(%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_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 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_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 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_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 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_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 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_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), 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 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_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), 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 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_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) 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_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) 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_y2_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_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, 1, 1 array_complex_pole : glob_large_float) 1, 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 : 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_y1_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_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, 2, 1 array_complex_pole : glob_large_float) 2, 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 : 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_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) 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_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) 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_y2_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_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, 1, 1 array_complex_pole : glob_large_float) 1, 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 : 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_y1_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_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, 2, 1 array_complex_pole : glob_large_float) 2, 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 : 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_y2 ! > array_norms ! iii! iii then array_norms : !array_y2 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_y1 ! > array_norms ! iii! iii then array_norms : !array_y1 !, 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_y2 ! > array_norms ! iii! iii then array_norms : !array_y2 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_y1 ! > array_norms ! iii! iii then array_norms : !array_y1 !, iii : 1 + iii)) iii ! iii! (%i8) atomall() := (array_tmp1 : array_m1 array_y1 , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : array_const_1D0 + array_tmp2 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp5 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_tmp1 : ats(2, array_m1, array_y1, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 array_tmp3 : array_const_1D0 + array_tmp2 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 2 2 2 if not array_y1_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp5 glob_h factorial_3(1, 2), 2 array_y1 : temporary, array_y1_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_m1, array_y1, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 array_tmp3 : array_const_1D0 + array_tmp2 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 3 3 3 if not array_y1_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp5 glob_h factorial_3(2, 3), 3 array_y1 : temporary, array_y1_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_m1, array_y1, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 array_tmp3 : array_const_1D0 + array_tmp2 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 4 4 4 if not array_y1_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp5 glob_h factorial_3(3, 4), 4 array_y1 : temporary, array_y1_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_m1, array_y1, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 array_tmp3 : array_const_1D0 + array_tmp2 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp3 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 array_tmp5 : array_y2 - array_const_1D0 , 5 5 5 if not array_y1_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp5 glob_h factorial_3(4, 5), 5 array_y1 : temporary, array_y1_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_m1, array_y1, 1), array_tmp2 : kkk array_tmp1 + array_const_0D0 , array_tmp3 : kkk kkk kkk array_const_1D0 + array_tmp2 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 1, order_d + kkk order_d array_tmp3 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))), array_tmp5 : kkk array_y2 - array_const_1D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 2, order_d + kkk order_d array_tmp5 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))), kkk : 1 + kkk)) (%o8) atomall() := (array_tmp1 : array_m1 array_y1 , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : array_const_1D0 + array_tmp2 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp5 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_tmp1 : ats(2, array_m1, array_y1, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 array_tmp3 : array_const_1D0 + array_tmp2 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 2 2 2 if not array_y1_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp5 glob_h factorial_3(1, 2), 2 array_y1 : temporary, array_y1_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_m1, array_y1, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 array_tmp3 : array_const_1D0 + array_tmp2 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 3 3 3 if not array_y1_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp5 glob_h factorial_3(2, 3), 3 array_y1 : temporary, array_y1_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_m1, array_y1, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 array_tmp3 : array_const_1D0 + array_tmp2 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp3 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_tmp5 : array_y2 - array_const_1D0 , 4 4 4 if not array_y1_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp5 glob_h factorial_3(3, 4), 4 array_y1 : temporary, array_y1_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_m1, array_y1, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 array_tmp3 : array_const_1D0 + array_tmp2 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp3 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 array_tmp5 : array_y2 - array_const_1D0 , 5 5 5 if not array_y1_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp5 glob_h factorial_3(4, 5), 5 array_y1 : temporary, array_y1_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_m1, array_y1, 1), array_tmp2 : kkk array_tmp1 + array_const_0D0 , array_tmp3 : kkk kkk kkk array_const_1D0 + array_tmp2 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 1, order_d + kkk order_d array_tmp3 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))), array_tmp5 : kkk array_y2 - array_const_1D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 2, order_d + kkk order_d array_tmp5 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))), 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) := cos(x) + 1.0 (%o47) exact_soln_y1(x) := cos(x) + 1.0 (%i48) exact_soln_y2(x) := 1.0 - sin(x) (%o48) exact_soln_y2(x) := 1.0 - sin(x) (%i49) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_almost_1, 0.999, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_log10normmin, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_normmax, 0.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(years_in_century, 100.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_h, 0.1, float), define_variable(glob_disp_incr, 0.1, float), define_variable(min_in_hour, 60.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 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/mtest3postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 0.5,"), omniout_str(ALWAYS, "glob_h : 0.00001,"), 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, "glob_max_iter : 20,"), 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, "1.0 + cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "1.0 - sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* 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_type_pole, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_x, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y2_higher, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 2, 1 + max_terms), array(array_y2_higher_work, 1 + 2, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_fact_1 : 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_norms : 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_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 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 <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 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 <= 2 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term term : 1 + term), array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 0.5, glob_h : 1.0E-5, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), glob_max_iter : 20, 1 + 0 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_y2_set_initial : true, array_y2_set_initial : false, 1, 1 1, 2 array_y2_set_initial : false, array_y2_set_initial : false, 1, 3 1, 4 array_y2_set_initial : false, array_y2_set_initial : false, 1, 5 1, 6 array_y2_set_initial : false, array_y2_set_initial : false, 1, 7 1, 8 array_y2_set_initial : false, array_y2_set_initial : false, 1, 9 1, 10 array_y2_set_initial : false, array_y2_set_initial : false, 1, 11 1, 12 array_y2_set_initial : false, array_y2_set_initial : false, 1, 13 1, 14 array_y2_set_initial : false, array_y2_set_initial : false, 1, 15 1, 16 array_y2_set_initial : false, array_y2_set_initial : false, 1, 17 1, 18 array_y2_set_initial : false, array_y2_set_initial : false, 1, 19 1, 20 array_y2_set_initial : false, array_y2_set_initial : false, 1, 21 1, 22 array_y2_set_initial : false, array_y2_set_initial : false, 1, 23 1, 24 array_y2_set_initial : false, array_y2_set_initial : false, 1, 25 1, 26 array_y2_set_initial : false, array_y2_set_initial : false, 1, 27 1, 28 array_y2_set_initial : false, array_y2_set_initial : false, 1, 29 1, 30 array_y1_set_initial : true, array_y1_set_initial : false, 2, 1 2, 2 array_y1_set_initial : false, array_y1_set_initial : false, 2, 3 2, 4 array_y1_set_initial : false, array_y1_set_initial : false, 2, 5 2, 6 array_y1_set_initial : false, array_y1_set_initial : false, 2, 7 2, 8 array_y1_set_initial : false, array_y1_set_initial : false, 2, 9 2, 10 array_y1_set_initial : false, array_y1_set_initial : false, 2, 11 2, 12 array_y1_set_initial : false, array_y1_set_initial : false, 2, 13 2, 14 array_y1_set_initial : false, array_y1_set_initial : false, 2, 15 2, 16 array_y1_set_initial : false, array_y1_set_initial : false, 2, 17 2, 18 array_y1_set_initial : false, array_y1_set_initial : false, 2, 19 2, 20 array_y1_set_initial : false, array_y1_set_initial : false, 2, 21 2, 22 array_y1_set_initial : false, array_y1_set_initial : false, 2, 23 2, 24 array_y1_set_initial : false, array_y1_set_initial : false, 2, 25 2, 26 array_y1_set_initial : false, array_y1_set_initial : false, 2, 27 2, 28 array_y1_set_initial : false, array_y1_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_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), order_diff : 1, term_no : 1, 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), 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), 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), 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_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 : 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 order_diff : 1, ord : 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 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 ( y2 , x , 1 ) = m1 * y1 + 1.0;"), omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-17T21:41:44-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest3"), logitem_str(html_log_file, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 092 "), logitem_str(html_log_file, "mtest3 diffeq.max"), logitem_str(html_log_file, "\ mtest3 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 ( y1 , x , 1 ) = y2 - 1.0;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o49) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_almost_1, 0.999, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_log10normmin, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_normmax, 0.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(years_in_century, 100.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_h, 0.1, float), define_variable(glob_disp_incr, 0.1, float), define_variable(min_in_hour, 60.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 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/mtest3postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 0.5,"), omniout_str(ALWAYS, "glob_h : 0.00001,"), 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, "glob_max_iter : 20,"), 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, "1.0 + cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "1.0 - sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* 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_type_pole, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_x, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y2_higher, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 2, 1 + max_terms), array(array_y2_higher_work, 1 + 2, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_fact_1 : 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_norms : 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_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 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 <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 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 <= 2 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term term : 1 + term), array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 0.5, glob_h : 1.0E-5, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), glob_max_iter : 20, 1 + 0 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_y2_set_initial : true, array_y2_set_initial : false, 1, 1 1, 2 array_y2_set_initial : false, array_y2_set_initial : false, 1, 3 1, 4 array_y2_set_initial : false, array_y2_set_initial : false, 1, 5 1, 6 array_y2_set_initial : false, array_y2_set_initial : false, 1, 7 1, 8 array_y2_set_initial : false, array_y2_set_initial : false, 1, 9 1, 10 array_y2_set_initial : false, array_y2_set_initial : false, 1, 11 1, 12 array_y2_set_initial : false, array_y2_set_initial : false, 1, 13 1, 14 array_y2_set_initial : false, array_y2_set_initial : false, 1, 15 1, 16 array_y2_set_initial : false, array_y2_set_initial : false, 1, 17 1, 18 array_y2_set_initial : false, array_y2_set_initial : false, 1, 19 1, 20 array_y2_set_initial : false, array_y2_set_initial : false, 1, 21 1, 22 array_y2_set_initial : false, array_y2_set_initial : false, 1, 23 1, 24 array_y2_set_initial : false, array_y2_set_initial : false, 1, 25 1, 26 array_y2_set_initial : false, array_y2_set_initial : false, 1, 27 1, 28 array_y2_set_initial : false, array_y2_set_initial : false, 1, 29 1, 30 array_y1_set_initial : true, array_y1_set_initial : false, 2, 1 2, 2 array_y1_set_initial : false, array_y1_set_initial : false, 2, 3 2, 4 array_y1_set_initial : false, array_y1_set_initial : false, 2, 5 2, 6 array_y1_set_initial : false, array_y1_set_initial : false, 2, 7 2, 8 array_y1_set_initial : false, array_y1_set_initial : false, 2, 9 2, 10 array_y1_set_initial : false, array_y1_set_initial : false, 2, 11 2, 12 array_y1_set_initial : false, array_y1_set_initial : false, 2, 13 2, 14 array_y1_set_initial : false, array_y1_set_initial : false, 2, 15 2, 16 array_y1_set_initial : false, array_y1_set_initial : false, 2, 17 2, 18 array_y1_set_initial : false, array_y1_set_initial : false, 2, 19 2, 20 array_y1_set_initial : false, array_y1_set_initial : false, 2, 21 2, 22 array_y1_set_initial : false, array_y1_set_initial : false, 2, 23 2, 24 array_y1_set_initial : false, array_y1_set_initial : false, 2, 25 2, 26 array_y1_set_initial : false, array_y1_set_initial : false, 2, 27 2, 28 array_y1_set_initial : false, array_y1_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_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), order_diff : 1, term_no : 1, 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), 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), 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), 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_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 : 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 order_diff : 1, ord : 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 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 ( y2 , x , 1 ) = m1 * y1 + 1.0;"), omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-17T21:41:44-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest3"), logitem_str(html_log_file, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 092 "), logitem_str(html_log_file, "mtest3 diffeq.max"), logitem_str(html_log_file, "\ mtest3 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 ( y1 , x , 1 ) = y2 - 1.0;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i50) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/mtest3postode.ode#################" "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;" "diff ( y1 , x , 1 ) = y2 - 1.0;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms : 30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.1," "x_end : 0.5," "glob_h : 0.00001," "array_y1_init[0 + 1] : exact_soln_y1(x_start)," "array_y2_init[0 + 1] : exact_soln_y2(x_start)," "glob_max_iter : 20," "/* 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) := (" "1.0 + cos(x) " ");" "exact_soln_y2 (x) := (" "1.0 - sin(x) " ");" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.1 " " y2[1] (analytic) = 0.9001665833531718 " " y2[1] (numeric) = 0.9001665833531718 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9950041652780257 " " y1[1] (numeric) = 1.9950041652780257 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " x[1] = 0.1 " " y2[1] (analytic) = 0.9001665833531718 " " y2[1] (numeric) = 0.9001665833531718 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9950041652780257 " " y1[1] (numeric) = 1.9950041652780257 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.101 " " y2[1] (analytic) = 0.899171629270432 " " y2[1] (numeric) = 0.8991716292704319 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.234717587259694700000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9949038343759766 " " y1[1] (numeric) = 1.9949038343759766 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10200000000000001 " " y2[1] (analytic) = 0.8981767760160545 " " y2[1] (numeric) = 0.8981767760160544 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.236085205353062700000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9948025085701762 " " y1[1] (numeric) = 1.9948025085701762 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10300000000000001 " " y2[1] (analytic) = 0.8971820245848925 " " y2[1] (numeric) = 0.8971820245848924 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.237455716011289500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.99470018796195 " " y1[1] (numeric) = 1.99470018796195 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10400000000000001 " " y2[1] (analytic) = 0.8961873759716973 " " y2[1] (numeric) = 0.8961873759716972 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.238829127024233800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9945968726536185 " " y1[1] (numeric) = 1.9945968726536185 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10500000000000001 " " y2[1] (analytic) = 0.8951928311711175 " " y2[1] (numeric) = 0.8951928311711174 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.240205446208422400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9944925627484973 " " y1[1] (numeric) = 1.9944925627484975 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113288708477529900000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10600000000000001 " " y2[1] (analytic) = 0.8941983911776978 " " y2[1] (numeric) = 0.8941983911776976 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.483169362814319000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9943872583508964 " " y1[1] (numeric) = 1.9943872583508966 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113347490540196500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10700000000000001 " " y2[1] (analytic) = 0.8932040569858781 " " y2[1] (numeric) = 0.8932040569858779 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.485933680981275400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9942809595661202 " " y1[1] (numeric) = 1.9942809595661202 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10800000000000001 " " y2[1] (analytic) = 0.8922098295899925 " " y2[1] (numeric) = 0.8922098295899923 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.488703862712093600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9941736665004668 " " y1[1] (numeric) = 1.994173666500467 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113466738905908300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10900000000000001 " " y2[1] (analytic) = 0.8912157099842684 " " y2[1] (numeric) = 0.8912157099842681 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.491479923855368700000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.99406537926123 " " y1[1] (numeric) = 1.9940653792612302 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11352720544847600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11000000000000001 " " y2[1] (analytic) = 0.8902216991628251 " " y2[1] (numeric) = 0.8902216991628249 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.49426188031413600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9939560979566968 " " y1[1] (numeric) = 1.993956097956697 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113588233725763300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11100000000000002 " " y2[1] (analytic) = 0.8892277981196737 " " y2[1] (numeric) = 0.8892277981196733 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.745574622069139400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9938458226961484 " " y1[1] (numeric) = 1.9938458226961486 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113649823860376500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11200000000000002 " " y2[1] (analytic) = 0.8882340078487148 " " y2[1] (numeric) = 0.8882340078487144 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.749765314595738000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9937345535898603 " " y1[1] (numeric) = 1.9937345535898603 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11300000000000002 " " y2[1] (analytic) = 0.8872403293437388 " " y2[1] (numeric) = 0.8872403293437384 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.75396492215254800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9936222907491012 " " y1[1] (numeric) = 1.9936222907491012 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11400000000000002 " " y2[1] (analytic) = 0.886246763598424 " " y2[1] (numeric) = 0.8862467635984237 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.758173468924126400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9935090342861344 " " y1[1] (numeric) = 1.9935090342861344 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11500000000000002 " " y2[1] (analytic) = 0.8852533116063361 " " y2[1] (numeric) = 0.8852533116063358 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.762390979178383000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9933947843142157 " " y1[1] (numeric) = 1.993394784314216 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11390180546409400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11600000000000002 " " y2[1] (analytic) = 0.8842599743609272 " " y2[1] (numeric) = 0.8842599743609267 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.022156636355898000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9932795409475959 " " y1[1] (numeric) = 1.9932795409475959 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11700000000000002 " " y2[1] (analytic) = 0.8832667528555341 " " y2[1] (numeric) = 0.8832667528555337 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.027803983500523000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9931633043015178 " " y1[1] (numeric) = 1.9931633043015178 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11800000000000002 " " y2[1] (analytic) = 0.8822736480833785 " " y2[1] (numeric) = 0.882273648083378 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.03346337969843100000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.993046074492218 " " y1[1] (numeric) = 1.993046074492218 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11900000000000002 " " y2[1] (analytic) = 0.8812806610375651 " " y2[1] (numeric) = 0.8812806610375645 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.29891857219497500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9929278516369267 " " y1[1] (numeric) = 1.9929278516369267 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12000000000000002 " " y2[1] (analytic) = 0.8802877927110806 " " y2[1] (numeric) = 0.8802877927110802 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.044818450592977000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9928086358538661 " " y1[1] (numeric) = 1.9928086358538664 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114229439445855500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12100000000000002 " " y2[1] (analytic) = 0.8792950440967935 " " y2[1] (numeric) = 0.879295044096793 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.05051419124315000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.992688427262253 " " y1[1] (numeric) = 1.992688427262253 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12200000000000003 " " y2[1] (analytic) = 0.8783024161874522 " " y2[1] (numeric) = 0.8783024161874518 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.05622211285460700000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9925672259822949 " " y1[1] (numeric) = 1.9925672259822949 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12300000000000003 " " y2[1] (analytic) = 0.8773099099756847 " " y2[1] (numeric) = 0.8773099099756841 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.32742781086290900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9924450321351936 " " y1[1] (numeric) = 1.9924450321351936 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12400000000000003 " " y2[1] (analytic) = 0.8763175264539969 " " y2[1] (numeric) = 0.8763175264539963 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.33459329016078300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9923218458431429 " " y1[1] (numeric) = 1.9923218458431429 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12500000000000003 " " y2[1] (analytic) = 0.8753252666147723 " " y2[1] (numeric) = 0.8753252666147717 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.34177412082954300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9921976672293291 " " y1[1] (numeric) = 1.9921976672293291 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12600000000000003 " " y2[1] (analytic) = 0.8743331314502707 " " y2[1] (numeric) = 0.8743331314502701 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.34897034488222800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9920724964179306 " " y1[1] (numeric) = 1.9920724964179308 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11464118562102300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12700000000000003 " " y2[1] (analytic) = 0.8733411219526273 " " y2[1] (numeric) = 0.8733411219526267 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.35618200447784800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9919463335341185 " " y1[1] (numeric) = 1.9919463335341188 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114711783078407300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12800000000000003 " " y2[1] (analytic) = 0.8723492391138512 " " y2[1] (numeric) = 0.8723492391138508 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.09072731353760100000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9918191787040556 " " y1[1] (numeric) = 1.9918191787040558 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114782944652139400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12900000000000003 " " y2[1] (analytic) = 0.8713574839258255 " " y2[1] (numeric) = 0.871357483925825 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.096521439733980000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9916910320548964 " " y1[1] (numeric) = 1.9916910320548968 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.229709340970825500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13000000000000003 " " y2[1] (analytic) = 0.8703658573803051 " " y2[1] (numeric) = 0.8703658573803046 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.3779100203148600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.991561893714788 " " y1[1] (numeric) = 1.9915618937147883 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114926960722569200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13100000000000003 " " y2[1] (analytic) = 0.8693743604689166 " " y2[1] (numeric) = 0.869374360468916 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.38518384661317000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9914317638128685 " " y1[1] (numeric) = 1.9914317638128687 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114999815509101500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13200000000000003 " " y2[1] (analytic) = 0.8683829941831567 " " y2[1] (numeric) = 0.8683829941831561 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.39247332146045900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9913006424792679 " " y1[1] (numeric) = 1.9913006424792679 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13300000000000003 " " y2[1] (analytic) = 0.8673917595143915 " " y2[1] (numeric) = 0.8673917595143911 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.11982279032355000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9911685298451072 " " y1[1] (numeric) = 1.9911685298451072 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13400000000000004 " " y2[1] (analytic) = 0.8664006574538559 " " y2[1] (numeric) = 0.8664006574538554 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.12567951131448300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9910354260424992 " " y1[1] (numeric) = 1.9910354260424994 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115221768637137800000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13500000000000004 " " y2[1] (analytic) = 0.8654096889926517 " " y2[1] (numeric) = 0.8654096889926511 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.41443606852536400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9909013312045478 " " y1[1] (numeric) = 1.990901331204548 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11529688309911600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13600000000000004 " " y2[1] (analytic) = 0.8644188551217472 " " y2[1] (numeric) = 0.8644188551217467 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.42178856955167600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9907662454653479 " " y1[1] (numeric) = 1.990766245465348 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115372562855201900000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13700000000000004 " " y2[1] (analytic) = 0.8634281568319764 " " y2[1] (numeric) = 0.8634281568319758 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.42915693587466900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.990630168959985 " " y1[1] (numeric) = 1.9906301689599852 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115448808057800400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13800000000000004 " " y2[1] (analytic) = 0.8624375951140373 " " y2[1] (numeric) = 0.8624375951140367 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.43654121129978900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9904931018245358 " " y1[1] (numeric) = 1.990493101824536 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115525618860470600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13900000000000004 " " y2[1] (analytic) = 0.8614471709584917 " " y2[1] (numeric) = 0.8614471709584911 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.44394143978593400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9903550441960673 " " y1[1] (numeric) = 1.9903550441960673 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14000000000000004 " " y2[1] (analytic) = 0.8604568853557635 " " y2[1] (numeric) = 0.8604568853557629 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.45135766544610200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9902159962126371 " " y1[1] (numeric) = 1.9902159962126371 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14100000000000004 " " y2[1] (analytic) = 0.8594667392961384 " " y2[1] (numeric) = 0.8594667392961378 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.45878993254803200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9900759580132932 " " y1[1] (numeric) = 1.9900759580132932 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14200000000000004 " " y2[1] (analytic) = 0.8584767337697622 " " y2[1] (numeric) = 0.8584767337697616 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.46623828551485800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.989934929738074 " " y1[1] (numeric) = 1.9899349297380737 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115838521183494200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14300000000000004 " " y2[1] (analytic) = 0.8574868697666405 " " y2[1] (numeric) = 0.8574868697666399 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.4737027689257600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9897929115280073 " " y1[1] (numeric) = 1.989792911528007 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115918162330361300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14400000000000004 " " y2[1] (analytic) = 0.8564971482766371 " " y2[1] (numeric) = 0.8564971482766366 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.48118342751661600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9896499035251116 " " y1[1] (numeric) = 1.9896499035251114 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115998370022934400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14500000000000005 " " y2[1] (analytic) = 0.8555075702894736 " " y2[1] (numeric) = 0.855507570289473 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.4886803061806700000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9895059058723947 " " y1[1] (numeric) = 1.9895059058723947 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14600000000000005 " " y2[1] (analytic) = 0.8545181367947277 " " y2[1] (numeric) = 0.8545181367947271 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.49619344996918600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9893609187138546 " " y1[1] (numeric) = 1.9893609187138546 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14700000000000005 " " y2[1] (analytic) = 0.8535288487818328 " " y2[1] (numeric) = 0.8535288487818322 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.50372290409211600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.989214942194478 " " y1[1] (numeric) = 1.989214942194478 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14800000000000005 " " y2[1] (analytic) = 0.852539707240077 " " y2[1] (numeric) = 0.8525397072400764 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.51126871391877200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.989067976460242 " " y1[1] (numeric) = 1.989067976460242 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14900000000000005 " " y2[1] (analytic) = 0.8515507131586016 " " y2[1] (numeric) = 0.8515507131586011 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.51883092497849400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9889200216581118 " " y1[1] (numeric) = 1.9889200216581118 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15000000000000005 " " y2[1] (analytic) = 0.8505618675264007 " " y2[1] (numeric) = 0.8505618675264002 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.52640958296132600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9887710779360424 " " y1[1] (numeric) = 1.9887710779360424 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15100000000000005 " " y2[1] (analytic) = 0.8495731713323198 " " y2[1] (numeric) = 0.8495731713323194 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.22720378697495800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9886211454429774 " " y1[1] (numeric) = 1.9886211454429774 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15200000000000005 " " y2[1] (analytic) = 0.8485846255650551 " " y2[1] (numeric) = 0.8485846255650547 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.233293138611281000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9884702243288492 " " y1[1] (numeric) = 1.9884702243288492 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15300000000000005 " " y2[1] (analytic) = 0.8475962312131522 " " y2[1] (numeric) = 0.8475962312131518 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.2393957582190300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9883183147445793 " " y1[1] (numeric) = 1.988318314744579 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116745760869558200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15400000000000005 " " y2[1] (analytic) = 0.8466079892650054 " " y2[1] (numeric) = 0.8466079892650049 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.24551168286995400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9881654168420768 " " y1[1] (numeric) = 1.9881654168420766 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116831643102001900000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15500000000000005 " " y2[1] (analytic) = 0.8456199007088565 " " y2[1] (numeric) = 0.8456199007088561 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.251640949767107000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9880115307742399 " " y1[1] (numeric) = 1.9880115307742396 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116918093722298700000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15600000000000006 " " y2[1] (analytic) = 0.844631966532794 " " y2[1] (numeric) = 0.8446319665327936 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.257783596245410000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9878566566949545 " " y1[1] (numeric) = 1.9878566566949543 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117005112904904300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15700000000000006 " " y2[1] (analytic) = 0.8436441877247521 " " y2[1] (numeric) = 0.8436441877247517 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.263939659772200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9877007947590948 " " y1[1] (numeric) = 1.9877007947590946 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117092700825441200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15800000000000006 " " y2[1] (analytic) = 0.8426565652725094 " " y2[1] (numeric) = 0.842656565272509 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.27010917794780600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9875439451225225 " " y1[1] (numeric) = 1.9875439451225223 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11718085766070100000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15900000000000006 " " y2[1] (analytic) = 0.8416691001636885 " " y2[1] (numeric) = 0.8416691001636879 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.59536523563262200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9873861079420876 " " y1[1] (numeric) = 1.9873861079420874 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117269583588644500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16000000000000006 " " y2[1] (analytic) = 0.840681793385754 " " y2[1] (numeric) = 0.8406817933857534 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.60311091164383800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9872272833756268 " " y1[1] (numeric) = 1.9872272833756266 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117358878788402300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16100000000000006 " " y2[1] (analytic) = 0.8396946459260128 " " y2[1] (numeric) = 0.8396946459260124 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.288698838377400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9870674715819652 " " y1[1] (numeric) = 1.9870674715819647 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.234897486880551600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16200000000000006 " " y2[1] (analytic) = 0.8387076587716125 " " y2[1] (numeric) = 0.838707658771612 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.29492255383102500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.986906672720914 " " y1[1] (numeric) = 1.9869066727209137 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117539177725738300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16300000000000006 " " y2[1] (analytic) = 0.8377208329095399 " " y2[1] (numeric) = 0.8377208329095395 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.30115991394972200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9867448869532724 " " y1[1] (numeric) = 1.9867448869532722 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117630181827435200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16400000000000006 " " y2[1] (analytic) = 0.8367341693266209 " " y2[1] (numeric) = 0.8367341693266205 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.307410957143683000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9865821144408262 " " y1[1] (numeric) = 1.986582114440826 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117721755929184800000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16500000000000006 " " y2[1] (analytic) = 0.8357476690095189 " " y2[1] (numeric) = 0.8357476690095186 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.98525679147007500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9864183553463477 " " y1[1] (numeric) = 1.9864183553463475 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117813900215979800000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16600000000000006 " " y2[1] (analytic) = 0.8347613329447343 " " y2[1] (numeric) = 0.834761332944734 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.989965685312807400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9862536098335961 " " y1[1] (numeric) = 1.986253609833596 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117906614873987500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16700000000000007 " " y2[1] (analytic) = 0.8337751621186029 " " y2[1] (numeric) = 0.8337751621186026 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.99468492850316940000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9860878780673166 " " y1[1] (numeric) = 1.9860878780673166 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16800000000000007 " " y2[1] (analytic) = 0.8327891575172957 " " y2[1] (numeric) = 0.8327891575172952 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.33255273368325100000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9859211602132416 " " y1[1] (numeric) = 1.9859211602132414 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118093756054187500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16900000000000007 " " y2[1] (analytic) = 0.8318033201268169 " " y2[1] (numeric) = 0.8318033201268165 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.3388727732218800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.985753456438088 " " y1[1] (numeric) = 1.985753456438088 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17000000000000007 " " y2[1] (analytic) = 0.8308176509330039 " " y2[1] (numeric) = 0.8308176509330035 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.00890504689584500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9855847669095605 " " y1[1] (numeric) = 1.9855847669095605 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17100000000000007 " " y2[1] (analytic) = 0.829832150921526 " " y2[1] (numeric) = 0.8298321509215256 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.01366598073691400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9854150917963485 " " y1[1] (numeric) = 1.9854150917963482 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118378750330398200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17200000000000007 " " y2[1] (analytic) = 0.8288468210778829 " " y2[1] (numeric) = 0.8288468210778825 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.018437411081657300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9852444312681263 " " y1[1] (numeric) = 1.9852444312681263 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17300000000000007 " " y2[1] (analytic) = 0.8278616623874044 " " y2[1] (numeric) = 0.8278616623874041 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.02321936767843300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9850727854955552 " " y1[1] (numeric) = 1.9850727854955552 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17400000000000007 " " y2[1] (analytic) = 0.8268766758352494 " " y2[1] (numeric) = 0.8268766758352489 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.37068250717649900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9849001546502807 " " y1[1] (numeric) = 1.9849001546502807 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17500000000000007 " " y2[1] (analytic) = 0.825891862406404 " " y2[1] (numeric) = 0.8258918624064036 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.377086638874469000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9847265389049333 " " y1[1] (numeric) = 1.9847265389049336 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118766744800740700000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17600000000000007 " " y2[1] (analytic) = 0.8249072230856817 " " y2[1] (numeric) = 0.8249072230856812 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.38350492542524200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9845519384331296 " " y1[1] (numeric) = 1.9845519384331296 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17700000000000007 " " y2[1] (analytic) = 0.8239227588577217 " " y2[1] (numeric) = 0.8239227588577213 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.38993740706645200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.984376353409469 " " y1[1] (numeric) = 1.9843763534094692 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118964175034256600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17800000000000007 " " y2[1] (analytic) = 0.8229384707069882 " " y2[1] (numeric) = 0.8229384707069878 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.39638412418056800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9841997840095373 " " y1[1] (numeric) = 1.9841997840095373 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17900000000000008 " " y2[1] (analytic) = 0.8219543596177692 " " y2[1] (numeric) = 0.8219543596177687 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.40284511729551500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9840222304099036 " " y1[1] (numeric) = 1.9840222304099036 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18000000000000008 " " y2[1] (analytic) = 0.8209704265741757 " " y2[1] (numeric) = 0.8209704265741753 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.40932042708530600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9838436927881213 " " y1[1] (numeric) = 1.9838436927881213 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18100000000000008 " " y2[1] (analytic) = 0.8199866725601408 " " y2[1] (numeric) = 0.8199866725601404 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.41581009437066800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9836641713227285 " " y1[1] (numeric) = 1.9836641713227283 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11936590948743900000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18200000000000008 " " y2[1] (analytic) = 0.8190030985594183 " " y2[1] (numeric) = 0.8190030985594179 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.42231416011967800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.983483666193246 " " y1[1] (numeric) = 1.983483666193246 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18300000000000008 " " y2[1] (analytic) = 0.8180197055555822 " " y2[1] (numeric) = 0.8180197055555818 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.42883266544839900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9833021775801796 " " y1[1] (numeric) = 1.9833021775801793 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11957021695981400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18400000000000008 " " y2[1] (analytic) = 0.8170364945320253 " " y2[1] (numeric) = 0.817036494532025 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.07652423871614200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9831197056650174 " " y1[1] (numeric) = 1.9831197056650172 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.119673231478334200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18500000000000008 " " y2[1] (analytic) = 0.8160534664719588 " " y2[1] (numeric) = 0.8160534664719583 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.44191316005300600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9829362506302315 " " y1[1] (numeric) = 1.9829362506302313 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.1197768201295400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18600000000000008 " " y2[1] (analytic) = 0.8150706223584103 " " y2[1] (numeric) = 0.8150706223584099 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.448475232306724000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9827518126592767 " " y1[1] (numeric) = 1.9827518126592767 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18700000000000008 " " y2[1] (analytic) = 0.814087963174224 " " y2[1] (numeric) = 0.8140879631742237 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.091288932572841300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9825663919365915 " " y1[1] (numeric) = 1.9825663919365912 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.119985720670548800000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18800000000000008 " " y2[1] (analytic) = 0.8131054899020592 " " y2[1] (numeric) = 0.8131054899020589 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.09623242646739200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.982379988647596 " " y1[1] (numeric) = 1.9823799886475957 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120091032983605200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18900000000000008 " " y2[1] (analytic) = 0.8121232035243888 " " y2[1] (numeric) = 0.8121232035243885 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.101186937426848400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9821926029786936 " " y1[1] (numeric) = 1.9821926029786934 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.12019692027585500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.19000000000000009 " " y2[1] (analytic) = 0.8111411050234993 " " y2[1] (numeric) = 0.811141105023499 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.106152497078763300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9820042351172704 " " y1[1] (numeric) = 1.98200423511727 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24060676552382320000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1910000000000001 " " y2[1] (analytic) = 0.8101591953814891 " " y2[1] (numeric) = 0.8101591953814887 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.111129137165589500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9818148852516937 " " y1[1] (numeric) = 1.9818148852516932 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.240820841315169200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1920000000000001 " " y2[1] (analytic) = 0.8091774755802675 " " y2[1] (numeric) = 0.8091774755802672 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.116116889545177000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9816245535713135 " " y1[1] (numeric) = 1.981624553571313 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.241036068359762700000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1930000000000001 " " y2[1] (analytic) = 0.8081959466015546 " " y2[1] (numeric) = 0.8081959466015542 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.12111578619127800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9814332402664618 " " y1[1] (numeric) = 1.9814332402664612 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36187867064101900000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1940000000000001 " " y2[1] (analytic) = 0.8072146094268791 " " y2[1] (numeric) = 0.8072146094268787 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.126125859194048600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9812409455284512 " " y1[1] (numeric) = 1.9812409455284508 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24146997795672900000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1950000000000001 " " y2[1] (analytic) = 0.806233465037578 " " y2[1] (numeric) = 0.8062334650375776 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.131147140760560400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9810476695495773 " " y1[1] (numeric) = 1.9810476695495767 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.362532992083678300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1960000000000001 " " y2[1] (analytic) = 0.8052525144147957 " " y2[1] (numeric) = 0.8052525144147954 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.13617966321530800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9808534125231154 " " y1[1] (numeric) = 1.9808534125231148 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36286274675219300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1970000000000001 " " y2[1] (analytic) = 0.8042717585394829 " " y2[1] (numeric) = 0.8042717585394825 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.14122345900072100000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9806581746433225 " " y1[1] (numeric) = 1.980658174643322 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24212948773977300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1980000000000001 " " y2[1] (analytic) = 0.8032911983923952 " " y2[1] (numeric) = 0.8032911983923948 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.14627856067768140000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.980461956105437 " " y1[1] (numeric) = 1.9804619561054364 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36352744732870750000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1990000000000001 " " y2[1] (analytic) = 0.8023108349540926 " " y2[1] (numeric) = 0.8023108349540923 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.1513450009260400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.980264757105677 " " y1[1] (numeric) = 1.9802647571056764 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36386239458558200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2000000000000001 " " y2[1] (analytic) = 0.8013306692049387 " " y2[1] (numeric) = 0.8013306692049383 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.15642281254513900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9800665778412416 " " y1[1] (numeric) = 1.980066577841241 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36419907406014240000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2010000000000001 " " y2[1] (analytic) = 0.800350702125099 " " y2[1] (numeric) = 0.8003507021250986 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.16151202845433200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.97986741851031 " " y1[1] (numeric) = 1.9798674185103093 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36453748643586300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2020000000000001 " " y2[1] (analytic) = 0.7993709346945406 " " y2[1] (numeric) = 0.7993709346945401 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.555483575591350000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9796672793120416 " " y1[1] (numeric) = 1.979667279312041 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36487763239984200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2030000000000001 " " y2[1] (analytic) = 0.7983913678930307 " " y2[1] (numeric) = 0.7983913678930302 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.562299740564858000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9794661604465755 " " y1[1] (numeric) = 1.9794661604465749 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.365219512642800300000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2040000000000001 " " y2[1] (analytic) = 0.7974120027001361 " " y2[1] (numeric) = 0.7974120027001357 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.56913124390304400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9792640621150306 " " y1[1] (numeric) = 1.97926406211503 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.365563127859085000000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2050000000000001 " " y2[1] (analytic) = 0.7964328400952219 " " y2[1] (numeric) = 0.7964328400952215 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.18198359760912600000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.979060984519505 " " y1[1] (numeric) = 1.9790609845195044 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36590847874667200000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2060000000000001 " " y2[1] (analytic) = 0.7954538810574507 " " y2[1] (numeric) = 0.7954538810574503 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.582840443995379000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9788569278630765 " " y1[1] (numeric) = 1.978856927863076 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.244170377338116400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2070000000000001 " " y2[1] (analytic) = 0.7944751265657815 " " y2[1] (numeric) = 0.794475126565781 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.58971823032011100000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.978651892349802 " " y1[1] (numeric) = 1.9786518923498013 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36660439034583600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2080000000000001 " " y2[1] (analytic) = 0.7934965775989684 " " y2[1] (numeric) = 0.793496577598968 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.596611534152128000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9784458781847165 " " y1[1] (numeric) = 1.9784458781847158 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.366954952471541400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2090000000000001 " " y2[1] (analytic) = 0.7925182351355606 " " y2[1] (numeric) = 0.7925182351355602 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.60352040068959300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9782388855738344 " " y1[1] (numeric) = 1.9782388855738338 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36730725309681840000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2100000000000001 " " y2[1] (analytic) = 0.7915401001539003 " " y2[1] (numeric) = 0.7915401001539 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.20783365647284700000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9780309147241484 " " y1[1] (numeric) = 1.9780309147241475 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.4902150572504500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2110000000000001 " " y2[1] (analytic) = 0.7905621736321226 " " y2[1] (numeric) = 0.7905621736321222 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.21303875262991230000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9778219658436287 " " y1[1] (numeric) = 1.977821965843628 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.368017072714420400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2120000000000001 " " y2[1] (analytic) = 0.7895844565481537 " " y2[1] (numeric) = 0.7895844565481533 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.21825562326320300000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.977612039141225 " " y1[1] (numeric) = 1.9776120391412242 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.491166124200049500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2130000000000001 " " y2[1] (analytic) = 0.7886069498797108 " " y2[1] (numeric) = 0.7886069498797104 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.631312403698715000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9774011348268636 " " y1[1] (numeric) = 1.9774011348268627 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.49164513996241800000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2140000000000001 " " y2[1] (analytic) = 0.7876296546043003 " " y2[1] (numeric) = 0.7876296546042999 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.63829976758772400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9771892531114488 " " y1[1] (numeric) = 1.9771892531114479 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.492126478547377500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2150000000000001 " " y2[1] (analytic) = 0.7866525716992177 " " y2[1] (numeric) = 0.7866525716992172 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.645302968892644000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9769763942068623 " " y1[1] (numeric) = 1.9769763942068614 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.492610140934187000000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2160000000000001 " " y2[1] (analytic) = 0.7856757021415454 " " y2[1] (numeric) = 0.785675702141545 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.23924154049430500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9767625583259631 " " y1[1] (numeric) = 1.9767625583259623 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.4930961281069900000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2170000000000001 " " y2[1] (analytic) = 0.7846990469081532 " " y2[1] (numeric) = 0.7846990469081528 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.244517802078221500000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9765477456825868 " " y1[1] (numeric) = 1.976547745682586 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.493584441054820400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2180000000000001 " " y2[1] (analytic) = 0.7837226069756962 " " y2[1] (numeric) = 0.7837226069756957 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.666408061951366000000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9763319564915465 " " y1[1] (numeric) = 1.9763319564915454 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.61759385096450700000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2190000000000001 " " y2[1] (analytic) = 0.7827463833206141 " " y2[1] (numeric) = 0.7827463833206136 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.6734750784298800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9761151909686308 " " y1[1] (numeric) = 1.9761151909686296 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.61821006032021600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2200000000000001 " " y2[1] (analytic) = 0.7817703769191305 " " y2[1] (numeric) = 0.7817703769191302 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.26041862445755870000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9758974493306054 " " y1[1] (numeric) = 1.9758974493306043 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.618829180640310000000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2210000000000001 " " y2[1] (analytic) = 0.7807945887472519 " " y2[1] (numeric) = 0.7807945887472516 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.26574302880271100000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9756787317952123 " " y1[1] (numeric) = 1.975678731795211 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74334145582270300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22200000000000011 " " y2[1] (analytic) = 0.7798190197807664 " " y2[1] (numeric) = 0.779819019780766 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.69477274323100200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9754590385811683 " " y1[1] (numeric) = 1.9754590385811672 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.62007615922297600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22300000000000011 " " y2[1] (analytic) = 0.7788436709952427 " " y2[1] (numeric) = 0.7788436709952422 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.70190432802239800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9752383699081673 " " y1[1] (numeric) = 1.9752383699081661 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.620704020025558000000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22400000000000012 " " y2[1] (analytic) = 0.7778685433660295 " " y2[1] (numeric) = 0.7778685433660291 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.70905217388504900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9750167259968778 " " y1[1] (numeric) = 1.9750167259968765 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.7456017562470700000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22500000000000012 " " y2[1] (analytic) = 0.7768936378682545 " " y2[1] (numeric) = 0.776893637868254 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.7162163287707490000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9747941070689432 " " y1[1] (numeric) = 1.974794107068942 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.62196849104936500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22600000000000012 " " y2[1] (analytic) = 0.7759189554768229 " " y2[1] (numeric) = 0.7759189554768225 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.29254763060748400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.974570513346983 " " y1[1] (numeric) = 1.9745705133469817 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74712612461702300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22700000000000012 " " y2[1] (analytic) = 0.7749444971664172 " " y2[1] (numeric) = 0.7749444971664169 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.297945318734507400000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9743459450545906 " " y1[1] (numeric) = 1.9743459450545893 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74789356387768500000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22800000000000012 " " y2[1] (analytic) = 0.7739702639114957 " " y2[1] (numeric) = 0.7739702639114954 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.303355347326800000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9741204024163344 " " y1[1] (numeric) = 1.974120402416333 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74866450860588400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.22900000000000012 " " y2[1] (analytic) = 0.7729962566862913 " " y2[1] (numeric) = 0.772996256686291 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.30877775288783900000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9738938856577568 " " y1[1] (numeric) = 1.9738938856577555 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74943896037369400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.23000000000000012 " " y2[1] (analytic) = 0.7720224764648115 " " y2[1] (numeric) = 0.7720224764648111 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.31421257205751860000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9736663950053748 " " y1[1] (numeric) = 1.9736663950053734 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.75021692076061200000000000000E-14 "%" h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;" "diff ( y1 , x , 1 ) = y2 - 1.0;" Iterations = 130 "Total Elapsed Time "= 15 Minutes 11 Seconds "Elapsed Time(since restart) "= 15 Minutes 10 Seconds "Expected Time Remaining "= 31 Minutes 10 Seconds "Optimized Time Remaining "= 31 Minutes 9 Seconds "Time to Timeout " Unknown Percent Done = 32.75000000000003 "%" (%o50) true (%o50) diffeq.max