(%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 - 5 + 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 - 5 + 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 - 5 + 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 - 5 + 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_y1 + array_const_0D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 1, 6 5 then (temporary : array_tmp1 glob_h factorial_3(0, 5), 1 array_y2 : temporary, array_y2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 5 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 4 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 3 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 2 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 6, 1 array_tmp3 : array_m1 array_y2 , array_tmp4 : 1 1 1 1 array_const_1D0 + array_tmp3 , if not array_y1_set_initial 1 1 2, 2 then (if 1 <= glob_max_terms then (temporary : 1 array_tmp4 glob_h factorial_3(0, 1), array_y1 : temporary, 1 2 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 2 glob_h array_y1_higher : temporary)), kkk : 2, 2, 1 array_tmp1 : array_y1 + array_const_0D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 1, 7 5 then (temporary : array_tmp1 glob_h factorial_3(1, 6), 2 array_y2 : temporary, array_y2_higher : temporary, 7 1, 7 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 6 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 5 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 4 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 3 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 3, glob_h 6, 2 array_tmp3 : ats(2, array_m1, array_y2, 1), 2 array_tmp4 : array_const_1D0 + array_tmp3 , 2 2 2 if not array_y1_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp4 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 : array_y1 + array_const_0D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 1, 8 5 then (temporary : array_tmp1 glob_h factorial_3(2, 7), 3 array_y2 : temporary, array_y2_higher : temporary, 8 1, 8 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 7 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 6 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 5 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 4 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 4, glob_h 6, 3 array_tmp3 : ats(3, array_m1, array_y2, 1), 3 array_tmp4 : array_const_1D0 + array_tmp3 , 3 3 3 if not array_y1_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp4 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 : array_y1 + array_const_0D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 1, 9 5 then (temporary : array_tmp1 glob_h factorial_3(3, 8), 4 array_y2 : temporary, array_y2_higher : temporary, 9 1, 9 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 8 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 7 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 6 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 5 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 5, glob_h 6, 4 array_tmp3 : ats(4, array_m1, array_y2, 1), 4 array_tmp4 : array_const_1D0 + array_tmp3 , 4 4 4 if not array_y1_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp4 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 : array_y1 + array_const_0D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 1, 10 5 then (temporary : array_tmp1 glob_h factorial_3(4, 9), 5 array_y2 : temporary, array_y2_higher : temporary, 10 1, 10 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 9 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 8 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 7 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 6 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 6, glob_h 6, 5 array_tmp3 : ats(5, array_m1, array_y2, 1), 5 array_tmp4 : array_const_1D0 + array_tmp3 , 5 5 5 if not array_y1_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp4 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 array_y1 + array_const_0D0 , order_d : 5, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 1, order_d + kkk order_d array_tmp1 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_tmp3 : kkk ats(kkk, array_m1, array_y2, 1), array_tmp4 : kkk array_const_1D0 + array_tmp3 , 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_tmp4 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_y1 + array_const_0D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 1, 6 5 then (temporary : array_tmp1 glob_h factorial_3(0, 5), 1 array_y2 : temporary, array_y2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 5 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 4 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 3 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 2 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 6, 1 array_tmp3 : array_m1 array_y2 , array_tmp4 : 1 1 1 1 array_const_1D0 + array_tmp3 , if not array_y1_set_initial 1 1 2, 2 then (if 1 <= glob_max_terms then (temporary : 1 array_tmp4 glob_h factorial_3(0, 1), array_y1 : temporary, 1 2 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 2 glob_h array_y1_higher : temporary)), kkk : 2, 2, 1 array_tmp1 : array_y1 + array_const_0D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 1, 7 5 then (temporary : array_tmp1 glob_h factorial_3(1, 6), 2 array_y2 : temporary, array_y2_higher : temporary, 7 1, 7 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 6 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 5 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 4 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 3 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 3, glob_h 6, 2 array_tmp3 : ats(2, array_m1, array_y2, 1), 2 array_tmp4 : array_const_1D0 + array_tmp3 , 2 2 2 if not array_y1_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp4 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 : array_y1 + array_const_0D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 1, 8 5 then (temporary : array_tmp1 glob_h factorial_3(2, 7), 3 array_y2 : temporary, array_y2_higher : temporary, 8 1, 8 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 7 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 6 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 5 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 4 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 4, glob_h 6, 3 array_tmp3 : ats(3, array_m1, array_y2, 1), 3 array_tmp4 : array_const_1D0 + array_tmp3 , 3 3 3 if not array_y1_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp4 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 : array_y1 + array_const_0D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 1, 9 5 then (temporary : array_tmp1 glob_h factorial_3(3, 8), 4 array_y2 : temporary, array_y2_higher : temporary, 9 1, 9 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 8 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 7 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 6 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 5 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 5, glob_h 6, 4 array_tmp3 : ats(4, array_m1, array_y2, 1), 4 array_tmp4 : array_const_1D0 + array_tmp3 , 4 4 4 if not array_y1_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp4 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 : array_y1 + array_const_0D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 1, 10 5 then (temporary : array_tmp1 glob_h factorial_3(4, 9), 5 array_y2 : temporary, array_y2_higher : temporary, 10 1, 10 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 9 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 8 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 7 temporary 5.0 temporary : -------------, array_y2_higher : temporary, glob_h 5, 6 temporary 6.0 temporary : -------------, array_y2_higher : temporary)), kkk : 6, glob_h 6, 5 array_tmp3 : ats(5, array_m1, array_y2, 1), 5 array_tmp4 : array_const_1D0 + array_tmp3 , 5 5 5 if not array_y1_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp4 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 array_y1 + array_const_0D0 , order_d : 5, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 1, order_d + kkk order_d array_tmp1 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_tmp3 : kkk ats(kkk, array_m1, array_y2, 1), array_tmp4 : kkk array_const_1D0 + array_tmp3 , 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_tmp4 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) mode_declare(factorial_1, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o39) [factorial_1] (%i40) factorial_1(nnn) := nnn! (%o40) factorial_1(nnn) := nnn! (%i41) mode_declare(factorial_3, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o41) [factorial_3] mmm2! (%i42) factorial_3(mmm2, nnn2) := ----- nnn2! mmm2! (%o42) factorial_3(mmm2, nnn2) := ----- nnn2! (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) exact_soln_y1(x) := cos(x) + 1.0 (%o49) exact_soln_y1(x) := cos(x) + 1.0 (%i50) exact_soln_y2(x) := sin(x) + 1.0 (%o50) exact_soln_y2(x) := sin(x) + 1.0 (%i51) exact_soln_y2p(x) := cos(x) (%o51) exact_soln_y2p(x) := cos(x) (%i52) exact_soln_y2pp(x) := - sin(x) (%o52) exact_soln_y2pp(x) := - sin(x) (%i53) exact_soln_y2ppp(x) := - cos(x) (%o53) exact_soln_y2ppp(x) := - cos(x) (%i54) exact_soln_y2pppp(x) := sin(x) (%o54) exact_soln_y2pppp(x) := sin(x) (%i55) mainprog() := (define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(min_in_hour, 60.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(djd_debug2, true, boolean), define_variable(glob_normmax, 0.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_almost_1, 0.999, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(djd_debug, true, boolean), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_hmax, 1.0, float), define_variable(hours_in_day, 24.0, float), define_variable(sec_in_min, 60.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_hours, 0.0, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_dump, false, boolean), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest7postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * 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 : 0.0,"), omniout_str(ALWAYS, "x_end : 5.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"), omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 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, "exact_soln_y2p (x) := ("), omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("), omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("), omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("), omniout_str(ALWAYS, "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_x, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y1_init, 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_y2_init, 1 + max_terms), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_x : 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_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 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_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), ord : 1, term while ord <= 6 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 <= 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 <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 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 <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 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_5, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term), term array_const_5 : 5, array(array_const_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, x_start : 0.0, x_end : 5.0, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 20, 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 : true, 1, 1 1, 2 array_y2_set_initial : true, array_y2_set_initial : true, 1, 3 1, 4 array_y2_set_initial : true, 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 : 5, 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 <= 6 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 6 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 : 5, ord : 6, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 6, iii array_y2_higher 6, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no 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 convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no 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 , 5 ) = y1 ;"), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * 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, "2012-06-15T22:49:49-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest7"), logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest7 diffeq.max"), logitem_str(html_log_file, "\ mtest7 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * 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)) (%o55) mainprog() := (define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(min_in_hour, 60.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(djd_debug2, true, boolean), define_variable(glob_normmax, 0.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_almost_1, 0.999, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(djd_debug, true, boolean), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_hmax, 1.0, float), define_variable(hours_in_day, 24.0, float), define_variable(sec_in_min, 60.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_hours, 0.0, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_dump, false, boolean), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest7postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * 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 : 0.0,"), omniout_str(ALWAYS, "x_end : 5.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"), omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 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, "exact_soln_y2p (x) := ("), omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("), omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("), omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("), omniout_str(ALWAYS, "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_x, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y1_init, 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_y2_init, 1 + max_terms), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_x : 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_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 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_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), ord : 1, term while ord <= 6 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 <= 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 <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 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 <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 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_5, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term), term array_const_5 : 5, array(array_const_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, x_start : 0.0, x_end : 5.0, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 20, 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 : true, 1, 1 1, 2 array_y2_set_initial : true, array_y2_set_initial : true, 1, 3 1, 4 array_y2_set_initial : true, 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 : 5, 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 <= 6 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 6 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 : 5, ord : 6, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 6, iii array_y2_higher 6, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no 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 convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no 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 , 5 ) = y1 ;"), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * 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, "2012-06-15T22:49:49-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest7"), logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest7 diffeq.max"), logitem_str(html_log_file, "\ mtest7 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * 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)) (%i56) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/mtest7postode.ode#################" "diff ( y2 , x , 5 ) = y1 ;" "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms : 30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.0," "x_end : 5.0," "array_y1_init[0 + 1] : exact_soln_y1(x_start)," "array_y2_init[0 + 1] : exact_soln_y2(x_start)," "array_y2_init[1 + 1] : exact_soln_y2p(x_start)," "array_y2_init[2 + 1] : exact_soln_y2pp(x_start)," "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start)," "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start)," "glob_h : 0.00001," "glob_look_poles : true," "glob_max_iter : 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) " ");" "exact_soln_y2p (x) := (" "cos(x) " ");" "exact_soln_y2pp (x) := (" "-sin(x) " ");" "exact_soln_y2ppp (x) := (" "-cos(x) " ");" "exact_soln_y2pppp (x) := (" "sin(x) " ");" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.0 " " y2[1] (analytic) = 1. " " y2[1] (numeric) = 1. " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y1[1] (analytic) = 2. " " y1[1] (numeric) = 2. " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " x[1] = 0.0 " " y2[1] (analytic) = 1. " " y2[1] (numeric) = 1. " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y1[1] (analytic) = 2. " " y1[1] (numeric) = 2. " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.000E-3 " " y2[1] (analytic) = 1.0009999998333334 " " y2[1] (numeric) = 1.0009999998333334 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999995000000417 " " y1[1] (numeric) = 1.9999995000000417 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.000E-3 " " y2[1] (analytic) = 1.001999998666667 " " y2[1] (numeric) = 1.0019999986666672 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.216014024156684200000000000000E-14 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999980000006667 " " y1[1] (numeric) = 1.9999980000006667 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.000E-3 " " y2[1] (analytic) = 1.002999995500002 " " y2[1] (numeric) = 1.0029999955000042 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.21380464527659970000000000000E-13 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999995500003375 " " y1[1] (numeric) = 1.9999955000033751 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11022552263070910000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.000E-3 " " y2[1] (analytic) = 1.0039999893333418 " " y2[1] (numeric) = 1.0039999893333504 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 8.6252387291620470000000000000E-13 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999920000106668 " " y1[1] (numeric) = 1.9999920000106668 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.000E-3 " " y2[1] (analytic) = 1.0049999791666928 " " y2[1] (numeric) = 1.0049999791667188 " " absolute error = 2.597921877622866300000000000000E-14 " " relative error = 2.584996946743186000000000000E-12 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999875000260416 " " y1[1] (numeric) = 1.9999875000260419 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.110229963547972600000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.000E-3 " " y2[1] (analytic) = 1.0059999640000648 " " y2[1] (numeric) = 1.0059999640001296 " " absolute error = 6.48370246381091400000000000000E-14 " " relative error = 6.445032500826706000000000000E-12 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999982000054 " " y1[1] (numeric) = 1.999982000054 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.000E-3 " " y2[1] (analytic) = 1.0069999428334735 " " y2[1] (numeric) = 1.0069999428336134 " " absolute error = 1.39888101102769720000000000000E-13 " " relative error = 1.38915699150047400000000000E-11 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999755001000414 " " y1[1] (numeric) = 1.9999755001000414 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.000E-3 " " y2[1] (analytic) = 1.0079999146669398 " " y2[1] (numeric) = 1.0079999146672127 " " absolute error = 2.7289281945286350000000000000E-13 " " relative error = 2.70727026344076470000000000E-11 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999680001706663 " " y1[1] (numeric) = 1.9999680001706661 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.110240788383030400000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.000000000000001000E-3 " " y2[1] (analytic) = 1.008999878500492 " " y2[1] (numeric) = 1.0089998785009842 " " absolute error = 4.9205084451386940000000000000E-13 " " relative error = 4.876619462483209300000000000E-11 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999595002733743 " " y1[1] (numeric) = 1.9999595002733737 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.330736520834747000000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.000000000000000200E-2 " " y2[1] (analytic) = 1.0099998333341667 " " y2[1] (numeric) = 1.009999833335 " " absolute error = 8.3333340228364250000000000000E-13 " " relative error = 8.250827126700400000000000E-11 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999500004166653 " " y1[1] (numeric) = 1.999950000416664 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.6615046839802300000000000000E-14 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.100000000000000300E-2 " " y2[1] (analytic) = 1.0109997781680087 " " y2[1] (numeric) = 1.010999778169351 " " absolute error = 1.3422596367718143000000000000E-12 " " relative error = 1.3276557183860790000000000E-10 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999395006100391 " " y1[1] (numeric) = 1.999939500610037 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.11025660954894540000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.200000000000000400E-2 " " y2[1] (analytic) = 1.0119997120020736 " " y2[1] (numeric) = 1.0119997120041473 " " absolute error = 2.0736745653948674000000000000E-12 " " relative error = 2.04908612206266940000000000E-10 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999280008639957 " " y1[1] (numeric) = 1.999928000863992 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.88744708914260230000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.300000000000000600E-2 " " y2[1] (analytic) = 1.0129996338364273 " " y2[1] (numeric) = 1.0129996338395217 " " absolute error = 3.0944136142352363000000000000E-12 " " relative error = 3.05470358613663840000000000E-10 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999915501190035 " " y1[1] (numeric) = 1.9999155011900285 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.21978280532065200000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.400000000000000700E-2 " " y2[1] (analytic) = 1.0139995426711486 " " y2[1] (numeric) = 1.0139995426756305 " " absolute error = 4.481970350411757000000000000E-12 " " relative error = 4.42009109649599800000000000E-10 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999020016006561 " " y1[1] (numeric) = 1.999902001600646 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1072761657203440000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.500000000000000800E-2 " " y2[1] (analytic) = 1.014999437506328 " " y2[1] (numeric) = 1.0149994375126563 " " absolute error = 6.328271240363392000000000000E-12 " " relative error = 6.2347534456874410000000000E-10 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998875021093592 " " y1[1] (numeric) = 1.9998875021093434 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 7.8830268867869260000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.600000000000001000E-2 " " y2[1] (analytic) = 1.0159993173420714 " " y2[1] (numeric) = 1.0159993173508097 " " absolute error = 8.738343382219682000000000000E-12 " " relative error = 8.6007374543123000000000000E-10 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998720027306434 " " y1[1] (numeric) = 1.99987200273062 " " absolute error = 2.331468351712828700000000000000E-14 " " relative error = 1.165808786027016100000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.700000000000001000E-2 " " y2[1] (analytic) = 1.0169991811784986 " " y2[1] (numeric) = 1.016999181190331 " " absolute error = 1.183231290724506800000000000E-11 " " relative error = 1.1634535333188552000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999855503480008 " " y1[1] (numeric) = 1.9998555034799745 " " absolute error = 3.35287353436797300000000000000E-14 " " relative error = 1.6765578955747243000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.80000000000000100E-2 " " y2[1] (analytic) = 1.0179990280157463 " " y2[1] (numeric) = 1.0179990280314928 " " absolute error = 1.57465152028635200000000000E-11 " " relative error = 1.5468104359152646000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998380043739528 " " y1[1] (numeric) = 1.9998380043739055 " " absolute error = 4.72955008490316700000000000000E-14 " " relative error = 2.364966599574023000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 1.90000000000000100E-2 " " y2[1] (analytic) = 1.0189988568539674 " " y2[1] (numeric) = 1.0189988568746016 " " absolute error = 2.06341610464733100000000000E-11 " " relative error = 2.0249444744402093000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998195054299763 " " y1[1] (numeric) = 1.9998195054299108 " " absolute error = 6.55031584528842400000000000000E-14 " " relative error = 3.275453523431884000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.00000000000000120E-2 " " y2[1] (analytic) = 1.0199986666933332 " " y2[1] (numeric) = 1.0199986667199998 " " absolute error = 2.66666688730765600000000000E-11 " " relative error = 2.614382718707416000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998000066665778 " " y1[1] (numeric) = 1.9998000066664887 " " absolute error = 8.90398865749375500000000000000E-14 " " relative error = 4.452439557861396000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.10000000000000130E-2 " " y2[1] (analytic) = 1.0209984565340338 " " y2[1] (numeric) = 1.020998456568068 " " absolute error = 3.403433090909402400000000000E-11 " " relative error = 3.3334360783100290000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9997795081032559 " " y1[1] (numeric) = 1.9997795081031366 " " absolute error = 1.1923795284474181000000000000E-13 " " relative error = 5.962554989766659000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.200000000000001400E-2 " " y2[1] (analytic) = 1.0219982253762798 " " y2[1] (numeric) = 1.0219982254192268 " " absolute error = 4.294697930617985500000000000E-11 " " relative error = 4.202255761292307000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9997580097605092 " " y1[1] (numeric) = 1.9997580097603516 " " absolute error = 1.57651669496772230000000000000E-13 " " relative error = 7.883537344383613000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.300000000000001500E-2 " " y2[1] (analytic) = 1.0229979722203022 " " y2[1] (numeric) = 1.0229979722739384 " " absolute error = 5.36362065872708600000000000E-11 " " relative error = 5.243041339647966000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999735511659836 " " y1[1] (numeric) = 1.9997355116596303 " " absolute error = 2.05835348765504020000000000000E-13 " " relative error = 1.029312864453034300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.400000000000001600E-2 " " y2[1] (analytic) = 1.0239976960663544 " " y2[1] (numeric) = 1.0239976961327095 " " absolute error = 6.63551436019815800000000000E-11 " " relative error = 6.480009071981526000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9997120138237345 " " y1[1] (numeric) = 1.999712013823469 " " absolute error = 2.65565347490337440000000000000E-13 " " relative error = 1.32801796285925500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.500000000000001700E-2 " " y2[1] (analytic) = 1.0249973959147123 " " y2[1] (numeric) = 1.0249973959960925 " " absolute error = 8.13802358834436700000000000E-11 " " relative error = 7.939555379145093000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9996875162757026 " " y1[1] (numeric) = 1.9996875162753633 " " absolute error = 3.39284156325447840000000000000E-13 " " relative error = 1.696685874987828600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.600000000000002000E-2 " " y2[1] (analytic) = 1.0259970707656765 " " y2[1] (numeric) = 1.025997070864688 " " absolute error = 9.90114656929108600000000000E-11 " " relative error = 9.650267872501919000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9996620190402377 " " y1[1] (numeric) = 1.9996620190398084 " " absolute error = 4.2921222132008550000000000000E-13 " " relative error = 2.14642383179379100000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.700000000000002000E-2 " " y2[1] (analytic) = 1.0269967196195722 " " y2[1] (numeric) = 1.0269967197391463 " " absolute error = 1.1957412837659831000000000E-10 " " relative error = 1.164308766447587600000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999635522142837 " " y1[1] (numeric) = 1.9996355221422988 " " absolute error = 5.3823612233827590000000000000E-13 " " relative error = 2.691671138955836000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.800000000000002000E-2 " " y2[1] (analytic) = 1.0279963414767503 " " y2[1] (numeric) = 1.02799634162017 " " absolute error = 1.43419720544102350000000000E-10 " " relative error = 1.395138433450796300000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9996080256099975 " " y1[1] (numeric) = 1.999608025609328 " " absolute error = 6.6946448384896940000000000000E-13 " " relative error = 3.347978580175700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 2.90000000000000200E-2 " " y2[1] (analytic) = 1.0289959353375895 " " y2[1] (numeric) = 1.0289959355085156 " " absolute error = 1.70926162113005380000000000E-10 " " relative error = 1.66109657232930200000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9995795294692156 " " y1[1] (numeric) = 1.9995795294683893 " " absolute error = 8.2622797492604150000000000000E-13 " " relative error = 4.13200856854821940000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.00000000000000200E-2 " " y2[1] (analytic) = 1.0299955002024956 " " y2[1] (numeric) = 1.0299955004049957 " " absolute error = 2.02500016754925130000000000E-10 " " relative error = 1.966028169201845300000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9995500337489875 " " y1[1] (numeric) = 1.999550033747975 " " absolute error = 1.0125233984581428000000000000E-12 " " relative error = 5.063756251999091000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.10000000000000200E-2 " " y2[1] (analytic) = 1.0309950350719042 " " y2[1] (numeric) = 1.0309950353104804 " " absolute error = 2.38576269850909740000000000E-10 " " relative error = 2.314038979191309400000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999519538478809 " " y1[1] (numeric) = 1.9995195384775764 " " absolute error = 1.2325696019388488000000000000E-12 " " relative error = 6.16432887110751200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.20000000000000230E-2 " " y2[1] (analytic) = 1.0319945389462801 " " y2[1] (numeric) = 1.0319945392259005 " " absolute error = 2.7962032689288210000000000E-10 " " relative error = 2.709513629581692400000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9994880436891753 " " y1[1] (numeric) = 1.999488043687684 " " absolute error = 1.4912515666765103000000000000E-12 " " relative error = 7.45816696120403700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.30000000000000240E-2 " " y2[1] (analytic) = 1.0329940108261197 " " y2[1] (numeric) = 1.0329940111522482 " " absolute error = 3.2612845757284960000000000E-10 " " relative error = 3.1571185714042405000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9994555494115813 " " y1[1] (numeric) = 1.9994555494097876 " " absolute error = 1.793676318584403000000000000E-12 " " relative error = 8.97082367803706800000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.40000000000000250E-2 " " y2[1] (analytic) = 1.0339934497119514 " " y2[1] (numeric) = 1.03399345009058 " " absolute error = 3.786286839613240000000000E-10 " " relative error = 3.66180930901256600000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9994220556785212 " " y1[1] (numeric) = 1.9994220556763755 " " absolute error = 2.1456170173905775000000000000E-12 " " relative error = 1.07311861009877870000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.500000000000002600E-2 " " y2[1] (analytic) = 1.0349928546043363 " " y2[1] (numeric) = 1.0349928550420187 " " absolute error = 4.37682334819555760000000000E-10 " " relative error = 4.22884402411527500000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9993875625234887 " " y1[1] (numeric) = 1.9993875625209354 " " absolute error = 2.553290912032935000000000000E-12 " " relative error = 1.27703650852481450000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.600000000000002600E-2 " " y2[1] (analytic) = 1.0359922245038693 " " y2[1] (numeric) = 1.0359922250077542 " " absolute error = 5.0388493377795380000000000E-10 " " relative error = 4.863790691279188400000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9993520699809768 " " y1[1] (numeric) = 1.9993520699779534 " " absolute error = 3.0233593406592263000000000000E-12 " " relative error = 1.51216956035561680000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.700000000000003000E-2 " " y2[1] (analytic) = 1.0369915584111808 " " y2[1] (numeric) = 1.0369915589890473 " " absolute error = 5.7786642138069060000000000E-10 " " relative error = 5.57252772882803800000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9993155780864782 " " y1[1] (numeric) = 1.9993155780829148 " " absolute error = 3.5633718198369024000000000000E-12 " " relative error = 1.78229583108003600000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.80000000000000300E-2 " " y2[1] (analytic) = 1.037990855326937 " " y2[1] (numeric) = 1.0379908559872302 " " absolute error = 6.6029315348714590000000000E-10 " " relative error = 6.36126175966331400000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999278086876485 " " y1[1] (numeric) = 1.9992780868723032 " " absolute error = 4.181766044553114600000000000E-12 " " relative error = 2.0916380127420780000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 3.90000000000000300E-2 " " y2[1] (analytic) = 1.0389901142518412 " " y2[1] (numeric) = 1.0389901150037095 " " absolute error = 7.5186834536111750000000000E-10 " " relative error = 7.23653031003596100000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9992395963884881 " " y1[1] (numeric) = 1.999239596383601 " " absolute error = 4.887201754399939000000000000E-12 " " relative error = 2.4445302920312250000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.00000000000000300E-2 " " y2[1] (analytic) = 1.0399893341866342 " " y2[1] (numeric) = 1.0399893350399676 " " absolute error = 8.5333340393844990000000000E-10 " " relative error = 8.20521303332244000000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999200106660978 " " y1[1] (numeric) = 1.9992001066552891 " " absolute error = 5.688782778179302000000000000E-12 " " relative error = 2.84552944911582060000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.10000000000000300E-2 " " y2[1] (analytic) = 1.0409885141320965 " " y2[1] (numeric) = 1.0409885150975648 " " absolute error = 9.654683719162449000000000E-10 " " relative error = 9.27453433740510600000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9991596177334445 " " y1[1] (numeric) = 1.9991596177268471 " " absolute error = 6.59738930153253000000000000E-12 " " relative error = 3.3000813156742070000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.20000000000000300E-2 " " y2[1] (analytic) = 1.041987653089048 " " y2[1] (numeric) = 1.0419876541781417 " " absolute error = 1.0890937041097004000000000E-9 " " relative error = 1.04520787830930930000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9991181296463765 " " y1[1] (numeric) = 1.999118129638753 " " absolute error = 7.6234574208911000000000000E-12 " " relative error = 3.81341017713626160000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.30000000000000300E-2 " " y2[1] (analytic) = 1.0429867500583498 " " y2[1] (numeric) = 1.0429867512834203 " " absolute error = 1.2250704894967157000000000E-9 " " relative error = 1.17457914918687050000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9990756424412623 " " y1[1] (numeric) = 1.9990756424324827 " " absolute error = 8.779643678735738000000000000E-12 " " relative error = 4.39185166000726050000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.40000000000000340E-2 " " y2[1] (analytic) = 1.0439858040409051 " " y2[1] (numeric) = 1.0439858054152074 " " absolute error = 1.3743022275747308000000000E-9 " " relative error = 1.31639934399039320000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9990321561605888 " " y1[1] (numeric) = 1.9990321561505107 " " absolute error = 1.007816052833732100000000000E-11 " " relative error = 5.0415199661889320000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.50000000000000340E-2 " " y2[1] (analytic) = 1.0449848140376603 " " y2[1] (numeric) = 1.044984815575395 " " absolute error = 1.5377346063161212000000000E-9 " " relative error = 1.47153775409859940000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9989876708478425 " " y1[1] (numeric) = 1.9989876708363095 " " absolute error = 1.153299677980612600000000000E-11 " " relative error = 5.7694186652559840000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.600000000000003500E-2 " " y2[1] (analytic) = 1.045983779049605 " " y2[1] (numeric) = 1.0459837807659633 " " absolute error = 1.7163583887480627000000000E-9 " " relative error = 1.640903447190710000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9989421865475085 " " y1[1] (numeric) = 1.9989421865343497 " " absolute error = 1.315880737706720500000000000E-11 " " relative error = 6.5828854209108270000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.700000000000003600E-2 " " y2[1] (analytic) = 1.0469826980777746 " " y2[1] (numeric) = 1.046982699988983 " " absolute error = 1.9112085247741106000000000E-9 " " relative error = 1.8254442296735430000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9988957033050712 " " y1[1] (numeric) = 1.9988957032901 " " absolute error = 1.49711354424653100000000000E-11 " " relative error = 7.4897031484490710000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.800000000000003700E-2 " " y2[1] (analytic) = 1.04798157012325 " " y2[1] (numeric) = 1.0479815722466164 " " absolute error = 2.12336637162025000000000E-9 " " relative error = 2.02614858138252100000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9988482211670138 " " y1[1] (numeric) = 1.998848221150027 " " absolute error = 1.698685636597474500000000000E-11 " " relative error = 8.4983222768445540000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 4.90000000000000400E-2 " " y2[1] (analytic) = 1.0489803941871592 " " y2[1] (numeric) = 1.0489803965411197 " " absolute error = 2.3539605820133147000000000E-9 " " relative error = 2.2440463092137838000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9987997401808184 " " y1[1] (numeric) = 1.9987997401615945 " " absolute error = 1.922395576059443600000000000E-11 " " relative error = 9.6177497796029190000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.00000000000000300E-2 " " y2[1] (analytic) = 1.0499791692706784 " " y2[1] (numeric) = 1.0499791718748452 " " absolute error = 2.604166882136383000000000E-9 " " relative error = 2.4802081396960020000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9987502603949663 " " y1[1] (numeric) = 1.9987502603732648 " " absolute error = 2.170152946234793500000000000E-11 " " relative error = 1.0857549285852035000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.10000000000000300E-2 " " y2[1] (analytic) = 1.0509778943750323 " " y2[1] (numeric) = 1.050977897250243 " " absolute error = 2.8752107361640356000000000E-9 " " relative error = 2.73574806049920740000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.998699781858937 " " y1[1] (numeric) = 1.9986997818344974 " " absolute error = 2.443956148567849600000000000E-11 " " relative error = 1.2227730101089979000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.20000000000000400E-2 " " y2[1] (analytic) = 1.0519765685014963 " " y2[1] (numeric) = 1.0519765716698635 " " absolute error = 3.1683671242177525000000000E-9 " " relative error = 3.01182290469737400000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9986483046232089 " " y1[1] (numeric) = 1.9986483045957495 " " absolute error = 2.745936811265892000000000000E-11 " " relative error = 1.3738969507111778000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.30000000000000400E-2 " " y2[1] (analytic) = 1.052975190651396 " " y2[1] (numeric) = 1.0529751941363588 " " absolute error = 3.4849627628119606000000000E-9 " " relative error = 3.30963425705792570000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9985958287392593 " " y1[1] (numeric) = 1.9985958287084753 " " absolute error = 3.078404198220141600000000000E-11 " " relative error = 1.5402835100291587000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.40000000000000400E-2 " " y2[1] (analytic) = 1.0539737598261096 " " y2[1] (numeric) = 1.053973763652485 " " absolute error = 3.82637543872022000000000E-9 " " relative error = 3.6304276107893960000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9985423542595644 " " y1[1] (numeric) = 1.9985423542251268 " " absolute error = 3.44375639116378800000000000E-11 " " relative error = 1.7231340550896945000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.50000000000000400E-2 " " y2[1] (analytic) = 1.0549722750270678 " " y2[1] (numeric) = 1.0549722792211045 " " absolute error = 4.194036673510481700000000E-9 " " relative error = 3.97549468624933600000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9984878812375984 " " y1[1] (numeric) = 1.9984878811991529 " " absolute error = 3.844546903053469600000000000E-11 " " relative error = 1.923727904055474000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.60000000000000400E-2 " " y2[1] (analytic) = 1.0559707352557555 " " y2[1] (numeric) = 1.0559707398451872 " " absolute error = 4.58943172354509000000000E-9 " " relative error = 4.3461732132505850000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9984324097278345 " " y1[1] (numeric) = 1.9984324096849995 " " absolute error = 4.28350688252976400000000000E-11 " " relative error = 2.143433453980629000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.700000000000004000E-2 " " y2[1] (analytic) = 1.0569691395137126 " " y2[1] (numeric) = 1.0569691445278133 " " absolute error = 5.014100690203804000000000E-9 " " relative error = 4.7438477650451344000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9983759397857437 " " y1[1] (numeric) = 1.9983759397381096 " " absolute error = 4.76341188715423400000000000E-11 " " relative error = 2.383641532265918000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.800000000000004000E-2 " " y2[1] (analytic) = 1.057967486802535 " " y2[1] (numeric) = 1.057967492272175 " " absolute error = 5.469639852151431000000000E-9 " " relative error = 5.1699507975260830000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9983184714677966 " " y1[1] (numeric) = 1.9983184714149231 " " absolute error = 5.28734833693533800000000000E-11 " " relative error = 2.64589874558468000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 5.900000000000004000E-2 " " y2[1] (analytic) = 1.0589657761238755 " " y2[1] (numeric) = 1.058965782081578 " " absolute error = 5.957702553516242000000000E-9 " " relative error = 5.6259632632540560000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9982600048314612 " " y1[1] (numeric) = 1.998260004772877 " " absolute error = 5.85842485634202600000000000E-11 " " relative error = 2.931763054946467000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.000000000000004000E-2 " " y2[1] (analytic) = 1.0599640064794447 " " y2[1] (numeric) = 1.0599640129594448 " " absolute error = 6.480000092068394000000000E-9 " " relative error = 6.1134152220800510000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9982005399352043 " " y1[1] (numeric) = 1.998200539870404 " " absolute error = 6.48003872782965100000000000E-11 " " relative error = 3.2429371318455250000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.10000000000000400E-2 " " y2[1] (analytic) = 1.0609621768710125 " " y2[1] (numeric) = 1.060962183909315 " " absolute error = 7.03830260739835000000000E-9 " " relative error = 6.6338864483894210000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9981400768384905 " " y1[1] (numeric) = 1.998140076766934 " " absolute error = 7.15565384723504400000000000E-11 " " relative error = 3.581157262286089000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.20000000000000400E-2 " " y2[1] (analytic) = 1.0619602863004083 " " y2[1] (numeric) = 1.0619602939348487 " " absolute error = 7.634440413184507000000000E-9 " " relative error = 7.1890074531703050000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.998078615601783 " " y1[1] (numeric) = 1.9980786155228933 " " absolute error = 7.8889561549999600000000000E-11 " " relative error = 3.948271150794513400000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.30000000000000400E-2 " " y2[1] (analytic) = 1.062958333769523 " " y2[1] (numeric) = 1.0629583420398276 " " absolute error = 8.27030466332701000000000E-9 " " relative error = 7.7804598737171460000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.998016156286543 " " y1[1] (numeric) = 1.9980161561997045 " " absolute error = 8.6838536361710790000000000E-11 " " relative error = 4.346237946499214600000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.40000000000000500E-2 " " y2[1] (analytic) = 1.0639563182803093 " " y2[1] (numeric) = 1.0639563272281578 " " absolute error = 8.947848462170782000000000E-9 " " relative error = 8.4099772786098410000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9979526989552299 " " y1[1] (numeric) = 1.997952698859786 " " absolute error = 9.54438750255803800000000000E-11 " " relative error = 4.777083815622358000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.50000000000000500E-2 " " y2[1] (analytic) = 1.0649542388347826 " " y2[1] (numeric) = 1.0649542485038712 " " absolute error = 9.669088640862356000000000E-9 " " relative error = 9.0793465937482610000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.997888243671301 " " y1[1] (numeric) = 1.9978882435665524 " " absolute error = 1.04748654194963820000000000E-10 " " relative error = 5.242968645857721000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.60000000000000500E-2 " " y2[1] (analytic) = 1.0659520944350225 " " y2[1] (numeric) = 1.0659521048711273 " " absolute error = 1.043610486917145900000000E-8 " " relative error = 9.7904070207796890000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9978227904992116 " " y1[1] (numeric) = 1.9978227903844143 " " absolute error = 1.14797282790846110000000000E-10 " " relative error = 5.746119392409214000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.70000000000000500E-2 " " y2[1] (analytic) = 1.0669498840831735 " " y2[1] (numeric) = 1.066949895334216 " " absolute error = 1.125104254207087700000000E-8 " " relative error = 1.0545052499573455000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9977563395044151 " " y1[1] (numeric) = 1.9977563393787783 " " absolute error = 1.25636834269471360000000000E-10 " " relative error = 6.288896788115721000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.80000000000000500E-2 " " y2[1] (analytic) = 1.067947606781446 " " y2[1] (numeric) = 1.067947618897559 " " absolute error = 1.21161130017810590000000E-8 " " relative error = 1.1345231661969168000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.997688890753362 " " y1[1] (numeric) = 1.997688890616046 " " absolute error = 1.37316158443923100000000000E-10 " " relative error = 6.873750916847661000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 6.90000000000000500E-2 " " y2[1] (analytic) = 1.0689452615321173 " " y2[1] (numeric) = 1.0689452745657118 " " absolute error = 1.303359442594853600000000E-8 " " relative error = 1.2192948409039682000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9976204443135015 " " y1[1] (numeric) = 1.997620444163615 " " absolute error = 1.49886547617938960000000000E-10 " " relative error = 7.503254586956768000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.00000000000000500E-2 " " y2[1] (analytic) = 1.0699428473375328 " " y2[1] (numeric) = 1.0699428613433661 " " absolute error = 1.400583338195815500000000E-8 " " relative error = 1.3090263107801087000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9975510002532797 " " y1[1] (numeric) = 1.997551000089878 " " absolute error = 1.63401736585910840000000000E-10 " " relative error = 8.18010336482984900000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.10000000000000500E-2 " " y2[1] (analytic) = 1.0709403632001069 " " y2[1] (numeric) = 1.0709403782353515 " " absolute error = 1.503524460488847600000000E-8 " " relative error = 1.403929212263626000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9974805586421405 " " y1[1] (numeric) = 1.9974805584642232 " " absolute error = 1.77917236499070000000000000E-10 " " relative error = 8.907082260666188000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.20000000000000500E-2 " " y2[1] (analytic) = 1.0719378081223236 " " y2[1] (numeric) = 1.0719378242466373 " " absolute error = 1.61243136620470300000000E-8 " " relative error = 1.5042210042289145000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9974091195505261 " " y1[1] (numeric) = 1.997409119357034 " " absolute error = 1.93492111222326460000000000E-10 " " relative error = 9.68715469096625000000000E-9 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.30000000000000500E-2 " " y2[1] (analytic) = 1.0729351811067382 " " y2[1] (numeric) = 1.072935198382335 " " absolute error = 1.727559673092571300000000E-8 " " relative error = 1.610124920417452000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.997336683049875 " " y1[1] (numeric) = 1.9973366828396883 " " absolute error = 2.10186756888219860000000000E-10 " " relative error = 1.052335135442817700000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.40000000000000500E-2 " " y2[1] (analytic) = 1.0739324811559778 " " y2[1] (numeric) = 1.0739324996476998 " " absolute error = 1.84917219314684200000000E-8 " " relative error = 1.7218700668745937000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9972632492126245 " " y1[1] (numeric) = 1.9972632489845594 " " absolute error = 2.2806512234296860000000000E-10 " " relative error = 1.141888143352550500000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.50000000000000600E-2 " " y2[1] (analytic) = 1.0749297072727424 " " y2[1] (numeric) = 1.074929727048133 " " absolute error = 1.977539065833866500000000E-8 " " relative error = 1.8396915188539900000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9971888181122073 " " y1[1] (numeric) = 1.9971888178650146 " " absolute error = 2.4719271074502558000000000E-10 " " relative error = 1.237703258216107500000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.60000000000000600E-2 " " y2[1] (analytic) = 1.0759268584598058 " " y2[1] (numeric) = 1.075926879589184 " " absolute error = 2.11293782470534100000000E-8 " " relative error = 1.9638303552808606000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9971133898230555 " " y1[1] (numeric) = 1.9971133895554163 " " absolute error = 2.67639244100337240000000000E-10 " " relative error = 1.34013043758146400000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.70000000000000600E-2 " " y2[1] (analytic) = 1.0769239337200174 " " y2[1] (numeric) = 1.076923956276552 " " absolute error = 2.255653464011686500000000E-8 " " relative error = 2.0945336930343678000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9970369644205967 " " y1[1] (numeric) = 1.9970369641311208 " " absolute error = 2.8947599872708450000000000E-10 " " relative error = 1.449527494405045400000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.80000000000000600E-2 " " y2[1] (analytic) = 1.0779209320563015 " " y2[1] (numeric) = 1.0779209561160878 " " absolute error = 2.405978638542194400000000E-8 " " relative error = 2.232054844646551800000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9969595419812567 " " y1[1] (numeric) = 1.996959541668479 " " absolute error = 3.12777581612522200000000000E-10 " " relative error = 1.566268995626241600000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 7.90000000000000600E-2 " " y2[1] (analytic) = 1.07891785247166 " " y2[1] (numeric) = 1.0789178781137967 " " absolute error = 2.564213663625025700000000E-8 " " relative error = 2.3766532899152112000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9968811225824579 " " y1[1] (numeric) = 1.996881122244836 " " absolute error = 3.37621930412979050000000000E-10 " " relative error = 1.690746267240740600000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.00000000000000600E-2 " " y2[1] (analytic) = 1.0799146939691728 " " y2[1] (numeric) = 1.0799147212758393 " " absolute error = 2.730666648353974300000000E-8 " " relative error = 2.528594771053207000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9968017063026193 " " y1[1] (numeric) = 1.9968017059385301 " " absolute error = 3.64089203230832940000000000E-10 " " relative error = 1.823361839493813400000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.10000000000000600E-2 " " y2[1] (analytic) = 1.080911455551998 " " y2[1] (numeric) = 1.0809114846085346 " " absolute error = 2.905653651019690600000000E-8 " " relative error = 2.688151407865167000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9967212932211575 " " y1[1] (numeric) = 1.996721292828894 " " absolute error = 3.92263554971350460000000000E-10 " " relative error = 1.964538347455301300000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.20000000000000600E-2 " " y2[1] (analytic) = 1.0819081362233747 " " y2[1] (numeric) = 1.0819081671183615 " " absolute error = 3.08949867910968100000000E-8 " " relative error = 2.855601668635397000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.996639883418486 " " y1[1] (numeric) = 1.996639882996254 " " absolute error = 4.22232027119662230000000000E-10 " " relative error = 2.114712976667332500000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.30000000000000600E-2 " " y2[1] (analytic) = 1.0829047349866219 " " y2[1] (numeric) = 1.0829047678119603 " " absolute error = 3.282533844739532500000000E-8 " " relative error = 3.031230484720417000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9965574769760137 " " y1[1] (numeric) = 1.9965574765219294 " " absolute error = 4.540843256961580000000000E-10 " " relative error = 2.27433635611589900000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.40000000000000600E-2 " " y2[1] (analytic) = 1.0839012508451409 " " y2[1] (numeric) = 1.0839012856961359 " " absolute error = 3.485099497879673400000000E-8 " " relative error = 3.2153293440359690000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9964740739761475 " " y1[1] (numeric) = 1.9964740734882331 " " absolute error = 4.879143755687209700000000E-10 " " relative error = 2.443880348503590000000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.50000000000000600E-2 " " y2[1] (analytic) = 1.0848976828024162 " " y2[1] (numeric) = 1.0848977197778586 " " absolute error = 3.697544248559836400000000E-8 " " relative error = 3.4081962817070940000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9963896745022904 " " y1[1] (numeric) = 1.9963896739784712 " " absolute error = 5.2381921022970350000000000E-10 " " relative error = 2.623832495829222500000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.60000000000000700E-2 " " y2[1] (analytic) = 1.0858940298620157 " " y2[1] (numeric) = 1.0858940690642669 " " absolute error = 3.920225122300280400000000E-8 " " relative error = 3.6101359934711330000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.996304278638842 " " y1[1] (numeric) = 1.9963042780769424 " " absolute error = 5.6189963792974140000000000E-10 " " relative error = 2.814699361927263000000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.70000000000000700E-2 " " y2[1] (analytic) = 1.0868902910275924 " " y2[1] (numeric) = 1.0868903325626689 " " absolute error = 4.15350764892963300000000E-8 " " relative error = 3.821459887182109000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.996217886471198 " " y1[1] (numeric) = 1.9962178858689386 " " absolute error = 6.0225935349933480000000000E-10 " " relative error = 3.017002089706626000000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.80000000000000700E-2 " " y2[1] (analytic) = 1.0878864653028855 " " y2[1] (numeric) = 1.087886509280545 " " absolute error = 4.39776595140273230000000E-8 " " relative error = 4.042486134045543000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9961304980857502 " " y1[1] (numeric) = 1.996130497440744 " " absolute error = 6.4500627061647720000000000E-10 " " relative error = 3.23128308111631730000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 8.90000000000000700E-2 " " y2[1] (analytic) = 1.0888825516917204 " " y2[1] (numeric) = 1.088882598225549 " " absolute error = 4.653382856822929600000000E-8 " " relative error = 4.273539739977737000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9960421135698874 " " y1[1] (numeric) = 1.996042112879635 " " absolute error = 6.9025229976205080000000000E-10 " " relative error = 3.458104892023276500000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.00000000000000700E-2 " " y2[1] (analytic) = 1.0898785491980112 " " y2[1] (numeric) = 1.089878598405511 " " absolute error = 4.92074998525993100000000E-8 " " relative error = 4.514952596214387700000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9959527330119942 " " y1[1] (numeric) = 1.995952732273881 " " absolute error = 7.3811312617522160000000000E-10 " " relative error = 3.69804912695187600000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.10000000000000700E-2 " " y2[1] (analytic) = 1.0908744568257602 " " y2[1] (numeric) = 1.0908745088284388 " " absolute error = 5.20026786077210100000000E-8 " " relative error = 4.767063550010973000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9958623565014508 " " y1[1] (numeric) = 1.995862355712743 " " absolute error = 7.8870776576422940000000000E-10 " " relative error = 3.95171422114877700000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.20000000000000700E-2 " " y2[1] (analytic) = 1.09187027357906 " " y2[1] (numeric) = 1.0918703285025202 " " absolute error = 5.492346022428762000000000E-8 " " relative error = 5.030218474970757000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9957709841286342 " " y1[1] (numeric) = 1.9957709832864738 " " absolute error = 8.4216034146322730000000000E-10 " " relative error = 4.21972434793624200000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.30000000000000700E-2 " " y2[1] (analytic) = 1.0928659984620939 " " y2[1] (numeric) = 1.0928660564361246 " " absolute error = 5.7974030687191200000000E-8 " " relative error = 5.304770280050216000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9956786159849162 " " y1[1] (numeric) = 1.9956786150863182 " " absolute error = 8.9859808483083730000000000E-10 " " relative error = 4.502719414004228700000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.40000000000000700E-2 " " y2[1] (analytic) = 1.0938616304791369 " " y2[1] (numeric) = 1.0938616916378054 " " absolute error = 6.11586685739240500000000E-8 " " relative error = 5.591079060624434000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9955852521626654 " " y1[1] (numeric) = 1.9955852512045122 " " absolute error = 9.5815311240698970000000000E-10 " " relative error = 4.80136396763112700000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.50000000000000700E-2 " " y2[1] (analytic) = 1.0948571686345574 " " y2[1] (numeric) = 1.0948572331163022 " " absolute error = 6.4481744832534100000000E-8 " " relative error = 5.8895120459367320000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9954908927552453 " " y1[1] (numeric) = 1.9954908917342837 " " absolute error = 1.0209615375345038000000000E-9 " " relative error = 5.11634275676811500000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.60000000000000700E-2 " " y2[1] (analytic) = 1.0958526119328171 " " y2[1] (numeric) = 1.095852679880542 " " absolute error = 6.79477247800264200000000E-8 " " relative error = 6.2004437494731320000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9953955378570152 " " y1[1] (numeric) = 1.9953955367698513 " " absolute error = 1.087163914448297000000000E-9 " " relative error = 5.448362962743081000000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.70000000000000800E-2 " " y2[1] (analytic) = 1.096847959378473 " " y2[1] (numeric) = 1.0968480309396418 " " absolute error = 7.15611687684969400000000E-8 " " relative error = 6.524255997070638000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9952991875633304 " " y1[1] (numeric) = 1.9952991864064245 " " absolute error = 1.1569059044092000000000E-9 " " relative error = 5.79815754760076600000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.80000000000000800E-2 " " y2[1] (analytic) = 1.0978432099761775 " " y2[1] (numeric) = 1.0978432853029105 " " absolute error = 7.53267330733109500000000E-8 " " relative error = 6.861337975114451000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.995201841970541 " " y1[1] (numeric) = 1.995201840740204 " " absolute error = 1.2303371654809325000000000E-9 " " relative error = 6.1664796994463600000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 9.90000000000000800E-2 " " y2[1] (analytic) = 1.0988383627306801 " " y2[1] (numeric) = 1.098838441979851 " " absolute error = 7.92491707812814600000000E-8 " " relative error = 7.21208627848981000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9951035011759926 " " y1[1] (numeric) = 1.9951034998683808 " " absolute error = 1.3076117966193124000000000E-9 " " relative error = 6.5541050669729900000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10000000000000007 " " y2[1] (analytic) = 1.0998334166468282 " " y2[1] (numeric) = 1.0998334999801616 " " absolute error = 8.3333333344981500000000E-8 " " relative error = 7.576905018857141000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9950041652780257 " " y1[1] (numeric) = 1.9950041638891365 " " absolute error = 1.3888892258506758000000000E-9 " " relative error = 6.96183622081369900000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10100000000000008 " " y2[1] (analytic) = 1.100828370729568 " " y2[1] (numeric) = 1.1008284583137389 " " absolute error = 8.75841708047886400000000E-8 " " relative error = 7.956205811333034000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9949038343759766 " " y1[1] (numeric) = 1.9949038329016426 " " absolute error = 1.4743339882272720000000000E-9 " " relative error = 7.39050155111089200000000E-8 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10200000000000008 " " y2[1] (analytic) = 1.1018232239839456 " " y2[1] (numeric) = 1.1018233159906792 " " absolute error = 9.20067335652419200000000E-8 " " relative error = 8.350407902328125000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9948025085701762 " " y1[1] (numeric) = 1.994802507006061 " " absolute error = 1.5641150596934494000000000E-9 " " relative error = 7.84095193871882200000000E-8 "%" h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y2 , x , 5 ) = y1 ;" "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;" Iterations = 102 "Total Elapsed Time "= 15 Minutes 11 Seconds "Elapsed Time(since restart) "= 15 Minutes 11 Seconds "Expected Time Remaining "= 12 Hours 2 Minutes 19 Seconds "Optimized Time Remaining "= 12 Hours 2 Minutes 4 Seconds "Time to Timeout " Unknown Percent Done = 2.0600000000000014 "%" (%o56) true (%o56) diffeq.max