832497 " " relative error = 4.914395270311124 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2057353403192215 " " y2[1] (numeric) = 1.2060355843659323 " " absolute error = 3.00244046710806960000E-4 " " relative error = 2.490132259300922600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6540000000000001 " " y1[1] (analytic) = 2.6083658909538916 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1289403523496886 " " relative error = 4.9433383865687075 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2063433092804687 " " y2[1] (numeric) = 1.206649644795155 " " absolute error = 3.0633551468617350000E-4 " " relative error = 2.53937260089658300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6550000000000001 " " y1[1] (analytic) = 2.609159243329415 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.12973370472521184 " " relative error = 4.972241731005474 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2069520718983406 " " y2[1] (numeric) = 1.2072645823230388 " " absolute error = 3.1251042469815360000E-4 " " relative error = 2.589252978427098500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6560000000000001 " " y1[1] (analytic) = 2.6099519865457457 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13052644794154267 " " relative error = 5.00110533122464 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2075616275640746 " " y2[1] (numeric) = 1.2078803969495842 " " absolute error = 3.18769385509565240000E-4 " " relative error = 2.639777368154661600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6570000000000001 " " y1[1] (analytic) = 2.610744119810141 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13131858120593787 " " relative error = 5.02992921479749 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2081719756681149 " " y2[1] (numeric) = 1.208497088674791 " " absolute error = 3.2511300667614760000E-4 " " relative error = 2.69094974245170100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6580000000000001 " " y1[1] (analytic) = 2.611535642330467 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13211010372626397 " " relative error = 5.058713409263384 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2087831156001134 " " y2[1] (numeric) = 1.209114657498659 " " absolute error = 3.31541898545673060000E-4 " " relative error = 2.74277406978071100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6590000000000001 " " y1[1] (analytic) = 2.6123265533152016 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13290101471099858 " " relative error = 5.08745794212975 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2093950467489305 " " y2[1] (numeric) = 1.2097331034211887 " " absolute error = 3.38056672258169040000E-4 " " relative error = 2.795254314683408600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6600000000000001 " " y1[1] (analytic) = 2.613116851973434 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1336913133692308 " " relative error = 5.116162840872068 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.210007768502635 " " y2[1] (numeric) = 1.2103524264423795 " " absolute error = 3.4465793974458590000E-4 " " relative error = 2.848394437757160000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6610000000000001 " " y1[1] (analytic) = 2.6139065375148656 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13448099891066256 " " relative error = 5.144828132933875 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.210621280248505 " " y2[1] (numeric) = 1.2109726265622318 " " absolute error = 3.5134631372679690000E-4 " " relative error = 2.90219839564257340E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6620000000000001 " " y1[1] (analytic) = 2.614695609149811 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1352700705456078 " " relative error = 5.173453845726690 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2112355813730291 " " y2[1] (numeric) = 1.2115937037807456 " " absolute error = 3.58122407716487960000E-4 " " relative error = 2.95667014100203800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6630000000000001 " " y1[1] (analytic) = 2.615484066089198 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13605852748499503 " " relative error = 5.202040006630074 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2118506712619062 " " y2[1] (numeric) = 1.2122156580979206 " " absolute error = 3.64986836014491440000E-4 " " relative error = 3.01181362250209300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6640000000000001 " " y1[1] (analytic) = 2.6162719075445704 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1368463689403674 " " relative error = 5.230586642991582 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2124665493000464 " " y2[1] (numeric) = 1.2128384895137572 " " absolute error = 3.71940213710786340000E-4 " " relative error = 3.067632784801415000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6650000000000001 " " y1[1] (analytic) = 2.6170591327280865 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13763359412388354 " " relative error = 5.259093782126769 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2130832148715713 " " y2[1] (numeric) = 1.2134621980282552 " " absolute error = 3.789831566838320000E-4 " " relative error = 3.12413156853344800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6660000000000001 " " y1[1] (analytic) = 2.6178457408525215 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13842020224831852 " " relative error = 5.287561451319164 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.213700667359816 " " y2[1] (numeric) = 1.2140867836414144 " " absolute error = 3.86116281598347650000E-4 " " relative error = 3.18131391027635400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6670000000000001 " " y1[1] (analytic) = 2.6186317311312672 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13920619252706423 " " relative error = 5.315989677820263 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2143189061473278 " " y2[1] (numeric) = 1.2147122463532352 " " absolute error = 3.933402059073110000E-4 " " relative error = 3.23918374255789450E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6680000000000001 " " y1[1] (analytic) = 2.6194171027783333 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.13999156417413028 " " relative error = 5.344378488849510 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.214937930615868 " " y2[1] (numeric) = 1.2153385861637174 " " absolute error = 4.00655547849293470000E-4 " " relative error = 3.29774499382199600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6690000000000002 " " y1[1] (analytic) = 2.6202018550083483 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14077631640414534 " " relative error = 5.372727911594308 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2155577401464122 " " y2[1] (numeric) = 1.2159658030728608 " " absolute error = 4.08062926448682360000E-4 " " relative error = 3.35700158841925330E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6700000000000002 " " y1[1] (analytic) = 2.6209859870365597 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1415604484323567 " " relative error = 5.401037973209970 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2161783341191508 " " y2[1] (numeric) = 1.2165938970806658 " " absolute error = 4.1556296151501470000E-4 " " relative error = 3.416957446590241400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6710000000000002 " " y1[1] (analytic) = 2.621769498078836 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14234395947463296 " " relative error = 5.4293087008197665 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.21679971191349 " " y2[1] (numeric) = 1.2172228681871322 " " absolute error = 4.2315627364231110000E-4 " " relative error = 3.477616484448970400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6720000000000002 " " y1[1] (analytic) = 2.622552387351666 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14312684874746306 " " relative error = 5.457540121514863 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.217421872908052 " " y2[1] (numeric) = 1.21785271639226 " " absolute error = 4.3084348420796560000E-4 " " relative error = 3.53898261396282550E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6730000000000002 " " y1[1] (analytic) = 2.6233346540721607 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1439091154679577 " " relative error = 5.485732262354324 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2180448164806759 " " y2[1] (numeric) = 1.218483441696049 " " absolute error = 4.38625215373189550000E-4 " " relative error = 3.60105974294541300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6740000000000002 " " y1[1] (analytic) = 2.6241162974580527 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14469075885384974 " " relative error = 5.5138851503650885 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2186685420084182 " " y2[1] (numeric) = 1.2191150440984997 " " absolute error = 4.4650209008145760000E-4 " " relative error = 3.663851775033127000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6750000000000002 " " y1[1] (analytic) = 2.6248973167277 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14547177812349688 " " relative error = 5.541998812542035 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.219293048867553 " " y2[1] (numeric) = 1.2197475235996116 " " absolute error = 4.5447473205850740000E-4 " " relative error = 3.727362609674609300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6760000000000002 " " y1[1] (analytic) = 2.6256777111000824 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1462521724958794 " " relative error = 5.570073275847857 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2199183364335744 " " y2[1] (numeric) = 1.220380880199385 " " absolute error = 4.62543765810563560000E-4 " " relative error = 3.79159614210577500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6770000000000002 " " y1[1] (analytic) = 2.6264574797948055 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14703194119060248 " " relative error = 5.5981085672131075 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2205444040811941 " " y2[1] (numeric) = 1.2210151138978196 " " absolute error = 4.70709816625447530000E-4 " " relative error = 3.856556263348650500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6780000000000002 " " y1[1] (analytic) = 2.6272366220321013 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14781108342789828 " " relative error = 5.626104713536238 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2211712511843449 " " y2[1] (numeric) = 1.2216502246949157 " " absolute error = 4.7897351057080150000E-4 " " relative error = 3.92224686018666300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6790000000000002 " " y1[1] (analytic) = 2.6280151370328273 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1485895984286243 " " relative error = 5.6540617416835 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2217988771161794 " " y2[1] (numeric) = 1.2222862125906733 " " absolute error = 4.87335474493866270000E-4 " " relative error = 3.98867181515281550E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6800000000000002 " " y1[1] (analytic) = 2.6287930240184685 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.14936748541426548 " " relative error = 5.681979678488986 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2224272812490722 " " y2[1] (numeric) = 1.222923077585092 " " absolute error = 4.9579633601992690000E-4 " " relative error = 4.05583500650708530E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6810000000000002 " " y1[1] (analytic) = 2.629570282211138 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1501447436069352 " " relative error = 5.709858550754625 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2230564629546188 " " y2[1] (numeric) = 1.2235608196781724 " " absolute error = 5.043567235536450000E-4 " " relative error = 4.12374030823758450E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6820000000000002 " " y1[1] (analytic) = 2.630346910833578 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.15092137222937518 " " relative error = 5.737698385250141 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2236864216036376 " " y2[1] (numeric) = 1.2241994388699142 " " absolute error = 5.1301726627661640000E-4 " " relative error = 4.19239159003095500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6830000000000002 " " y1[1] (analytic) = 2.63112290910916 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1516973705049569 " " relative error = 5.765499208713070 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2243171565661704 " " y2[1] (numeric) = 1.2248389351603173 " " absolute error = 5.2177859414692660000E-4 " " relative error = 4.26179271725925730E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6840000000000002 " " y1[1] (analytic) = 2.631898276261885 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.152472737657682 " " relative error = 5.793261047848731 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2249486672114818 " " y2[1] (numeric) = 1.2254793085493818 " " absolute error = 5.3064133790003960000E-4 " " relative error = 4.3319475509778800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6850000000000002 " " y1[1] (analytic) = 2.6326730115163866 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.15324747291218355 " " relative error = 5.820983929330248 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2255809529080612 " " y2[1] (numeric) = 1.2261205590371078 " " absolute error = 5.396061290465770000E-4 " " relative error = 4.402859947898165600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6860000000000002 " " y1[1] (analytic) = 2.633447114097929 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1540215754937262 " " relative error = 5.848667879798502 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2262140130236237 " " y2[1] (numeric) = 1.226762686623495 " " absolute error = 5.4867359987142980000E-4 " " relative error = 4.47453376037107330E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6870000000000002 " " y1[1] (analytic) = 2.634220583232411 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1547950446282078 " " relative error = 5.8763129258621625 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.226847846925108 " " y2[1] (numeric) = 1.2274056913085438 " " absolute error = 5.5784438343575720000E-4 " " relative error = 4.54697283639452200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6880000000000002 " " y1[1] (analytic) = 2.6349934181463617 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.15556787954215867 " " relative error = 5.903919094097623 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2274824539786815 " " y2[1] (numeric) = 1.228049573092254 " " absolute error = 5.6711911357254510000E-4 " " relative error = 4.62018101956832240E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6890000000000002 " " y1[1] (analytic) = 2.6357656180669475 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.15634007946274453 " " relative error = 5.93148641104907 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2281178335497365 " " y2[1] (numeric) = 1.2286943319746255 " " absolute error = 5.7649842488904920000E-4 " " relative error = 4.69416214910539400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6900000000000002 " " y1[1] (analytic) = 2.636537182221968 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.15711164361776486 " " relative error = 5.959014903228388 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2287539850028935 " " y2[1] (numeric) = 1.2293399679556585 " " absolute error = 5.8598295276501840000E-4 " " relative error = 4.76892005980870600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6910000000000002 " " y1[1] (analytic) = 2.63730810983986 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.15788257123565685 " " relative error = 5.986504597115263 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2293909077020013 " " y2[1] (numeric) = 1.229986481035353 " " absolute error = 5.9557333335158450000E-4 " " relative error = 4.84445858205377830E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6920000000000002 " " y1[1] (analytic) = 2.6380784001496944 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1586528615454914 " " relative error = 6.013955519157006 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2300286010101371 " " y2[1] (numeric) = 1.2306338712137086 " " absolute error = 6.0527020357148410000E-4 " " relative error = 4.92078154178218100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6930000000000002 " " y1[1] (analytic) = 2.6388480523811824 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.15942251377697936 " " relative error = 6.041367695768741 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2306670642896078 " " y2[1] (numeric) = 1.2312821384907258 " " absolute error = 6.1507420111794890000E-4 " " relative error = 4.997892760484292700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6940000000000002 " " y1[1] (analytic) = 2.639617065764671 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16019152716046792 " " relative error = 6.0687411533332405 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2313062969019501 " " y2[1] (numeric) = 1.2319312828664042 " " absolute error = 6.249859644540390000E-4 " " relative error = 5.07579605518582900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6950000000000002 " " y1[1] (analytic) = 2.6403854395311472 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16095990092694423 " " relative error = 6.096075918201014 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2319462982079314 " " y2[1] (numeric) = 1.232581304340744 " " absolute error = 6.3500613281264330000E-4 " " relative error = 5.154495238439891000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6960000000000002 " " y1[1] (analytic) = 2.641153172912237 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16172763430803405 " " relative error = 6.123372016690231 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2325870675675508 " " y2[1] (numeric) = 1.2332322029137455 " " absolute error = 6.4513534619470290000E-4 " " relative error = 5.23399411830472600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6970000000000002 " " y1[1] (analytic) = 2.641920265140208 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16249472653600483 " " relative error = 6.150629475086796 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2332286043400384 " " y2[1] (numeric) = 1.233883978585408 " " absolute error = 6.5537424536965540000E-4 " " relative error = 5.31429649833964500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6980000000000002 " " y1[1] (analytic) = 2.6426867154479665 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1632611768437635 " " relative error = 6.177848319644231 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2338709078838577 " " y2[1] (numeric) = 1.2345366313557322 " " absolute error = 6.6572347187454640000E-4 " " relative error = 5.39540617759025600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.6990000000000002 " " y1[1] (analytic) = 2.6434525230690635 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16402698446486053 " " relative error = 6.205028576583787 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2345139775567053 " " y2[1] (numeric) = 1.2351901612247178 " " absolute error = 6.7618366801247550000E-4 " " relative error = 5.47732695056841600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7000000000000002 " " y1[1] (analytic) = 2.644217687237691 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.164792148633488 " " relative error = 6.232170272094345 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2351578127155118 " " y2[1] (numeric) = 1.2358445681923647 " " absolute error = 6.8675547685281830000E-4 " " relative error = 5.56006260724673500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7010000000000002 " " y1[1] (analytic) = 2.6449822071886855 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16555666858448248 " " relative error = 6.259273432332475 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2358024127164415 " " y2[1] (numeric) = 1.236499852258673 " " absolute error = 6.9743954223144830000E-4 " " relative error = 5.6436169330531790E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7020000000000002 " " y1[1] (analytic) = 2.645746082157526 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16632054355332304 " " relative error = 6.286338083422339 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2364477769148952 " " y2[1] (numeric) = 1.2371560134236428 " " absolute error = 7.0823650874762830000E-4 " " relative error = 5.727993708838836000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7030000000000002 " " y1[1] (analytic) = 2.646509311380338 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16708377277613495 " " relative error = 6.313364251455787 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.237093904665508 " " y2[1] (numeric) = 1.2378130516872738 " " absolute error = 7.1914702176578690000E-4 " " relative error = 5.81319671088536900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7040000000000002 " " y1[1] (analytic) = 2.6472718940938926 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16784635548968962 " " relative error = 6.340351962492317 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2377407953221526 " " y2[1] (numeric) = 1.2384709670495664 " " absolute error = 7.301717274137420000E-4 " " relative error = 5.89922971088382700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7050000000000002 " " y1[1] (analytic) = 2.648033829535607 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16860829093140417 " " relative error = 6.367301242559030 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2383884482379384 " " y2[1] (numeric) = 1.2391297595105204 " " absolute error = 7.4131127258203480000E-4 " " relative error = 5.98609647592257400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7060000000000002 " " y1[1] (analytic) = 2.648795116943546 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.16936957833934319 " " relative error = 6.394212117650660 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2390368627652126 " " y2[1] (numeric) = 1.2397894290701357 " " absolute error = 7.5256630492304130000E-4 " " relative error = 6.07380076847355700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7070000000000002 " " y1[1] (analytic) = 2.6495557555564226 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17013021695221964 " " relative error = 6.421084613729568 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2396860382555603 " " y2[1] (numeric) = 1.2404499757284124 " " absolute error = 7.6393747285208310000E-4 " " relative error = 6.16234634639482800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7080000000000002 " " y1[1] (analytic) = 2.6503157446135974 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17089020600939442 " " relative error = 6.447918756725695 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2403359740598068 " " y2[1] (numeric) = 1.2411113994853507 " " absolute error = 7.7542542554387420000E-4 " " relative error = 6.25173696289554300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7090000000000002 " " y1[1] (analytic) = 2.6510750833550816 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17164954475087857 " " relative error = 6.474714572536610 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2409866695280156 " " y2[1] (numeric) = 1.2417737003409501 " " absolute error = 7.8703081293451940000E-4 " " relative error = 6.3419763665459100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7100000000000002 " " y1[1] (analytic) = 2.6518337710215367 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17240823241733372 " " relative error = 6.501472087027492 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.241638124009492 " " y2[1] (numeric) = 1.242436878295211 " " absolute error = 7.9875428571907210000E-4 " " relative error = 6.43306830125140300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7110000000000002 " " y1[1] (analytic) = 2.652591806854275 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1731662682500721 " " relative error = 6.528191326031088 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.242290336852781 " " y2[1] (numeric) = 1.2431009333481333 " " absolute error = 8.1059649535242250000E-4 " " relative error = 6.5250165062539900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7120000000000002 " " y1[1] (analytic) = 2.6533491900952613 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17392365149105826 " " relative error = 6.55487231534776 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.24294330740567 " " y2[1] (numeric) = 1.243765865499717 " " absolute error = 8.2255809404707670000E-4 " " relative error = 6.61782471610840300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7130000000000002 " " y1[1] (analytic) = 2.6541059199871118 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17468038138290876 " " relative error = 6.581515080745420 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2435970350151884 " " y2[1] (numeric) = 1.2444316747499622 " " absolute error = 8.3463973477382320000E-4 " " relative error = 6.71149666068180600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7140000000000002 " " y1[1] (analytic) = 2.654861995773097 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17543645716889378 " " relative error = 6.608119647959578 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2442515190276089 " " y2[1] (numeric) = 1.2450983610988686 " " absolute error = 8.4684207125973470000E-4 " " relative error = 6.80603606513213300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7150000000000002 " " y1[1] (analytic) = 2.6556174166971402 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17619187809293724 " " relative error = 6.634686042693288 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2449067587884473 " " y2[1] (numeric) = 1.2457659245464365 " " absolute error = 8.5916575798927750000E-4 " " relative error = 6.9014466499115490E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7160000000000002 " " y1[1] (analytic) = 2.656372182003822 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17694664339961896 " " relative error = 6.661214290617217 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.245562753642464 " " y2[1] (numeric) = 1.246434365092666 " " absolute error = 8.7161145020187010000E-4 " " relative error = 6.99773213074147600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7170000000000002 " " y1[1] (analytic) = 2.6571262909383764 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17770075233417337 " " relative error = 6.687704417369546 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2462195029336642 " " y2[1] (numeric) = 1.2471036827375566 " " absolute error = 8.8417980389232650000E-4 " " relative error = 7.09489621861094500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7180000000000002 " " y1[1] (analytic) = 2.6578797427466947 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1784542041424917 " " relative error = 6.714156448556032 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2468770060052987 " " y2[1] (numeric) = 1.2477738774811087 " " absolute error = 8.9687147580996830000E-4 " " relative error = 7.1929426197643510E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7190000000000002 " " y1[1] (analytic) = 2.658632536675325 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17920699807112195 " " relative error = 6.74057040974997 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2475352621998643 " " y2[1] (numeric) = 1.2484449493233223 " " absolute error = 9.0968712345795840000E-4 " " relative error = 7.29187503569113300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7200000000000002 " " y1[1] (analytic) = 2.6593846719714733 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.17995913336727032 " " relative error = 6.766946326492202 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2481942708591052 " " y2[1] (numeric) = 1.2491168982641971 " " absolute error = 9.2262740509196920000E-4 " " relative error = 7.39169716311023200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7210000000000002 " " y1[1] (analytic) = 2.660136147883005 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.180710609278802 " " relative error = 6.793284224291132 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2488540313240124 " " y2[1] (numeric) = 1.2497897243037335 " " absolute error = 9.35692979721070000E-4 " " relative error = 7.49241269397245100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7220000000000002 " " y1[1] (analytic) = 2.6608869636584433 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18146142505424034 " " relative error = 6.81958412862265 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2495145429348258 " " y2[1] (numeric) = 1.2504634274419313 " " absolute error = 9.4888450710550740000E-4 " " relative error = 7.59402531543805200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7230000000000002 " " y1[1] (analytic) = 2.6616371185469734 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18221157994277037 " " relative error = 6.845846064930232 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2501758050310336 " " y2[1] (numeric) = 1.2511380076787904 " " absolute error = 9.6220264775670470000E-4 " " relative error = 7.69653870987224600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7240000000000002 " " y1[1] (analytic) = 2.66238661179844 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18296107319423704 " " relative error = 6.8720700586248435 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.250837816951374 " " y2[1] (numeric) = 1.251813465014311 " " absolute error = 9.756480629368180000E-4 " " relative error = 7.79995655483724500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7250000000000002 " " y1[1] (analytic) = 2.66313544266335 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.183709904059147 " " relative error = 6.898256135084977 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.251500578033835 " " y2[1] (numeric) = 1.252489799448493 " " absolute error = 9.8922141465784820000E-4 " " relative error = 7.90428252308089700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7260000000000002 " " y1[1] (analytic) = 2.6638836103928725 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18445807178866946 " " relative error = 6.924404319656645 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2521640876156557 " " y2[1] (numeric) = 1.2531670109813362 " " absolute error = 1.0029233656805303000E-3 " " relative error = 8.00952028252364100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7270000000000002 " " y1[1] (analytic) = 2.6646311142388397 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1852055756346367 " " relative error = 6.950514637653372 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2528283450333264 " " y2[1] (numeric) = 1.253845099612841 " " absolute error = 1.016754579514556000E-3 " " relative error = 8.11567349625626000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7280000000000002 " " y1[1] (analytic) = 2.6653779534537483 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18595241484954528 " " relative error = 6.976587114356203 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2534933496225897 " " y2[1] (numeric) = 1.254524065343007 " " absolute error = 1.0307157204172412000E-3 " " relative error = 8.22274582252531400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7290000000000002 " " y1[1] (analytic) = 2.666124127290759 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1866985886865562 " " relative error = 7.002621775013682 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2541591007184412 " " y2[1] (numeric) = 1.2552039081718345 " " absolute error = 1.0448074533933038000E-3 " " relative error = 8.33074091472755800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7300000000000002 " " y1[1] (analytic) = 2.666869635003698 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18744409639949478 " " relative error = 7.028618644841815 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2548255976551297 " " y2[1] (numeric) = 1.2558846280993234 " " absolute error = 1.0590304441937537000E-3 " " relative error = 8.43966242139740500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7310000000000002 " " y1[1] (analytic) = 2.6676144758470572 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18818893724285424 " " relative error = 7.05457774902417 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2554928397661587 " " y2[1] (numeric) = 1.2565662251254737 " " absolute error = 1.0733853593150045000E-3 " " relative error = 8.5495139861962690E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7320000000000002 " " y1[1] (analytic) = 2.6683586490759965 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1889331104717935 " " relative error = 7.080499112711763 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2561608263842858 " " y2[1] (numeric) = 1.2572486992502854 " " absolute error = 1.0878728659995396000E-3 " " relative error = 8.66029924791442700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7330000000000002 " " y1[1] (analytic) = 2.6691021539463424 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.18967661534213942 " " relative error = 7.106382761023111 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2568295568415244 " " y2[1] (numeric) = 1.2579320504737586 " " absolute error = 1.102493632234136100E-3 " " relative error = 8.77202184045351200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7340000000000002 " " y1[1] (analytic) = 2.66984498971459 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19041945111038716 " " relative error = 7.132228719044220 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2574990304691442 " " y2[1] (numeric) = 1.258616278795893 " " absolute error = 1.1172483267487543000E-3 " " relative error = 8.88468539281445300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7350000000000002 " " y1[1] (analytic) = 2.6705871556379037 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19116161703370071 " " relative error = 7.158037011828559 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.258169246597672 " " y2[1] (numeric) = 1.259301384216689 " " absolute error = 1.1321376190169818000E-3 " " relative error = 8.99829352909790600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7360000000000002 " " y1[1] (analytic) = 2.671328650974118 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19190311236991509 " " relative error = 7.183807664397127 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2588402045568912 " " y2[1] (numeric) = 1.2599873667361463 " " absolute error = 1.1471621792551456000E-3 " " relative error = 9.11284986849418300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7370000000000002 " " y1[1] (analytic) = 2.672069474981737 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19264393637753408 " " relative error = 7.209540701738331 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.259511903675844 " " y2[1] (numeric) = 1.260674226354265 " " absolute error = 1.1623226784209795000E-3 " " relative error = 9.22835802526978000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7380000000000002 " " y1[1] (analytic) = 2.672809626919937 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19338408831573384 " " relative error = 7.235236148808088 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2601843432828315 " " y2[1] (numeric) = 1.261361963071045 " " absolute error = 1.1776197882136241000E-3 " " relative error = 9.34482160876460900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7390000000000002 " " y1[1] (analytic) = 2.673549106048566 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19412356744436288 " " relative error = 7.26089403052979 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.260857522705414 " " y2[1] (numeric) = 1.2620505768864867 " " absolute error = 1.193054181072739100E-3 " " relative error = 9.46224422338227700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7400000000000002 " " y1[1] (analytic) = 2.674287911628145 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19486237302394205 " " relative error = 7.2865143717942855 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2615314412704124 " " y2[1] (numeric) = 1.2627400678005896 " " absolute error = 1.2086265301771704000E-3 " " relative error = 9.5806294685769800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7410000000000002 " " y1[1] (analytic) = 2.675026042919869 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1956005043156659 " " relative error = 7.312097197459889 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2622060983039076 " " y2[1] (numeric) = 1.263430435813354 " " absolute error = 1.2243375094462827000E-3 " " relative error = 9.69998093886164100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7420000000000002 " " y1[1] (analytic) = 2.675763499185606 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19633796058140307 " " relative error = 7.33764253235237 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2628814931312433 " " y2[1] (numeric) = 1.2641216809247797 " " absolute error = 1.240187793536407000E-3 " " relative error = 9.82030222377739800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7430000000000002 " " y1[1] (analytic) = 2.6765002796879003 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19707474108369727 " " relative error = 7.363150401264955 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2635576250770244 " " y2[1] (numeric) = 1.2648138031348668 " " absolute error = 1.2561780578423942000E-3 " " relative error = 9.94159690790374300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7440000000000002 " " y1[1] (analytic) = 2.677236383689971 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19781084508576807 " " relative error = 7.388620828958334 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.264234493465119 " " y2[1] (numeric) = 1.2655068024436154 " " absolute error = 1.2723089784962838000E-3 " " relative error = 0.10063868570845852 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7450000000000002 " " y1[1] (analytic) = 2.677971810455715 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.19854627185151186 " " relative error = 7.41405384016066 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2649120976186587 " " y2[1] (numeric) = 1.2662006788510252 " " absolute error = 1.2885812323664148000E-3 " " relative error = 0.10187120787225577 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7460000000000002 " " y1[1] (analytic) = 2.678706559249705 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.1992810206455018 " " relative error = 7.439449459567518 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.26559043686004 " " y2[1] (numeric) = 1.2668954323570965 " " absolute error = 1.304995497056538000E-3 " " relative error = 0.10311357126672537 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7470000000000002 " " y1[1] (analytic) = 2.6794406293371917 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20001509073298873 " " relative error = 7.464807711841933 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2662695105109227 " " y2[1] (numeric) = 1.2675910629618292 " " absolute error = 1.3215524509064824000E-3 " " relative error = 0.10436581153827622 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7480000000000002 " " y1[1] (analytic) = 2.680174019984106 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20074848137990298 " " relative error = 7.490128621614407 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2669493178922342 " " y2[1] (numeric) = 1.2682875706652232 " " absolute error = 1.3382527729890460000E-3 " " relative error = 0.1056279642831677 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7490000000000002 " " y1[1] (analytic) = 2.680906730457057 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20148119185285385 " " relative error = 7.5154122134828665 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2676298583241663 " " y2[1] (numeric) = 1.2689849554672787 " " absolute error = 1.3550971431124380000E-3 " " relative error = 0.10690006504768713 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7500000000000002 " " y1[1] (analytic) = 2.6816387600233345 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20221322141913145 " " relative error = 7.540658512012702 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2683111311261792 " " y2[1] (numeric) = 1.2696832173679957 " " absolute error = 1.3720862418165058000E-3 " " relative error = 0.10818214932783732 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7510000000000002 " " y1[1] (analytic) = 2.6823701079509084 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20294456934670535 " " relative error = 7.565867541736696 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2689931356170001 " " y2[1] (numeric) = 1.270382356367374 " " absolute error = 1.389220750373843000E-3 " " relative error = 0.109474252569411 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7520000000000002 " " y1[1] (analytic) = 2.683100773508431 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20367523490422812 " " relative error = 7.591039327155116 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2696758711146243 " " y2[1] (numeric) = 1.2710823724654137 " " absolute error = 1.4065013507893465000E-3 " " relative error = 0.11077641016794354 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7530000000000002 " " y1[1] (analytic) = 2.683830755965238 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.2044052173610349 " " relative error = 7.616173892735674 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2703593369363166 " " y2[1] (numeric) = 1.2717832656621149 " " absolute error = 1.423928725798218000E-3 " " relative error = 0.11208865746854427 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7540000000000002 " " y1[1] (analytic) = 2.684560054591345 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20513451598714205 " " relative error = 7.641271262913449 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2710435323986113 " " y2[1] (numeric) = 1.2724850359574773 " " absolute error = 1.4415035588659642000E-3 " " relative error = 0.11341102976588649 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7550000000000002 " " y1[1] (analytic) = 2.685288668657455 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20586313005325207 " " relative error = 7.66633146209104 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2717284568173128 " " y2[1] (numeric) = 1.2731876833515012 " " absolute error = 1.4592265341883960000E-3 " " relative error = 0.11474356230419853 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7560000000000002 " " y1[1] (analytic) = 2.6860165974349535 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20659105883075046 " " relative error = 7.691354514638416 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2724141095074968 " " y2[1] (numeric) = 1.2738912078441866 " " absolute error = 1.4770983366898527000E-3 " " relative error = 0.11608629027711595 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7570000000000002 " " y1[1] (analytic) = 2.6867438401959114 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.2073183015917084 " " relative error = 7.716340444892998 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2731004897835105 " " y2[1] (numeric) = 1.2745956094355333 " " absolute error = 1.4951196520227583000E-3 " " relative error = 0.11743924882763983 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7580000000000002 " " y1[1] (analytic) = 2.6874703962130866 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20804485760888358 " " relative error = 7.741289277159648 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2737875969589738 " " y2[1] (numeric) = 1.2753008881255414 " " absolute error = 1.5132911665676207000E-3 " " relative error = 0.11880247304813103 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7590000000000002 " " y1[1] (analytic) = 2.688196264759923 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.2087707261557199 " " relative error = 7.766201035710641 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2744754303467798 " " y2[1] (numeric) = 1.276007043914211 " " absolute error = 1.5316135674312560000E-3 " " relative error = 0.12017599798016583 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7600000000000002 " " y1[1] (analytic) = 2.6889214451105516 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.20949590650634864 " " relative error = 7.791075744785675 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2751639892590951 " " y2[1] (numeric) = 1.276714076801542 " " absolute error = 1.5500875424467875000E-3 " " relative error = 0.12155985861453243 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7610000000000002 " " y1[1] (analytic) = 2.6896459365397924 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.21022039793558944 " " relative error = 7.815913428591880 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2758532730073604 " " y2[1] (numeric) = 1.2774219867875343 " " absolute error = 1.5687137801738693000E-3 " " relative error = 0.12295408989124562 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7620000000000002 " " y1[1] (analytic) = 2.6903697383231546 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.21094419971895162 " " relative error = 7.840714111303835 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2765432809022927 " " y2[1] (numeric) = 1.2781307738721879 " " absolute error = 1.5874929698951323000E-3 " " relative error = 0.12435872669926652 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7630000000000002 " " y1[1] (analytic) = 2.691092849736836 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.21166731113263282 " " relative error = 7.865477817063500 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2772340122538837 " " y2[1] (numeric) = 1.278840438055503 " " absolute error = 1.6064258016192934000E-3 " " relative error = 0.12577380387674597 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.7640000000000002 " " y1[1] (analytic) = 2.6918152700577247 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.2123897314535217 " " relative error = 7.890204569980283 "%" h = 1.000E-3 " " y2[1] (analytic) = 1.2779254663714021 " " y2[1] (numeric) = 1.2795509793374795 " " absolute error = 1.6255129660773804000E-3 " " relative error = 0.12719935621072906 "%" h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff(y1,x,1) = diff(y2,x,5);" "diff(y2,x,1) = y1 - 2.0;" Iterations = 264 "Total Elapsed Time "= 15 Minutes 10 Seconds "Elapsed Time(since restart) "= 15 Minutes 10 Seconds "Expected Time Remaining "= 8 Hours 49 Minutes 0 Seconds "Optimized Time Remaining "= 8 Hours 48 Minutes 41 Seconds "Time to Timeout " Unknown Percent Done = 2.7894736842105288 "%" (%o54) true (%o54) diffeq.max