(%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) factorial_1(nnn) := (if nnn <= glob_max_terms then ret : array_fact_1 nnn else ret : nnn!, ret) (%o39) factorial_1(nnn) := (if nnn <= glob_max_terms then ret : array_fact_1 nnn else ret : nnn!, ret) (%i40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms) mmm! and (mmm <= glob_max_terms) then ret : array_fact_2 else ret : ----, mmm, nnn nnn! ret) (%o40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms) mmm! and (mmm <= glob_max_terms) then ret : array_fact_2 else ret : ----, mmm, nnn nnn! ret) (%i41) convfp(mmm) := mmm (%o41) convfp(mmm) := mmm (%i42) convfloat(mmm) := mmm (%o42) convfloat(mmm) := mmm (%i43) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o43) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i44) arcsin(x) := asin(x) (%o44) arcsin(x) := asin(x) (%i45) arccos(x) := acos(x) (%o45) arccos(x) := acos(x) (%i46) arctan(x) := atan(x) (%o46) arctan(x) := atan(x) (%i47) exact_soln_y1(x) := cos(x) + 1.0 (%o47) exact_soln_y1(x) := cos(x) + 1.0 (%i48) exact_soln_y2(x) := sin(x) + 1.0 (%o48) exact_soln_y2(x) := sin(x) + 1.0 (%i49) exact_soln_y2p(x) := cos(x) (%o49) exact_soln_y2p(x) := cos(x) (%i50) exact_soln_y2pp(x) := - sin(x) (%o50) exact_soln_y2pp(x) := - sin(x) (%i51) exact_soln_y2ppp(x) := - cos(x) (%o51) exact_soln_y2ppp(x) := - cos(x) (%i52) exact_soln_y2pppp(x) := sin(x) (%o52) exact_soln_y2pppp(x) := sin(x) (%i53) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_almost_1, 0.999, float), define_variable(djd_debug, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_hmax, 1.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_max_hours, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(min_in_hour, 60.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_h, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_optimal_done, false, boolean), define_variable(hours_in_day, 24.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/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_norms, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 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_last_rel_error : 0.0, term : 1 + term), term ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 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_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_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_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (temp1 : iiif!, temp2 : jjjf!, temp1 array_fact_1 : temp1, array_fact_2 : -----, jjjf : 1 + jjjf), iiif iiif, jjjf temp2 iiif : 1 + iiif), x_start : 0.0, x_end : 5.0, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 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 factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term factorial_1(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term factorial_1(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y2 , x , 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, "2012-06-17T00:37:58-05:00"), 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, " 091 "), 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 for speeding factorials"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = 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)) (%o53) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_almost_1, 0.999, float), define_variable(djd_debug, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_hmax, 1.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_max_hours, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(min_in_hour, 60.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_h, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_optimal_done, false, boolean), define_variable(hours_in_day, 24.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/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_norms, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y2_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 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_last_rel_error : 0.0, term : 1 + term), term ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 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_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_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_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (temp1 : iiif!, temp2 : jjjf!, temp1 array_fact_1 : temp1, array_fact_2 : -----, jjjf : 1 + jjjf), iiif iiif, jjjf temp2 iiif : 1 + iiif), x_start : 0.0, x_end : 5.0, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 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 factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term factorial_1(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term factorial_1(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term factorial_1(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y2 , x , 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, "2012-06-17T00:37:58-05:00"), 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, " 091 "), 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 for speeding factorials"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = 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)) (%i54) 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) = 1.0019999988319448 " " absolute error = 1.65277791452922430000000000E-10 " " relative error = 1.649478958810907000000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999980000006667 " " y1[1] (numeric) = 1.9999980000006254 " " absolute error = 4.130029651605582300000000000000E-14 " " relative error = 2.0650168908189934000000000000E-12 "%" 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) = 1.0029999968236007 " " absolute error = 1.3235987861293097000000000E-9 " " relative error = 1.31963987245033550000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999995500003375 " " y1[1] (numeric) = 1.9999955000027136 " " absolute error = 6.6124883346674320000000000000E-13 " " relative error = 3.306251606394251500000000000E-11 "%" 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) = 1.0039999938068664 " " absolute error = 4.4735246618188285000000000E-9 " " relative error = 4.45570190173932070000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999920000106668 " " y1[1] (numeric) = 1.9999920000073144 " " absolute error = 3.3524294451581227000000000000E-12 " " relative error = 1.67622142745583120000000000E-10 "%" 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) = 1.00499998978173 " " absolute error = 1.061503729360424600000000E-8 " " relative error = 1.0562226381741645000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999875000260416 " " y1[1] (numeric) = 1.9999875000154361 " " absolute error = 1.06055164650342700000000000E-11 " " relative error = 5.3027913748941810000000000E-10 "%" 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) = 1.005999984748192 " " absolute error = 2.07481272163079200000000E-8 " " relative error = 2.0624381668771696000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999982000054 " " y1[1] (numeric) = 1.9999820000280872 " " absolute error = 2.59128274393560800000000000E-11 " " relative error = 1.2956530328101165000000000E-9 "%" 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) = 1.0069999787062525 " " absolute error = 3.58727789695478800000000E-8 " " relative error = 3.5623417086410025000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999755001000414 " " y1[1] (numeric) = 1.999975500046276 " " absolute error = 5.37654365473372300000000000E-11 " " relative error = 2.688304758965688000000000E-9 "%" 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) = 1.0079999716559118 " " absolute error = 5.69889719859162400000000E-8 " " relative error = 5.653668334361551000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999680001706663 " " y1[1] (numeric) = 1.999968000071011 " " absolute error = 9.96553950471934500000000000E-11 " " relative error = 4.982849477526110600000000E-9 "%" 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) = 1.0089999635971705 " " absolute error = 8.50966783705331400000000E-8 " " relative error = 8.433764976958977000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999595002733743 " " y1[1] (numeric) = 1.9999595001033004 " " absolute error = 1.7007395491930310000000000E-10 " " relative error = 8.503869948169236000000000E-9 "%" 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) = 1.0099999545300287 " " absolute error = 1.21195862012868360000000E-7 " " relative error = 1.199959227842463700000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999500004166653 " " y1[1] (numeric) = 1.9999500001441528 " " absolute error = 2.7251245704462690000000000E-10 " " relative error = 1.362596349848007300000000E-8 "%" 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) = 1.0109999444544868 " " absolute error = 1.66286478142652070000000E-7 " " relative error = 1.64477264717083320000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999395006100391 " " y1[1] (numeric) = 1.9999395001945766 " " absolute error = 4.1546255324931280000000000E-10 " " relative error = 2.077375606225012000000000E-8 "%" 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) = 1.0119999333705454 " " absolute error = 2.21368471775562630000000E-7 " " relative error = 2.187436114360366800000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999280008639957 " " y1[1] (numeric) = 1.99992800025558 " " absolute error = 6.0841576221548620000000000E-10 " " relative error = 3.042188328543039600000000E-8 "%" 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) = 1.0129999212782046 " " absolute error = 2.87441777269137330000000E-7 " " relative error = 2.83753090986360200000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999915501190035 " " y1[1] (numeric) = 1.9999155003281714 " " absolute error = 8.6186346948124990000000000E-10 " " relative error = 4.30949942119256800000000E-8 "%" 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) = 1.0139999081774649 " " absolute error = 3.65506316324371030000000E-7 " " relative error = 3.60460040604681840000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9999020016006561 " " y1[1] (numeric) = 1.9999020004133596 " " absolute error = 1.1872964833514743000000000E-9 " " relative error = 5.93677331389838600000000E-8 "%" 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) = 1.0149998940683265 " " absolute error = 4.56561998429805270000000E-7 " " relative error = 4.49815026057055150000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998875021093592 " " y1[1] (numeric) = 1.9998875005121528 " " absolute error = 1.5972063671654269000000000E-9 " " relative error = 7.98648106696397300000000E-8 "%" 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) = 1.0159998789507896 " " absolute error = 5.6160871819699310000000E-7 " " relative error = 5.527648578211672000000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998720027306434 " " y1[1] (numeric) = 1.9998720006255593 " " absolute error = 2.1050841070291426000000000E-9 " " relative error = 1.05260941908024200000000E-7 "%" 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) = 1.0169998628248549 " " absolute error = 6.8164635624867740000000E-7 " " relative error = 6.70252610684293400000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999855503480008 " " y1[1] (numeric) = 1.9998555007545873 " " absolute error = 2.725420777949239000000000E-9 " " relative error = 1.3628088495427060000000E-7 "%" 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) = 1.0179998456905224 " " absolute error = 8.1767477611016660000000E-7 " " relative error = 8.0321763931735200000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998380043739528 " " y1[1] (numeric) = 1.9998380009002457 " " absolute error = 3.473707099743706000000000E-9 " " relative error = 1.73699424260673860000000E-7 "%" 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) = 1.0189998275477927 " " absolute error = 9.7069382531955740000000E-7 " " relative error = 9.52595597915049900000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998195054299763 " " y1[1] (numeric) = 1.9998195010635424 " " absolute error = 4.366433881131115400000000E-9 " " relative error = 2.1834139877500090000000E-7 "%" 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) = 1.019999808396666 " " absolute error = 1.1417033327631998000000E-6 " " relative error = 1.11931845603721520000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9998000066665778 " " y1[1] (numeric) = 1.9998000012454862 " " absolute error = 5.4210915756414120000000000E-9 " " relative error = 2.71081686047081700000000E-7 "%" 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) = 1.0209997882371427 " " absolute error = 1.3317031088977416000000E-6 " " relative error = 1.3043145172015752000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9997795081032559 " " y1[1] (numeric) = 1.9997795014470852 " " absolute error = 6.656170725705124000000000E-9 " " relative error = 3.3284523112342250000000E-7 "%" 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) = 1.0219997670692231 " " absolute error = 1.5416929433076376000000E-6 " " relative error = 1.50850843477738560000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9997580097605092 " " y1[1] (numeric) = 1.999758001669348 " " absolute error = 8.091161296519545000000000E-9 " " relative error = 4.0460702030084840000000E-7 "%" 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) = 1.0229997448929076 " " absolute error = 1.7726726053712838000000E-6 " " relative error = 1.7328212308416380000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999735511659836 " " y1[1] (numeric) = 1.9997355019132828 " " absolute error = 9.746553342182551000000000E-9 " " relative error = 4.8739212187578950000000E-7 "%" 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) = 1.0239997217081964 " " absolute error = 2.025641842040570900000E-6 " " relative error = 1.97817031212276340000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9997120138237345 " " y1[1] (numeric) = 1.9997120021798982 " " absolute error = 1.164383633955878800000000E-8 " " relative error = 5.8227566064846070000000E-7 "%" 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) = 1.0249996975150901 " " absolute error = 2.3016003778408844000000E-6 " " relative error = 2.245469488034090000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9996875162757026 " " y1[1] (numeric) = 1.9996875024702025 " " absolute error = 1.380550007645808800000000E-8 " " relative error = 6.9038287052819140000000E-7 "%" 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) = 1.025999672313589 " " absolute error = 2.6015479124286145000000E-6 " " relative error = 2.53562898623788800000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9996620190402377 " " y1[1] (numeric) = 1.9996620027852041 " " absolute error = 1.625503354141244500000000E-8 " " relative error = 8.1288904758086310000000E-7 "%" 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) = 1.026999646103693 " " absolute error = 2.9264841208132000000000E-6 " " relative error = 2.84955547072949730000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999635522142837 " " y1[1] (numeric) = 1.9996355031259114 " " absolute error = 1.90169255898098300000000E-8 " " relative error = 9.510195922820489000000E-7 "%" 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) = 1.0279996188854028 " " absolute error = 3.2774086524689494000000E-6 " " relative error = 3.1881520587523150000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9996080256099975 " " y1[1] (numeric) = 1.9996080034933328 " " absolute error = 2.211666472184958800000000E-8 " " relative error = 1.1060500077310258000000E-6 "%" 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) = 1.0289995906587188 " " absolute error = 3.6553211293366417000000E-6 " " relative error = 3.5523183365514616000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9995795294692156 " " y1[1] (numeric) = 1.9995795038884767 " " absolute error = 2.55807388604978300000000E-8 " " relative error = 1.2793058982399258000000E-6 "%" 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) = 1.0299995614236412 " " absolute error = 4.061221145601479000000E-6 " " relative error = 3.9429503767764507000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9995500337489875 " " y1[1] (numeric) = 1.9995500043123515 " " absolute error = 2.943663601762125400000000E-8 " " relative error = 1.4721630127169186000000E-6 "%" 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) = 1.0309995311801705 " " absolute error = 4.496108266360821000000E-6 " " relative error = 4.3609407547217250000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999519538478809 " " y1[1] (numeric) = 1.9995195047659655 " " absolute error = 3.37128434058087100000000E-8 " " relative error = 1.6860472106942606000000E-6 "%" 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) = 1.0319994999283069 " " absolute error = 4.960982026736005000000E-6 " " relative error = 4.80717856491898130000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9994880436891753 " " y1[1] (numeric) = 1.9994880052503272 " " absolute error = 3.84388481045050400000000E-8 " " relative error = 1.9224345064641177000000E-6 "%" 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) = 1.0329994676680507 " " absolute error = 5.456841930984169000000E-6 " " relative error = 5.2825494376488690000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9994555494115813 " " y1[1] (numeric) = 1.999455505766445 " " absolute error = 4.36451363938772400000000E-8 " " relative error = 2.1828510469623366000000E-6 "%" 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) = 1.0339994343994026 " " absolute error = 5.984687451165982000000E-6 " " relative error = 5.7879355549430110000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9994220556785212 " " y1[1] (numeric) = 1.9994220063153272 " " absolute error = 4.936319397685906600000000E-8 " " relative error = 2.468873134447206000000E-6 "%" 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) = 1.0349994001223626 " " absolute error = 6.545518026257469000000E-6 " " relative error = 6.3242156669378470000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9993875625234887 " " y1[1] (numeric) = 1.9993875068979823 " " absolute error = 5.56255064232402700000000E-8 " " relative error = 2.7821272606614400000000E-6 "%" 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) = 1.035999364836931 " " absolute error = 7.140333061705917000000E-6 " " relative error = 6.8922651085778000000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9993520699809768 " " y1[1] (numeric) = 1.9993520075154185 " " absolute error = 6.24655582814881400000000E-8 " " relative error = 3.1242900747381870000000E-6 "%" 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) = 1.0369993285431083 " " absolute error = 7.770131927431478000000E-6 " " relative error = 7.4929558147381940000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9993155780864782 " " y1[1] (numeric) = 1.9993155081686445 " " absolute error = 6.99178337448813600000000E-8 " " relative error = 3.4970884292213095000000E-6 "%" 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) = 1.0379992912408946 " " absolute error = 8.435913957605123000000E-6 " " relative error = 8.1271563369872410000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999278086876485 " " y1[1] (numeric) = 1.9992780088586684 " " absolute error = 7.80178166515099700000000E-8 " " relative error = 3.902299393147397600000E-6 "%" 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) = 1.0389992529302907 " " absolute error = 9.138678449538418000000E-6 " " relative error = 8.7957318594114080000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9992395963884881 " " y1[1] (numeric) = 1.9992395095864988 " " absolute error = 8.68019893740523700000000E-8 " " relative error = 4.341750209972591000000E-6 "%" 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) = 1.0399992136112965 " " absolute error = 9.879424662351255000000E-6 " " relative error = 9.4995442141508690000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.999200106660978 " " y1[1] (numeric) = 1.999200010353144 " " absolute error = 9.63078339299983100000000E-8 " " relative error = 4.817318366936746000000E-6 "%" 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) = 1.0409991732839126 " " absolute error = 1.065915181608367800000E-5 " " relative error = 1.0239451897286816000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9991596177334445 " " y1[1] (numeric) = 1.9991595111596123 " " absolute error = 1.06573832203693540000000E-7 " " relative error = 5.330931620383672000000E-6 "%" 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) = 1.0419991319481392 " " absolute error = 1.147885909125179200000E-5 " " relative error = 1.101631008507815000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9991181296463765 " " y1[1] (numeric) = 1.9991180120069123 " " absolute error = 1.17639464169982940000000E-7 " " relative error = 5.884567921496073000000E-6 "%" 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) = 1.0429990896039767 " " absolute error = 1.233954562684935800000E-5 " " relative error = 1.1830970648629066000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9990756424412623 " " y1[1] (numeric) = 1.9990755128960522 " " absolute error = 1.29545210114656580000000E-7 " " relative error = 6.480255542329381000000E-6 "%" 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) = 1.0439990462514255 " " absolute error = 1.324221052034779700000E-5 " " relative error = 1.2684282170400993000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9990321561605888 " " y1[1] (numeric) = 1.9990320138280404 " " absolute error = 1.42332548414003670000000E-7 " " relative error = 7.12007298008515000000E-6 "%" 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) = 1.0449990018904858 " " absolute error = 1.418785282547574400000E-5 " " relative error = 1.3577089958519173000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9989876708478425 " " y1[1] (numeric) = 1.9989875148038854 " " absolute error = 1.56043957089124770000000E-7 " " relative error = 7.806149050581234000000E-6 "%" 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) = 1.045998956521158 " " absolute error = 1.517747155310722500000E-5 " " relative error = 1.4510236063983403000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9989421865475085 " " y1[1] (numeric) = 1.9989420158245954 " " absolute error = 1.70722913139798040000000E-7 " " relative error = 8.540662871028987000000E-6 "%" 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) = 1.0469989101434425 " " absolute error = 1.621206566793098600000E-5 " " relative error = 1.5484559293764644000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9988957033050712 " " y1[1] (numeric) = 1.998895516891179 " " absolute error = 1.86413892100389940000000E-7 " " relative error = 9.325843854292356000000E-6 "%" 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) = 1.0479988627573396 " " absolute error = 1.72926340895607200000E-5 " " relative error = 1.6500895228078283000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9988482211670138 " " y1[1] (numeric) = 1.9988480180046446 " " absolute error = 2.03162369150078350000000E-7 " " relative error = 1.016397178128229200000E-5 "%" 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) = 1.0489988143628497 " " absolute error = 1.842017569053666600000E-5 " " relative error = 1.7560076234608954000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9987997401808184 " " y1[1] (numeric) = 1.9987995191660004 " " absolute error = 2.21014818002629450000000E-7 " " relative error = 1.105737676264835200000E-5 "%" 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) = 1.0499987649599731 " " absolute error = 1.95956892947712900000E-5 " " relative error = 1.8662931483090822000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9987502603949663 " " y1[1] (numeric) = 1.998750020376255 " " absolute error = 2.400187113504870200000E-7 " " relative error = 1.200843927860490900000E-5 "%" 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) = 1.05099871454871 " " absolute error = 2.082017367777133600000E-5 " " relative error = 1.9810286961508475000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.998699781858937 " " y1[1] (numeric) = 1.9986995216364165 " " absolute error = 2.60222520420683170000000E-7 " " relative error = 1.301959017470133400000E-5 "%" 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) = 1.051998663129061 " " absolute error = 2.209462756463942400000E-5 " " relative error = 2.100296549010825000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9986483046232089 " " y1[1] (numeric) = 1.9986480229474937 " " absolute error = 2.81675715196882950000000E-7 " " relative error = 1.4093310691296700000E-5 "%" 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) = 1.0529986107010263 " " absolute error = 2.34200496302960910000E-5 " " relative error = 2.224178673745188800E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9985958287392593 " " y1[1] (numeric) = 1.9985955243104947 " " absolute error = 3.044287646414290000000E-7 " " relative error = 1.523213249341497400000E-5 "%" 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) = 1.0539985572646062 " " absolute error = 2.479743849659321600000E-5 " " relative error = 2.352756723344273000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9985423542595644 " " y1[1] (numeric) = 1.998542025726428 " " absolute error = 3.28533136473296850000000E-7 " " relative error = 1.64386376787603480000E-5 "%" 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) = 1.0549985028198012 " " absolute error = 2.622779273342424000000E-5 " " relative error = 2.4861120386079627000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9984878812375984 " " y1[1] (numeric) = 1.9984875271963016 " " absolute error = 3.54041296724005860000000E-7 " " relative error = 1.771545877499940700000E-5 "%" 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) = 1.0559984473666115 " " absolute error = 2.771211085605962400000E-5 " " relative error = 2.6243256494554057000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9984324097278345 " " y1[1] (numeric) = 1.9984320287211244 " " absolute error = 3.8100671018170830000000E-7 " " relative error = 1.906527878186270000000E-5 "%" 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) = 1.0569983909050376 " " absolute error = 2.925139132492482500000E-5 " " relative error = 2.767478276459681700E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9983759397857437 " " y1[1] (numeric) = 1.9983755303019044 " " absolute error = 4.0948383928096630000000E-7 " " relative error = 2.049083113585070700000E-5 "%" 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) = 1.0579983334350795 " " absolute error = 3.08466325444900500000E-5 " " relative error = 2.9156503322911126000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9983184714677966 " " y1[1] (numeric) = 1.9983180319396503 " " absolute error = 4.39528146323198140000000E-7 " " relative error = 2.199489984198353000000E-5 "%" 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) = 1.058998274956738 " " absolute error = 3.24988328623820900000E-5 " " relative error = 3.0689219231746390000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9982600048314612 " " y1[1] (numeric) = 1.9982595336353703 " " absolute error = 4.71196090812142640000000E-7 " " relative error = 2.35803193614879300000E-5 "%" 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) = 1.059998215470013 " " absolute error = 3.42089905682740900000E-5 " " relative error = 3.22737285031928000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9982005399352043 " " y1[1] (numeric) = 1.9982000353900728 " " absolute error = 5.0454513145226090000000E-7 " " relative error = 2.52499747331977900000E-5 "%" 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) = 1.060998154974905 " " absolute error = 3.59781038925532900000E-5 " " relative error = 3.3910826113198345000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9981400768384905 " " y1[1] (numeric) = 1.9981395372047663 " " absolute error = 5.3963372415033460000000E-7 " " relative error = 2.700680149532645500000E-5 "%" 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) = 1.0619980934714146 " " absolute error = 3.78071710063210300000E-5 " " relative error = 3.5601304016773844000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.998078615601783 " " y1[1] (numeric) = 1.9980780390804591 " " absolute error = 5.7652132379182320000000E-7 " " relative error = 2.885378579652062600000E-5 "%" 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) = 1.0629980309595417 " " absolute error = 3.96971900187281800000E-5 " " relative error = 3.7345951160617710000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.998016156286543 " " y1[1] (numeric) = 1.9980155410181597 " " absolute error = 6.1526838335268510000000E-7 " " relative error = 3.079396437395209300000E-5 "%" 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) = 1.063997967439287 " " absolute error = 4.16491589776413200000E-5 " " relative error = 3.9145553498812397000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9979526989552299 " " y1[1] (numeric) = 1.9979520430188762 " " absolute error = 6.5593635367733330000000E-7 " " relative error = 3.283042456512287300000E-5 "%" 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) = 1.0649979029106507 " " absolute error = 4.3664075868088403000E-5 " " relative error = 4.100089400635971000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.997888243671301 " " y1[1] (numeric) = 1.997887545083617 " " absolute error = 6.9858768392272450000000E-7 " " relative error = 3.49663043533909700000E-5 "%" 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) = 1.0659978373736332 " " absolute error = 4.57429386107044400000E-5 " " relative error = 4.29127526926518950E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9978227904992116 " " y1[1] (numeric) = 1.997822047213391 " " absolute error = 7.4328582067018090000000E-7 " " relative error = 3.72047923471956300000E-5 "%" 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) = 1.0669977708282348 " " absolute error = 4.78867450612874300000E-5 " " relative error = 4.488190661591977500E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9977563395044151 " " y1[1] (numeric) = 1.997755549409206 " " absolute error = 7.9009520903561280000000E-7 " " relative error = 3.95491278596874500000E-5 "%" 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) = 1.0679977032744556 " " absolute error = 5.0096493009688100000E-5 " " relative error = 4.690912989698780600E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.997688890753362 " " y1[1] (numeric) = 1.9976880516720708 " " absolute error = 8.3908129133725140000000E-7 " " relative error = 4.20026008664852570000E-5 "%" 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) = 1.0689976347122965 " " absolute error = 5.23731801791438300000E-5 " " relative error = 4.8995193733379244000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9976204443135015 " " y1[1] (numeric) = 1.9976195540029933 " " absolute error = 8.9031050820587150000000E-7 " " relative error = 4.45685520860712900000E-5 "%" 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) = 1.0699975651417573 " " absolute error = 5.47178042245022300000E-5 " " relative error = 5.114086641231643000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9975510002532797 " " y1[1] (numeric) = 1.9975500564029822 " " absolute error = 9.4385029747456880000000E-7 " " relative error = 4.72503729494212270000E-5 "%" 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) = 1.0709974945628387 " " absolute error = 5.7131362731777100000E-5 " " relative error = 5.334691332490381000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9974805586421405 " " y1[1] (numeric) = 1.9974795588730458 " " absolute error = 9.9976909462284880000000E-7 " " relative error = 5.005150564781856000000E-5 "%" 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) = 1.0719974229755407 " " absolute error = 5.96148532170381900000E-5 " " relative error = 5.561409697962185000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9974091195505261 " " y1[1] (numeric) = 1.9974080614141927 " " absolute error = 1.0581363334427607000000E-6 " " relative error = 5.29754431921724400000E-5 "%" 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) = 1.072997350379864 " " absolute error = 6.21692731257450500000E-5 " " relative error = 5.794317701617084000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.997336683049875 " " y1[1] (numeric) = 1.997335564027431 " " absolute error = 1.1190224440404961000000E-6 " " relative error = 5.60257293393210600000E-5 "%" 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) = 1.0739972767758088 " " absolute error = 6.47956198309707100000E-5 " " relative error = 6.033491021821492000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9972632492126245 " " y1[1] (numeric) = 1.9972620667137693 " " absolute error = 1.1824988552788795000000E-6 " " relative error = 5.920595874104492000000E-5 "%" 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) = 1.0749972021633754 " " absolute error = 6.74948906329575500000E-5 " " relative error = 6.279005052730582000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9971888181122073 " " y1[1] (numeric) = 1.9971875694742156 " " absolute error = 1.248637991668744000000E-6 " " relative error = 6.25197768155435500000E-5 "%" 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) = 1.075997126542564 " " absolute error = 7.02680827582291600000E-5 " " relative error = 6.530934905632734000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9971133898230555 " " y1[1] (numeric) = 1.9971120723097786 " " absolute error = 1.3175132769216447000000E-6 " " relative error = 6.59708799528091100000E-5 "%" 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) = 1.0769970499133754 " " absolute error = 7.31161933580359900000E-5 " " relative error = 6.789355410225751000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9970369644205967 " " y1[1] (numeric) = 1.9970355752214666 " " absolute error = 1.3891991301751005000000E-6 " " relative error = 6.95630153535065400000E-5 "%" 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) = 1.0779969722758096 " " absolute error = 7.60402195081333300000E-5 " " relative error = 7.05434111601069100E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9969595419812567 " " y1[1] (numeric) = 1.996958078210288 " " absolute error = 1.4637709686571299000000E-6 " " relative error = 7.32999811906489200000E-5 "%" 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) = 1.0789968936298668 " " absolute error = 7.90411582067829200000E-5 " " relative error = 7.325966293514371000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9968811225824579 " " y1[1] (numeric) = 1.996879581277251 " " absolute error = 1.5413052067980715000000E-6 " " relative error = 7.71856265937746600000E-5 "%" 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) = 1.0799968139755476 " " absolute error = 8.21200063747529200000E-5 " " relative error = 7.604304935691255000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9968017063026193 " " y1[1] (numeric) = 1.9968000844233644 " " absolute error = 1.6218792548983174000000E-6 " " relative error = 8.1223851611258500000E-5 "%" 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) = 1.0809967333128523 " " absolute error = 8.52777608542076800000E-5 " " relative error = 7.889430759215905000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9967212932211575 " " y1[1] (numeric) = 1.9967195876496362 " " absolute error = 1.7055715213487588000000E-6 " " relative error = 8.54186073509183100000E-5 "%" 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) = 1.0819966516417812 " " absolute error = 8.85154184064873600000E-5 " " relative error = 8.181417205666724000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.996639883418486 " " y1[1] (numeric) = 1.996638090957075 " " absolute error = 1.7924614110764736000000E-6 " " relative error = 8.97738959319777500000E-5 "%" 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) = 1.0829965689623346 " " absolute error = 9.18339757127739600000E-5 " " relative error = 8.480337442970778000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9965574769760137 " " y1[1] (numeric) = 1.9965555943466888 " " absolute error = 1.882629324878593000000E-6 " " relative error = 9.42937704818808200000E-5 "%" 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) = 1.083996485274513 " " absolute error = 9.52344293720930300000E-5 " " relative error = 8.786264366595823000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9964740739761475 " " y1[1] (numeric) = 1.9964720978194863 " " absolute error = 1.976156661198658000000E-6 " " relative error = 9.898233525582301000E-5 "%" 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) = 1.0849964005783166 " " absolute error = 9.87177759004254100000E-5 " " relative error = 9.099270600839149000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9963896745022904 " " y1[1] (numeric) = 1.9963876013764759 " " absolute error = 2.0731258145723075000000E-6 " " relative error = 1.03843745589855730000E-4 "%" 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) = 1.0859963148737457 " " absolute error = 1.02285011730041120000E-4 " " relative error = 9.419428500130759000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.996304278638842 " " y1[1] (numeric) = 1.9963021050186658 " " absolute error = 2.1736201762934115000000E-6 " " relative error = 1.08882207965584820000E-4 "%" 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) = 1.0869962281608008 " " absolute error = 1.05937133208389160000E-4 " " relative error = 9.746810150289563000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.996217886471198 " " y1[1] (numeric) = 1.9962156087470644 " " absolute error = 2.2777241335258935000000E-6 " " relative error = 1.14101979997400310000E-4 "%" 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) = 1.087996140439482 " " absolute error = 1.09675136596543150000E-4 " " relative error = 1.008148736973281400E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9961304980857502 " " y1[1] (numeric) = 1.9961281125626802 " " absolute error = 2.3855230699698637000000E-6 " " relative error = 1.19507370497947570000E-4 "%" 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) = 1.0889960517097899 " " absolute error = 1.13500018069423450000E-4 " " relative error = 1.04235317108430510E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9960421135698874 " " y1[1] (numeric) = 1.9960396164665215 " " absolute error = 2.4971033658616193000000E-6 " " relative error = 1.25102739510620480000E-4 "%" 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) = 1.0899959619717248 " " absolute error = 1.17412773713576610000E-4 " " relative error = 1.077301446110440300E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9959527330119942 " " y1[1] (numeric) = 1.9959501204595966 " " absolute error = 2.612552397529555000000E-6 " " relative error = 1.3089249832019220000E-4 "%" 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) = 1.090995871225287 " " absolute error = 1.21414399526731390000E-4 " " relative error = 1.113000664439650500E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9958623565014508 " " y1[1] (numeric) = 1.995859624542914 " " absolute error = 2.7319585367280297000000E-6 " " relative error = 1.36881109452702070000E-4 "%" 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) = 1.0919957794704767 " " absolute error = 1.25505891416688440000E-4 " " relative error = 1.149457902222125500E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9957709841286342 " " y1[1] (numeric) = 1.9957681287174822 " " absolute error = 2.8554111519696335000000E-6 " " relative error = 1.43073086775851840000E-4 "%" 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) = 1.0929956867072943 " " absolute error = 1.2968824520043220000E-4 " " relative error = 1.186680209494416200E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9956786159849162 " " y1[1] (numeric) = 1.9956756329843093 " " absolute error = 2.983000606970876000000E-6 " " relative error = 1.49472995455167120000E-4 "%" 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) = 1.0939955929357403 " " absolute error = 1.33962456603464730000E-4 " " relative error = 1.224674610305016800E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9955852521626654 " " y1[1] (numeric) = 1.9955821373444038 " " absolute error = 3.114818261540364000000E-6 " " relative error = 1.56085452032919070000E-4 "%" 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) = 1.094995498155815 " " absolute error = 1.38329521257585240000E-4 " " relative error = 1.26344810282515490E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9954908927552453 " " y1[1] (numeric) = 1.995487641798774 " " absolute error = 3.2509564713567585000000E-6 " " relative error = 1.6291512445181080000E-4 "%" 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) = 1.0959954023675187 " " absolute error = 1.42790434701556280000E-4 " " relative error = 1.303007659485418700E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9953955378570152 " " y1[1] (numeric) = 1.9953921463484283 " " absolute error = 3.3915085868585493000000E-6 " " relative error = 1.6996673203453738000E-4 "%" 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) = 1.0969953055708517 " " absolute error = 1.4734619237866120000E-4 " " relative error = 1.34336022708338420E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.9952991875633304 " " y1[1] (numeric) = 1.9952956509943751 " " absolute error = 3.5365689552424584000000E-6 " " relative error = 1.77245045619516070000E-4 "%" 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 = 97 "Total Elapsed Time "= 15 Minutes 13 Seconds "Elapsed Time(since restart) "= 15 Minutes 11 Seconds "Expected Time Remaining "= 12 Hours 41 Minutes 9 Seconds "Optimized Time Remaining "= 12 Hours 39 Minutes 48 Seconds "Time to Timeout " Unknown Percent Done = 1.9600000000000015 "%" (%o54) true (%o54) diffeq.max