(%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 - 4 + 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 - 4 + 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 - 4 + 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 - 4 + 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 array_tmp2 : array_tmp1 - array_const_1D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 1, 5 4 then (temporary : array_tmp2 glob_h factorial_3(0, 4), 1 array_y2 : temporary, array_y2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 4 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 3 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 2 temporary 5.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 5, 1 array_tmp4 : array_y2_higher , array_tmp5 : array_m1 array_tmp4 , 1 4, 1 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp5 glob_h factorial_3(0, 1), 1 array_y1 : temporary, array_y1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : array_y1 + array_const_0D0 , 2 2 2 array_tmp2 : array_tmp1 - array_const_1D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 1, 6 4 then (temporary : array_tmp2 glob_h factorial_3(1, 5), 2 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)), kkk : 3, glob_h 5, 2 array_tmp4 : array_y2_higher , array_tmp5 : 2 4, 2 2 ats(2, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 3 then (if 2 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(1, 2), array_y1 : temporary, 2 3 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 3 glob_h array_y1_higher : temporary)), kkk : 3, 2, 2 array_tmp1 : array_y1 + array_const_0D0 , 3 3 3 array_tmp2 : array_tmp1 - array_const_1D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 1, 7 4 then (temporary : array_tmp2 glob_h factorial_3(2, 6), 3 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)), kkk : 4, glob_h 5, 3 array_tmp4 : array_y2_higher , array_tmp5 : 3 4, 3 3 ats(3, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 4 then (if 3 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(2, 3), array_y1 : temporary, 3 4 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 4 glob_h array_y1_higher : temporary)), kkk : 4, 2, 3 array_tmp1 : array_y1 + array_const_0D0 , 4 4 4 array_tmp2 : array_tmp1 - array_const_1D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 1, 8 4 then (temporary : array_tmp2 glob_h factorial_3(3, 7), 4 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)), kkk : 5, glob_h 5, 4 array_tmp4 : array_y2_higher , array_tmp5 : 4 4, 4 4 ats(4, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 5 then (if 4 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(3, 4), array_y1 : temporary, 4 5 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 5 glob_h array_y1_higher : temporary)), kkk : 5, 2, 4 array_tmp1 : array_y1 + array_const_0D0 , 5 5 5 array_tmp2 : array_tmp1 - array_const_1D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 1, 9 4 then (temporary : array_tmp2 glob_h factorial_3(4, 8), 5 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)), kkk : 6, glob_h 5, 5 array_tmp4 : array_y2_higher , array_tmp5 : 5 4, 5 5 ats(5, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 6 then (if 5 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(4, 5), array_y1 : temporary, 5 6 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 6 glob_h array_y1_higher : temporary)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk array_y1 + array_const_0D0 , array_tmp2 : kkk kkk kkk array_tmp1 - array_const_1D0 , order_d : 4, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 1, order_d + kkk order_d array_tmp2 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_tmp4 : array_y2_higher , kkk 4, kkk array_tmp5 : ats(kkk, array_m1, array_tmp4, 1), order_d : 1, kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 2, order_d + kkk order_d array_tmp5 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y1 : temporary, array_y1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) (%o8) atomall() := (array_tmp1 : array_y1 + array_const_0D0 , 1 1 1 array_tmp2 : array_tmp1 - array_const_1D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 1, 5 4 then (temporary : array_tmp2 glob_h factorial_3(0, 4), 1 array_y2 : temporary, array_y2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y2_higher : temporary, glob_h 2, 4 temporary 3.0 temporary : -------------, array_y2_higher : temporary, glob_h 3, 3 temporary 4.0 temporary : -------------, array_y2_higher : temporary, glob_h 4, 2 temporary 5.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 5, 1 array_tmp4 : array_y2_higher , array_tmp5 : array_m1 array_tmp4 , 1 4, 1 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp5 glob_h factorial_3(0, 1), 1 array_y1 : temporary, array_y1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : array_y1 + array_const_0D0 , 2 2 2 array_tmp2 : array_tmp1 - array_const_1D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 1, 6 4 then (temporary : array_tmp2 glob_h factorial_3(1, 5), 2 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)), kkk : 3, glob_h 5, 2 array_tmp4 : array_y2_higher , array_tmp5 : 2 4, 2 2 ats(2, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 3 then (if 2 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(1, 2), array_y1 : temporary, 2 3 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 3 glob_h array_y1_higher : temporary)), kkk : 3, 2, 2 array_tmp1 : array_y1 + array_const_0D0 , 3 3 3 array_tmp2 : array_tmp1 - array_const_1D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 1, 7 4 then (temporary : array_tmp2 glob_h factorial_3(2, 6), 3 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)), kkk : 4, glob_h 5, 3 array_tmp4 : array_y2_higher , array_tmp5 : 3 4, 3 3 ats(3, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 4 then (if 3 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(2, 3), array_y1 : temporary, 3 4 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 4 glob_h array_y1_higher : temporary)), kkk : 4, 2, 3 array_tmp1 : array_y1 + array_const_0D0 , 4 4 4 array_tmp2 : array_tmp1 - array_const_1D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 1, 8 4 then (temporary : array_tmp2 glob_h factorial_3(3, 7), 4 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)), kkk : 5, glob_h 5, 4 array_tmp4 : array_y2_higher , array_tmp5 : 4 4, 4 4 ats(4, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 5 then (if 4 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(3, 4), array_y1 : temporary, 4 5 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 5 glob_h array_y1_higher : temporary)), kkk : 5, 2, 4 array_tmp1 : array_y1 + array_const_0D0 , 5 5 5 array_tmp2 : array_tmp1 - array_const_1D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 1, 9 4 then (temporary : array_tmp2 glob_h factorial_3(4, 8), 5 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)), kkk : 6, glob_h 5, 5 array_tmp4 : array_y2_higher , array_tmp5 : 5 4, 5 5 ats(5, array_m1, array_tmp4, 1), if not array_y1_set_initial 2, 6 then (if 5 <= glob_max_terms then (temporary : 1 array_tmp5 glob_h factorial_3(4, 5), array_y1 : temporary, 5 6 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 6 glob_h array_y1_higher : temporary)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk array_y1 + array_const_0D0 , array_tmp2 : kkk kkk kkk array_tmp1 - array_const_1D0 , order_d : 4, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 1, order_d + kkk order_d array_tmp2 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_tmp4 : array_y2_higher , kkk 4, kkk array_tmp5 : ats(kkk, array_m1, array_tmp4, 1), order_d : 1, kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 2, order_d + kkk order_d array_tmp5 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y1 : temporary, array_y1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) log(x) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i21) mode_declare(ats, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o21) [ats] (%i22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i23) mode_declare(att, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o23) [att] (%i24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i29) log_revs(file, revs) := printf(file, revs) (%o29) log_revs(file, revs) := printf(file, revs) (%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i32) logstart(file) := printf(file, "") (%o32) logstart(file) := printf(file, "") (%i33) logend(file) := printf(file, "~%") (%o33) logend(file) := printf(file, "~%") (%i34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i35) mode_declare(comp_expect_sec, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o35) [comp_expect_sec] (%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i37) mode_declare(comp_percent, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o37) [comp_percent] (%i38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i39) mode_declare(factorial_1, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o39) [factorial_1] (%i40) factorial_1(nnn) := nnn! (%o40) factorial_1(nnn) := nnn! (%i41) mode_declare(factorial_3, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o41) [factorial_3] mmm2! (%i42) factorial_3(mmm2, nnn2) := ----- nnn2! mmm2! (%o42) factorial_3(mmm2, nnn2) := ----- nnn2! (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) exact_soln_y1(x) := sin(x) + 1.0 (%o49) exact_soln_y1(x) := sin(x) + 1.0 (%i50) exact_soln_y2(x) := sin(x) + 1.0 (%o50) exact_soln_y2(x) := sin(x) + 1.0 (%i51) exact_soln_y2p(x) := cos(x) (%o51) exact_soln_y2p(x) := cos(x) (%i52) exact_soln_y2pp(x) := - sin(x) (%o52) exact_soln_y2pp(x) := - sin(x) (%i53) exact_soln_y2ppp(x) := - cos(x) (%o53) exact_soln_y2ppp(x) := - cos(x) (%i54) mainprog() := (define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_max_hours, 0.0, float), define_variable(glob_almost_1, 0.999, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(min_in_hour, 60.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10normmin, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_optimal_done, false, boolean), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest8postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0;"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.1,"), 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, "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 + sin(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, ""), 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_y1_init, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 5, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y2_higher_work, 1 + 5, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 5, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y1_set_initial, 1 + 3, 1 + max_terms), term : 1, while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_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_y2_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 5 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_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term term : 1 + term), array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_const_3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term), term array_const_3 : 3, 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_4, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_4 : 0.0, term : 1 + term), term array_const_4 : 4, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : 0.1, x_end : 5.1, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), glob_h : 1.0E-5, 1 + 3 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 : false, array_y2_set_initial : false, 1, 5 1, 6 array_y2_set_initial : false, array_y2_set_initial : false, 1, 7 1, 8 array_y2_set_initial : false, array_y2_set_initial : false, 1, 9 1, 10 array_y2_set_initial : false, array_y2_set_initial : false, 1, 11 1, 12 array_y2_set_initial : false, array_y2_set_initial : false, 1, 13 1, 14 array_y2_set_initial : false, array_y2_set_initial : false, 1, 15 1, 16 array_y2_set_initial : false, array_y2_set_initial : false, 1, 17 1, 18 array_y2_set_initial : false, array_y2_set_initial : false, 1, 19 1, 20 array_y2_set_initial : false, array_y2_set_initial : false, 1, 21 1, 22 array_y2_set_initial : false, array_y2_set_initial : false, 1, 23 1, 24 array_y2_set_initial : false, array_y2_set_initial : false, 1, 25 1, 26 array_y2_set_initial : false, array_y2_set_initial : false, 1, 27 1, 28 array_y2_set_initial : false, array_y2_set_initial : false, 1, 29 1, 30 array_y1_set_initial : true, array_y1_set_initial : false, 2, 1 2, 2 array_y1_set_initial : false, array_y1_set_initial : false, 2, 3 2, 4 array_y1_set_initial : false, array_y1_set_initial : false, 2, 5 2, 6 array_y1_set_initial : false, array_y1_set_initial : false, 2, 7 2, 8 array_y1_set_initial : false, array_y1_set_initial : false, 2, 9 2, 10 array_y1_set_initial : false, array_y1_set_initial : false, 2, 11 2, 12 array_y1_set_initial : false, array_y1_set_initial : false, 2, 13 2, 14 array_y1_set_initial : false, array_y1_set_initial : false, 2, 15 2, 16 array_y1_set_initial : false, array_y1_set_initial : false, 2, 17 2, 18 array_y1_set_initial : false, array_y1_set_initial : false, 2, 19 2, 20 array_y1_set_initial : false, array_y1_set_initial : false, 2, 21 2, 22 array_y1_set_initial : false, array_y1_set_initial : false, 2, 23 2, 24 array_y1_set_initial : false, array_y1_set_initial : false, 2, 25 2, 26 array_y1_set_initial : false, array_y1_set_initial : false, 2, 27 2, 28 array_y1_set_initial : false, array_y1_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 4, 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 <= 5 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 5 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 : 4, ord : 5, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y2 , x , 4 ) = y1 - 1.0;"), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), 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, "2012-06-15T23:10:18-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest8"), logitem_str(html_log_file, "diff ( y2 , x , 4 ) = y1 - 1.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest8 diffeq.max"), logitem_str(html_log_file, "\ mtest8 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), 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)) (%o54) mainprog() := (define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(years_in_century, 100.0, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_max_hours, 0.0, float), define_variable(glob_almost_1, 0.999, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(min_in_hour, 60.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10normmin, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_optimal_done, false, boolean), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest8postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0;"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.1,"), 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, "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 + sin(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, ""), 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_y1_init, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 5, 1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_y2_higher_work, 1 + 5, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 5, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y1_set_initial, 1 + 3, 1 + max_terms), term : 1, while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_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_y2_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 5 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_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term term : 1 + term), array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_const_3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term), term array_const_3 : 3, 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_4, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_4 : 0.0, term : 1 + term), term array_const_4 : 4, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : 0.1, x_end : 5.1, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), glob_h : 1.0E-5, 1 + 3 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 : false, array_y2_set_initial : false, 1, 5 1, 6 array_y2_set_initial : false, array_y2_set_initial : false, 1, 7 1, 8 array_y2_set_initial : false, array_y2_set_initial : false, 1, 9 1, 10 array_y2_set_initial : false, array_y2_set_initial : false, 1, 11 1, 12 array_y2_set_initial : false, array_y2_set_initial : false, 1, 13 1, 14 array_y2_set_initial : false, array_y2_set_initial : false, 1, 15 1, 16 array_y2_set_initial : false, array_y2_set_initial : false, 1, 17 1, 18 array_y2_set_initial : false, array_y2_set_initial : false, 1, 19 1, 20 array_y2_set_initial : false, array_y2_set_initial : false, 1, 21 1, 22 array_y2_set_initial : false, array_y2_set_initial : false, 1, 23 1, 24 array_y2_set_initial : false, array_y2_set_initial : false, 1, 25 1, 26 array_y2_set_initial : false, array_y2_set_initial : false, 1, 27 1, 28 array_y2_set_initial : false, array_y2_set_initial : false, 1, 29 1, 30 array_y1_set_initial : true, array_y1_set_initial : false, 2, 1 2, 2 array_y1_set_initial : false, array_y1_set_initial : false, 2, 3 2, 4 array_y1_set_initial : false, array_y1_set_initial : false, 2, 5 2, 6 array_y1_set_initial : false, array_y1_set_initial : false, 2, 7 2, 8 array_y1_set_initial : false, array_y1_set_initial : false, 2, 9 2, 10 array_y1_set_initial : false, array_y1_set_initial : false, 2, 11 2, 12 array_y1_set_initial : false, array_y1_set_initial : false, 2, 13 2, 14 array_y1_set_initial : false, array_y1_set_initial : false, 2, 15 2, 16 array_y1_set_initial : false, array_y1_set_initial : false, 2, 17 2, 18 array_y1_set_initial : false, array_y1_set_initial : false, 2, 19 2, 20 array_y1_set_initial : false, array_y1_set_initial : false, 2, 21 2, 22 array_y1_set_initial : false, array_y1_set_initial : false, 2, 23 2, 24 array_y1_set_initial : false, array_y1_set_initial : false, 2, 25 2, 26 array_y1_set_initial : false, array_y1_set_initial : false, 2, 27 2, 28 array_y1_set_initial : false, array_y1_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 4, 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 <= 5 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 5 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 : 4, ord : 5, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y2 , x , 4 ) = y1 - 1.0;"), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), 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, "2012-06-15T23:10:18-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest8"), logitem_str(html_log_file, "diff ( y2 , x , 4 ) = y1 - 1.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest8 diffeq.max"), logitem_str(html_log_file, "\ mtest8 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), 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)) (%i55) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/mtest8postode.ode#################" "diff ( y2 , x , 4 ) = y1 - 1.0;" "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms : 30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.1," "x_end : 5.1," "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)," "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 + sin(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) " ");" "" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.1 " " y2[1] (analytic) = 1.0998334166468282 " " y2[1] (numeric) = 1.0998334166468282 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.0998334166468282 " " y1[1] (numeric) = 1.0998334166468282 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " x[1] = 0.1 " " y2[1] (analytic) = 1.0998334166468282 " " y2[1] (numeric) = 1.0998334166468282 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.0998334166468282 " " y1[1] (numeric) = 1.0998334166468282 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.101 " " y2[1] (analytic) = 1.100828370729568 " " y2[1] (numeric) = 1.1008283707295623 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 5.2443776719023730000000000000E-13 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.100828370729568 " " y1[1] (numeric) = 1.1008318740131053 " " absolute error = 3.503283537265034000000E-6 " " relative error = 3.182406658853870000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10200000000000001 " " y2[1] (analytic) = 1.1018232239839456 " " y2[1] (numeric) = 1.1018232239646466 " " absolute error = 1.929900683705909600000000000E-11 " " relative error = 1.7515520109730684000000000E-9 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1018232239839456 " " y1[1] (numeric) = 1.1018303708975024 " " absolute error = 7.146913556743684000000E-6 " " relative error = 6.486443016604830000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10300000000000001 " " y2[1] (analytic) = 1.1028179754151075 " " y2[1] (numeric) = 1.1028179752506486 " " absolute error = 1.64458890949958900000000000E-10 " " relative error = 1.491260521828686700000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1028179754151075 " " y1[1] (numeric) = 1.1028289062958572 " " absolute error = 1.093088074965997700000E-5 " " relative error = 9.9117723807009270000E-4 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10400000000000001 " " y2[1] (analytic) = 1.1038126240283028 " " y2[1] (numeric) = 1.1038126233837584 " " absolute error = 6.4454441783823310000000000E-10 " " relative error = 5.839255719743485000000000E-8 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1038126240283028 " " y1[1] (numeric) = 1.103827479203826 " " absolute error = 1.485517552324289200000E-5 " " relative error = 1.3458059094332292000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10500000000000001 " " y2[1] (analytic) = 1.1048071688288825 " " y2[1] (numeric) = 1.104807167057793 " " absolute error = 1.7710894972822190000000000E-9 " " relative error = 1.60307567442706660000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1048071688288825 " " y1[1] (numeric) = 1.1048260886168855 " " absolute error = 1.891978800294680200000E-5 " " relative error = 1.7124968534556262000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10600000000000001 " " y2[1] (analytic) = 1.1058016088223022 " " y2[1] (numeric) = 1.1058016048641992 " " absolute error = 3.958102956502785000000000E-9 " " relative error = 3.5793969957397990000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1058016088223022 " " y1[1] (numeric) = 1.1058247335303322 " " absolute error = 2.31247080300089900000E-5 " " relative error = 2.0912167106211035000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10700000000000001 " " y2[1] (analytic) = 1.1067959430141219 " " y2[1] (numeric) = 1.1067959352920573 " " absolute error = 7.722064543358442000000000E-9 " " relative error = 6.9769541459729710000000E-7 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1067959430141219 " " y1[1] (numeric) = 1.106823412939285 " " absolute error = 2.746992516322599400000E-5 " " relative error = 2.481932223966916000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10800000000000001 " " y2[1] (analytic) = 1.1077901704100075 " " y2[1] (numeric) = 1.1077901567280848 " " absolute error = 1.368192270589929600000000E-8 " " relative error = 1.235064461786607000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1077901704100075 " " y1[1] (numeric) = 1.1078221258386856 " " absolute error = 3.195542867806544500000E-5 " " relative error = 2.8846102386193160000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.10900000000000001 " " y2[1] (analytic) = 1.1087842900157316 " " y2[1] (numeric) = 1.10878426745664 " " absolute error = 2.255909170578718200000000E-8 " " relative error = 2.0345789446085236000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1087842900157316 " " y1[1] (numeric) = 1.1088208712232985 " " absolute error = 3.658120756688809600000E-5 " " relative error = 3.2992177014312740000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11000000000000001 " " y2[1] (analytic) = 1.1097783008371749 " " y2[1] (numeric) = 1.109778265659726 " " absolute error = 3.517744895376040400000000E-8 " " relative error = 3.1697726408259980000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1097783008371749 " " y1[1] (numeric) = 1.109819648087714 " " absolute error = 4.13472505391698800000E-5 " " relative error = 3.725721660621682000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11100000000000002 " " y2[1] (analytic) = 1.1107722018803263 " " y2[1] (numeric) = 1.1107721494169949 " " absolute error = 5.24633314569200600000000E-8 " " relative error = 4.723140475437682000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1107722018803263 " " y1[1] (numeric) = 1.1108184554263476 " " absolute error = 4.625354602127984500000E-5 " " relative error = 4.164089265376049000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11200000000000002 " " y2[1] (analytic) = 1.1117659921512852 " " y2[1] (numeric) = 1.1117659167057516 " " absolute error = 7.54455335982839900000000E-8 " " relative error = 6.786098345416705000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1117659921512852 " " y1[1] (numeric) = 1.1118172922334413 " " absolute error = 5.1300082156036100000E-5 " " relative error = 4.61428776542891050E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11300000000000002 " " y2[1] (analytic) = 1.1127596706562612 " " y2[1] (numeric) = 1.1127595654009579 " " absolute error = 1.05255303362028490000000E-7 " " relative error = 9.458943034838161000000E-6 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1127596706562612 " " y1[1] (numeric) = 1.112816157503065 " " absolute error = 5.64868468038159900000E-5 " " relative error = 5.076284510787699000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11400000000000002 " " y2[1] (analytic) = 1.113753236401576 " " y2[1] (numeric) = 1.1137530932752366 " " absolute error = 1.43126339446908450000000E-7 " " relative error = 1.285081243932768800000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.113753236401576 " " y1[1] (numeric) = 1.1138150502291175 " " absolute error = 6.18138275414459300000E-5 " " relative error = 5.550046951258265000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11500000000000002 " " y2[1] (analytic) = 1.1147466883936639 " " y2[1] (numeric) = 1.1147464979988768 " " absolute error = 1.90394787047409860000000E-7 " " relative error = 1.707964589890519000000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1147466883936639 " " y1[1] (numeric) = 1.114813969405327 " " absolute error = 6.72810116630895300000E-5 " " relative error = 6.035542636151773000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11600000000000002 " " y2[1] (analytic) = 1.1157400256390728 " " y2[1] (numeric) = 1.1157397771398374 " " absolute error = 2.4849923541125918000000E-7 " " relative error = 2.2272144917354197000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1157400256390728 " " y1[1] (numeric) = 1.1158129140252522 " " absolute error = 7.28883861793594400000E-5 " " relative error = 6.5327392138334800000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11700000000000002 " " y2[1] (analytic) = 1.1167332471444658 " " y2[1] (numeric) = 1.1167329281637521 " " absolute error = 3.1898071362057580000000E-7 " " relative error = 2.856373394776442500000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1167332471444658 " " y1[1] (numeric) = 1.1168118830822835 " " absolute error = 7.86359378177614600000E-5 " " relative error = 7.041604431392804000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11800000000000002 " " y2[1] (analytic) = 1.1177263519166214 " " y2[1] (numeric) = 1.1177259484339341 " " absolute error = 4.03482687261202950000000E-7 " " relative error = 3.60985214824121270000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1177263519166214 " " y1[1] (numeric) = 1.1178108755696443 " " absolute error = 8.45236530229165300000E-5 " " relative error = 7.56210613429482000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.11900000000000002 " " y2[1] (analytic) = 1.118719338962435 " " y2[1] (numeric) = 1.1187188352113808 " " absolute error = 5.0375105420386030000000E-7 " " relative error = 4.502926128648747600000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.118719338962435 " " y1[1] (numeric) = 1.1188098904803914 " " absolute error = 9.05515179563387600000E-5 " " relative error = 8.094212265993495000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12000000000000002 " " y2[1] (analytic) = 1.1197122072889194 " " y2[1] (numeric) = 1.119711585654779 " " absolute error = 6.2163414038529650000000E-7 " " relative error = 5.55173138542818600000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1197122072889194 " " y1[1] (numeric) = 1.119808926807416 " " absolute error = 9.67195184966573900000E-5 " " relative error = 8.637890867586197000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12100000000000002 " " y2[1] (analytic) = 1.1207049559032065 " " y2[1] (numeric) = 1.1207041968205098 " " absolute error = 7.5908269669966440000000E-7 " " relative error = 6.77326081857021100000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1207049559032065 " " y1[1] (numeric) = 1.1208079835434455 " " absolute error = 1.03027640238950720000E-4 " " relative error = 9.193110077390346000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12200000000000003 " " y2[1] (analytic) = 1.1216975838125478 " " y2[1] (numeric) = 1.121696665662653 " " absolute error = 9.181498947796740000000E-7 " " relative error = 8.18536036833534400000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1216975838125478 " " y1[1] (numeric) = 1.1218070596810434 " " absolute error = 1.09475868495634290000E-4 " " relative error = 9.759838130660475000E-3 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12300000000000003 " " y2[1] (analytic) = 1.1226900900243153 " " y2[1] (numeric) = 1.1226889890329936 " " absolute error = 1.1009913216675216000000E-6 " " relative error = 9.80672521696237900000E-5 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1226900900243153 " " y1[1] (numeric) = 1.122806154212611 " " absolute error = 1.16064188295794680000E-4 " " relative error = 1.033804335916788400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12400000000000003 " " y2[1] (analytic) = 1.1236824735460031 " " y2[1] (numeric) = 1.123681163681026 " " absolute error = 1.3098649771503545000000E-6 " " relative error = 1.16568960359132020000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1236824735460031 " " y1[1] (numeric) = 1.1238052661303883 " " absolute error = 1.22792584385189580000E-4 " " relative error = 1.092769419084140300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12500000000000003 " " y2[1] (analytic) = 1.1246747333852278 " " y2[1] (numeric) = 1.12467318625396 " " absolute error = 1.5471312677650673000000E-6 " " relative error = 1.37562552250841570000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1246747333852278 " " y1[1] (numeric) = 1.1248043944264547 " " absolute error = 1.2966104122691390000E-4 " " relative error = 1.152875914946885500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12600000000000003 " " y2[1] (analytic) = 1.1256668685497293 " " y2[1] (numeric) = 1.1256650532967267 " " absolute error = 1.8152530025794533000000E-6 " " relative error = 1.61260231894198250000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1256668685497293 " " y1[1] (numeric) = 1.1258035380927305 " " absolute error = 1.36669543001177730000E-4 " " relative error = 1.214120685432077100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12700000000000003 " " y2[1] (analytic) = 1.1266588780473727 " " y2[1] (numeric) = 1.1266567612519829 " " absolute error = 2.1167953898615366000000E-6 " " relative error = 1.87882546448325360000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1266588780473727 " " y1[1] (numeric) = 1.1268026961209774 " " absolute error = 1.43818073604640160000E-4 " " relative error = 1.276500601973626000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12800000000000003 " " y2[1] (analytic) = 1.1276507608861488 " " y2[1] (numeric) = 1.127648306460118 " " absolute error = 2.4544260308623222000000E-6 " " relative error = 2.17658349197897530000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1276507608861488 " " y1[1] (numeric) = 1.1278018675027999 " " absolute error = 1.5110661665107550000E-4 " " relative error = 1.340012545482880000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.12900000000000003 " " y2[1] (analytic) = 1.1286425160741744 " " y2[1] (numeric) = 1.1286396851592593 " " absolute error = 2.83091491515286000000E-6 " " relative error = 2.50824762919600400000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1286425160741744 " " y1[1] (numeric) = 1.1288010512296456 " " absolute error = 1.58535155471151160000E-4 " " relative error = 1.404653406311447400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13000000000000003 " " y2[1] (analytic) = 1.129634142619695 " " y2[1] (numeric) = 1.1296308934852783 " " absolute error = 3.2491344166274416000000E-6 " " relative error = 2.87627143518563200000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.129634142619695 " " y1[1] (numeric) = 1.1298002462928074 " " absolute error = 1.66103673112427690000E-4 " " relative error = 1.470420084216138000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13100000000000003 " " y2[1] (analytic) = 1.1306256395310834 " " y2[1] (numeric) = 1.1306219274717964 " " absolute error = 3.7120592870643065000000E-6 " " relative error = 3.28319043658327870000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1306256395310834 " " y1[1] (numeric) = 1.1307994516834232 " " absolute error = 1.73812152339802850000E-4 " " relative error = 1.537309488327983000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13200000000000003 " " y2[1] (analytic) = 1.1316170058168433 " " y2[1] (numeric) = 1.1316127830501912 " " absolute error = 4.22276665212884000000E-6 " " relative error = 3.7316217681623560000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1316170058168433 " " y1[1] (numeric) = 1.131798666392478 " " absolute error = 1.81660575634623460000E-4 " " relative error = 1.605318537109594600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13300000000000003 " " y2[1] (analytic) = 1.1326082404856084 " " y2[1] (numeric) = 1.1326034560496028 " " absolute error = 4.784436005600412000000E-6 " " relative error = 4.22426381389303160000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1326082404856084 " " y1[1] (numeric) = 1.1327978894108037 " " absolute error = 1.89648925195351480000E-4 " " relative error = 1.6744441583264402E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13400000000000004 " " y2[1] (analytic) = 1.1335993425461441 " " y2[1] (numeric) = 1.13359394219694 " " absolute error = 5.400349204043309000000E-6 " " relative error = 4.763895850463130000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1335993425461441 " " y1[1] (numeric) = 1.1337971197290817 " " absolute error = 1.97777182937564080000E-4 " " relative error = 1.744683289012346800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13500000000000004 " " y2[1] (analytic) = 1.1345903110073483 " " y2[1] (numeric) = 1.1345842371168875 " " absolute error = 6.073890460811526000000E-6 " " relative error = 5.3533776922692130000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1345903110073483 " " y1[1] (numeric) = 1.1347963563378423 " " absolute error = 2.06045330493953570000E-4 " " relative error = 1.816032875435149900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13600000000000004 " " y2[1] (analytic) = 1.1355811448782527 " " y2[1] (numeric) = 1.1355743363319108 " " absolute error = 6.808546341829924000000E-6 " " relative error = 5.9956493400212960000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1355811448782527 " " y1[1] (numeric) = 1.1357955982274666 " " absolute error = 2.14453349213883370000E-4 " " relative error = 1.888489873058567200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13700000000000004 " " y2[1] (analytic) = 1.1365718431680236 " " y2[1] (numeric) = 1.136564235262265 " " absolute error = 7.607905758710842000000E-6 " " relative error = 6.6937306290334840000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1365718431680236 " " y1[1] (numeric) = 1.1367948443881872 " " absolute error = 2.23001220163610010000E-4 " " relative error = 1.962051246510097800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13800000000000004 " " y2[1] (analytic) = 1.1375624048859627 " " y2[1] (numeric) = 1.1375539292259997 " " absolute error = 8.475659962980941000000E-6 " " relative error = 7.4507208805222450000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1375624048859627 " " y1[1] (numeric) = 1.1377940938100897 " " absolute error = 2.3168892412694930000E-4 " " relative error = 2.036713969552953200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.13900000000000004 " " y2[1] (analytic) = 1.1385528290415083 " " y2[1] (numeric) = 1.1385434134389676 " " absolute error = 9.415602540752133000000E-6 " " relative error = 8.2697985553104860000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1385528290415083 " " y1[1] (numeric) = 1.1387933454831127 " " absolute error = 2.40516441604388120000E-4 " " relative error = 2.112475025044442700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14000000000000004 " " y2[1] (analytic) = 1.1395431146442365 " " y2[1] (numeric) = 1.13953268301483 " " absolute error = 1.043162940650432800000E-5 " " relative error = 9.154220908755230000E-4 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1395431146442365 " " y1[1] (numeric) = 1.1397925983970498 " " absolute error = 2.4948375281330648000E-4 " " relative error = 2.189331404904279500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14100000000000004 " " y2[1] (analytic) = 1.1405332607038616 " " y2[1] (numeric) = 1.1405217329650648 " " absolute error = 1.152773879686819200000E-5 " " relative error = 1.0107323647671647000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1405332607038616 " " y1[1] (numeric) = 1.14079185154155 " " absolute error = 2.5859083768842160000E-4 " " relative error = 2.267280110084965400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14200000000000004 " " y2[1] (analytic) = 1.1415232662302377 " " y2[1] (numeric) = 1.141510558198973 " " absolute error = 1.270803126462993800000E-5 " " relative error = 1.1132520589437386000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1415232662302377 " " y1[1] (numeric) = 1.141791103906119 " " absolute error = 2.6783767588134390000E-4 " " relative error = 2.34631815053450500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14300000000000004 " " y2[1] (analytic) = 1.1425131302333595 " " y2[1] (numeric) = 1.1424991535236872 " " absolute error = 1.397670967229203100000E-5 " " relative error = 1.2233303322682404000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1425131302333595 " " y1[1] (numeric) = 1.1427903544801201 " " absolute error = 2.7722424676057680000E-4 " " relative error = 2.42644254516316520E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14400000000000004 " " y2[1] (analytic) = 1.1435028517233627 " " y2[1] (numeric) = 1.1434875136441778 " " absolute error = 1.533807918496776800000E-5 " " relative error = 1.3413240869361967000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1435028517233627 " " y1[1] (numeric) = 1.1437896022527752 " " absolute error = 2.8675052941240510000E-4 " " relative error = 2.507650321818139500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14500000000000005 " " y2[1] (analytic) = 1.1444924297105263 " " y2[1] (numeric) = 1.1444756331632606 " " absolute error = 1.67965472657183300000E-5 " " relative error = 1.4675979350922086000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1444924297105263 " " y1[1] (numeric) = 1.1447888462131655 " " absolute error = 2.96416502639118560000E-4 " " relative error = 2.589938517235020000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14600000000000005 " " y2[1] (analytic) = 1.1454818632052723 " " y2[1] (numeric) = 1.1454635065816052 " " absolute error = 1.835662366711510200000E-5 " " relative error = 1.6025241653106437000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1454818632052723 " " y1[1] (numeric) = 1.1457880853502331 " " absolute error = 3.06222144960788260000E-4 " " relative error = 2.673304177020503000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14700000000000005 " " y2[1] (analytic) = 1.1464711512181671 " " y2[1] (numeric) = 1.1464511282977425 " " absolute error = 2.002292042457831700000E-5 " " relative error = 1.7464827094256352000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1464711512181671 " " y1[1] (numeric) = 1.146787318652782 " " absolute error = 3.16167434614822440000E-4 " " relative error = 2.757744355615779000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14800000000000005 " " y2[1] (analytic) = 1.1474602927599231 " " y2[1] (numeric) = 1.1474384926080718 " " absolute error = 2.180015185127004400000E-5 " " relative error = 1.8998611096890627000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1474602927599231 " " y1[1] (numeric) = 1.147786545109478 " " absolute error = 3.2625234955485640000E-4 " " relative error = 2.843256116254267400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.14900000000000005 " " y2[1] (analytic) = 1.1484492868413985 " " y2[1] (numeric) = 1.1484255937068697 " " absolute error = 2.36931345287683110000E-5 " " relative error = 2.063054485751999000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1484492868413985 " " y1[1] (numeric) = 1.1487857637088512 " " absolute error = 3.36476867452750740000E-4 " " relative error = 2.929836530946607000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15000000000000005 " " y2[1] (analytic) = 1.1494381324735992 " " y2[1] (numeric) = 1.1494124256862972 " " absolute error = 2.570678730196007700000E-5 " " relative error = 2.23646550220488020E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1494381324735992 " " y1[1] (numeric) = 1.149784973439296 " " absolute error = 3.4684096569681520000E-4 " " relative error = 3.017482680432838600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15100000000000005 " " y2[1] (analytic) = 1.1504268286676802 " " y2[1] (numeric) = 1.150398982536409 " " absolute error = 2.78461312712696700000E-5 " " relative error = 2.4205043360748577000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1504268286676802 " " y1[1] (numeric) = 1.1507841732890727 " " absolute error = 3.5734462139247470000E-4 " " relative error = 3.106191654156038600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15200000000000005 " " y2[1] (analytic) = 1.151415374434945 " " y2[1] (numeric) = 1.1513852581451602 " " absolute error = 3.011628978466518400000E-5 " " relative error = 2.6155886444928445000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.151415374434945 " " y1[1] (numeric) = 1.1517833622463078 " " absolute error = 3.67987811362935350000E-4 " " relative error = 3.195960550236049400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15300000000000005 " " y2[1] (analytic) = 1.1524037687868478 " " y2[1] (numeric) = 1.1523712462984166 " " absolute error = 3.25224884312191900000E-5 " " relative error = 2.8221435326835215000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1524037687868478 " " y1[1] (numeric) = 1.1527825392989959 " " absolute error = 3.78770512148074450000E-4 " " relative error = 3.286786475427893600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15400000000000005 " " y2[1] (analytic) = 1.1533920107349946 " " y2[1] (numeric) = 1.1533569406799613 " " absolute error = 3.507005503333715500000E-5 " " relative error = 3.0406015220262270000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1533920107349946 " " y1[1] (numeric) = 1.1537817034349998 " " absolute error = 3.8969270000510650000E-4 " " relative error = 3.378666545095767600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15500000000000005 " " y2[1] (analytic) = 1.1543800992911435 " " y2[1] (numeric) = 1.1543423348715043 " " absolute error = 3.77644196392079600000E-5 " " relative error = 3.2714025183210893000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1543800992911435 " " y1[1] (numeric) = 1.154780853642052 " " absolute error = 4.00754350908583130000E-4 " " relative error = 3.47159788318136800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15600000000000006 " " y2[1] (analytic) = 1.1553680334672058 " " y2[1] (numeric) = 1.1553274223526908 " " absolute error = 4.0611114515032300000E-5 " " relative error = 3.5149937802208553000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1553680334672058 " " y1[1] (numeric) = 1.155779988907756 " " absolute error = 4.1195544055017130000E-4 " " relative error = 3.56557762217041900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15700000000000006 " " y2[1] (analytic) = 1.1563558122752478 " " y2[1] (numeric) = 1.1563121965011103 " " absolute error = 4.361577413747319600000E-5 " " relative error = 3.7718298878659780000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1563558122752478 " " y1[1] (numeric) = 1.1567791082195866 " " absolute error = 4.2329594433887510000E-4 " " relative error = 3.66060290306317700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15800000000000006 " " y2[1] (analytic) = 1.1573434347274905 " " y2[1] (numeric) = 1.1572966505923048 " " absolute error = 4.67841351856623800000E-5 " " relative error = 4.042372711664297700E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1573434347274905 " " y1[1] (numeric) = 1.1577782105648915 " " absolute error = 4.34775837401035760000E-4 " " relative error = 3.7566708753431400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.15900000000000006 " " y2[1] (analytic) = 1.1583308998363115 " " y2[1] (numeric) = 1.1582807777997788 " " absolute error = 5.01220365327625900000E-5 " " relative error = 4.327091381214603300E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1583308998363115 " " y1[1] (numeric) = 1.1587772949308917 " " absolute error = 4.46395094580109840000E-4 " " relative error = 3.85377869694395400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16000000000000006 " " y2[1] (analytic) = 1.159318206614246 " " y2[1] (numeric) = 1.1592645711950074 " " absolute error = 5.363541923864013000000E-5 " " relative error = 4.626462254507393000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.159318206614246 " " y1[1] (numeric) = 1.1597763603046831 " " absolute error = 4.58153690437113070000E-4 " " relative error = 3.951923534222215000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16100000000000006 " " y2[1] (analytic) = 1.1603053540739872 " " y2[1] (numeric) = 1.1602480237474457 " " absolute error = 5.73303265414271100000E-5 " " relative error = 4.940968887209964000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1603053540739872 " " y1[1] (numeric) = 1.1607754056732376 " " absolute error = 4.7005159925039840000E-4 " " relative error = 4.05110256192462100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16200000000000006 " " y2[1] (analytic) = 1.1612923412283875 " " y2[1] (numeric) = 1.1612311283245391 " " absolute error = 6.12129038484177100000E-5 " " relative error = 5.271102002073669000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1612923412283875 " " y1[1] (numeric) = 1.161774430023403 " " absolute error = 4.820887950154340000E-4 " " relative error = 4.151312963155271400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16300000000000006 " " y2[1] (analytic) = 1.16227916709046 " " y2[1] (numeric) = 1.162213877691731 " " absolute error = 6.52893987289626700000E-5 " " relative error = 5.61735945869201100E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.16227916709046 " " y1[1] (numeric) = 1.1627734323419054 " " absolute error = 4.9426525144546930000E-4 " " relative error = 4.25255192935072800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16400000000000006 " " y2[1] (analytic) = 1.163265830673379 " " y2[1] (numeric) = 1.1631962645124736 " " absolute error = 6.95661609053654900000E-5 " " relative error = 5.980246223264013000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.163265830673379 " " y1[1] (numeric) = 1.1637724116153496 " " absolute error = 5.0658094197064680000E-4 " " relative error = 4.354816660241818000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16500000000000006 " " y2[1] (analytic) = 1.164252330990481 " " y2[1] (numeric) = 1.1641782813482369 " " absolute error = 7.40496422442227200000E-5 " " relative error = 6.360274338572757000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.164252330990481 " " y1[1] (numeric) = 1.1647713668302198 " " absolute error = 5.1903583973866850000E-4 " " relative error = 4.45810436382894500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16600000000000006 " " y2[1] (analytic) = 1.1652386670552657 " " y2[1] (numeric) = 1.1651599206585188 " " absolute error = 7.874639674687600000E-5 " " relative error = 6.757962894063587000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1652386670552657 " " y1[1] (numeric) = 1.165770296972881 " " absolute error = 5.3162991761523950000E-4 " " relative error = 4.5624122563555900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16700000000000007 " " y2[1] (analytic) = 1.166224837881397 " " y2[1] (numeric) = 1.1661411748008546 " " absolute error = 8.36630805425286900000E-5 " " relative error = 7.173837996326148000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.166224837881397 " " y1[1] (numeric) = 1.1667692010295798 " " absolute error = 5.443631481827360000E-4 " " relative error = 4.667737562266674500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16800000000000007 " " y2[1] (analytic) = 1.1672108424827043 " " y2[1] (numeric) = 1.1671220360308265 " " absolute error = 8.88064518778097800000E-5 " " relative error = 7.608432739445333000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1672108424827043 " " y1[1] (numeric) = 1.1677680779864459 " " absolute error = 5.5723550374153770000E-4 " " relative error = 4.77407751418994200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.16900000000000007 " " y2[1] (analytic) = 1.168196679873183 " " y2[1] (numeric) = 1.1681024965020752 " " absolute error = 9.4183371107892100000E-5 " " relative error = 8.062287175659192000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.168196679873183 " " y1[1] (numeric) = 1.1687669268294922 " " absolute error = 5.7024695630913950000E-4 " " relative error = 4.88142935289838600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17000000000000007 " " y2[1] (analytic) = 1.1691823490669961 " " y2[1] (numeric) = 1.1690825482663079 " " absolute error = 9.98008006882766800000E-5 " " relative error = 8.535948286246144000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1691823490669961 " " y1[1] (numeric) = 1.169765746544617 " " absolute error = 5.8339747762081730000E-4 " " relative error = 4.989790327286130000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17100000000000007 " " y2[1] (analytic) = 1.170167849078474 " " y2[1] (numeric) = 1.1700621832733102 " " absolute error = 1.05665805163690510000E-4 " " relative error = 9.02996995233667000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.170167849078474 " " y1[1] (numeric) = 1.1707645361176038 " " absolute error = 5.9668703912985070000E-4 " " relative error = 5.09915769434061500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17200000000000007 " " y2[1] (analytic) = 1.171153178922117 " " y2[1] (numeric) = 1.1710413933709556 " " absolute error = 1.11785551161425190000E-4 " " relative error = 9.544912926275637000E-3 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.171153178922117 " " y1[1] (numeric) = 1.171763294534123 " " absolute error = 6.1011561200596810000E-4 " " relative error = 5.20952871909970300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17300000000000007 " " y2[1] (analytic) = 1.1721383376125956 " " y2[1] (numeric) = 1.1720201703052162 " " absolute error = 1.18167307379346550000E-4 " " relative error = 1.008134480269871800E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1721383376125956 " " y1[1] (numeric) = 1.172762020779733 " " absolute error = 6.2368316713734550000E-4 " " relative error = 5.32090067463930700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17400000000000007 " " y2[1] (analytic) = 1.1731233241647505 " " y2[1] (numeric) = 1.1729985057201733 " " absolute error = 1.2481844457723490000E-4 " " relative error = 1.063983999006277700E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1731233241647505 " " y1[1] (numeric) = 1.1737607138398807 " " absolute error = 6.3738967513016220000E-4 " " relative error = 5.43327084204020800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17500000000000007 " " y2[1] (analytic) = 1.174108137593596 " " y2[1] (numeric) = 1.1739763911580277 " " absolute error = 1.3174643556834730000E-4 " " relative error = 1.12209796823629390E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.174108137593596 " " y1[1] (numeric) = 1.1747593726999028 " " absolute error = 6.5123510630682450000E-4 " " relative error = 5.546636510343667000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17600000000000007 " " y2[1] (analytic) = 1.1750927769143182 " " y2[1] (numeric) = 1.174953818059111 " " absolute error = 1.3895885520720520000E-4 " " relative error = 1.182535183069526700E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1750927769143182 " " y1[1] (numeric) = 1.1757579963450273 " " absolute error = 6.6521943070907420000E-4 " " relative error = 5.660994976548805000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17700000000000007 " " y2[1] (analytic) = 1.1760772411422784 " " y2[1] (numeric) = 1.175930777761896 " " absolute error = 1.46463380382488850000E-4 " " relative error = 1.24535511154211800E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1760772411422784 " " y1[1] (numeric) = 1.1767565837603733 " " absolute error = 6.7934261809488030000E-4 " " relative error = 5.77634354555710100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17800000000000007 " " y2[1] (analytic) = 1.1770615292930118 " " y2[1] (numeric) = 1.1769072615030076 " " absolute error = 1.5426779000415890000E-4 " " relative error = 1.310617891800593000E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1770615292930118 " " y1[1] (numeric) = 1.177755133930953 " " absolute error = 6.9360463794132520000E-4 " " relative error = 5.89267953016806800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.17900000000000008 " " y2[1] (analytic) = 1.1780456403822308 " " y2[1] (numeric) = 1.1778832604172347 " " absolute error = 1.62379964996128830000E-4 " " relative error = 1.378384329349436300E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1780456403822308 " " y1[1] (numeric) = 1.1787536458416727 " " absolute error = 7.0800545944194050000E-4 " " relative error = 6.01000025102779400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18000000000000008 " " y2[1] (analytic) = 1.1790295734258243 " " y2[1] (numeric) = 1.1788587655375402 " " absolute error = 1.70807888284052470000E-4 " " relative error = 1.44871589427352400E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1790295734258243 " " y1[1] (numeric) = 1.1797521184773332 " " absolute error = 7.2254505150892710000E-4 " " relative error = 6.12830303661915900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18100000000000008 " " y2[1] (analytic) = 1.1800133274398592 " " y2[1] (numeric) = 1.179833767795073 " " absolute error = 1.79559644786220220000E-4 " " relative error = 1.521674718503310300E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1800133274398592 " " y1[1] (numeric) = 1.1807505508226313 " " absolute error = 7.3722338277204540000E-4 " " relative error = 6.24758522322383500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18200000000000008 " " y2[1] (analytic) = 1.1809969014405817 " " y2[1] (numeric) = 1.1808082580191792 " " absolute error = 1.88643421402456820000E-4 " " relative error = 1.597323593079281700E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1809969014405817 " " y1[1] (numeric) = 1.1817489418621605 " " absolute error = 7.5204042157883680000E-4 " " relative error = 6.36784415489572300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18300000000000008 " " y2[1] (analytic) = 1.1819802944444178 " " y2[1] (numeric) = 1.1817822269374139 " " absolute error = 1.9806750700390730000E-4 " " relative error = 1.67572596544012300E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1819802944444178 " " y1[1] (numeric) = 1.1827472905804124 " " absolute error = 7.6699613599462420000E-4 " " relative error = 6.4890771834326210E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18400000000000008 " " y2[1] (analytic) = 1.1829635054679746 " " y2[1] (numeric) = 1.182755665175552 " " absolute error = 2.07840292422600830000E-4 " " relative error = 1.756945936725074200E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1829635054679746 " " y1[1] (numeric) = 1.1837455959617775 " " absolute error = 7.820904938029560000E-4 " " relative error = 6.61128166835176300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18500000000000008 " " y2[1] (analytic) = 1.1839465335280412 " " y2[1] (numeric) = 1.1837285632576007 " " absolute error = 2.1797027044057060000E-4 " " relative error = 1.84104825908853500E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1839465335280412 " " y1[1] (numeric) = 1.1847438569905462 " " absolute error = 7.9732346250493970000E-4 " " relative error = 6.7344549768560590E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18600000000000008 " " y2[1] (analytic) = 1.1849293776415897 " " y2[1] (numeric) = 1.1847009116058107 " " absolute error = 2.28466035778973620000E-4 " " relative error = 1.928098333030600600E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1849293776415897 " " y1[1] (numeric) = 1.1857420726509096 " " absolute error = 8.1269500931990810000E-4 " " relative error = 6.85859448381173600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18700000000000008 " " y2[1] (analytic) = 1.1859120368257758 " " y2[1] (numeric) = 1.1856727005406889 " " absolute error = 2.39336285086988450000E-4 " " relative error = 2.01816220474157900E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1859120368257758 " " y1[1] (numeric) = 1.1867402419269608 " " absolute error = 8.2820510118497560000E-4 " " relative error = 6.98369757171668300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18800000000000008 " " y2[1] (analytic) = 1.186894510097941 " " y2[1] (numeric) = 1.1866439202810093 " " absolute error = 2.5058981693160120000E-4 " " relative error = 2.111306563469763600E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.186894510097941 " " y1[1] (numeric) = 1.1877383638026962 " " absolute error = 8.4385370475525970000E-4 " " relative error = 7.10976163067454000E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.18900000000000008 " " y2[1] (analytic) = 1.1878767964756112 " " y2[1] (numeric) = 1.1876145609438262 " " absolute error = 2.62235531784948960000E-4 " " relative error = 2.207598738884306600E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1878767964756112 " " y1[1] (numeric) = 1.1887364372620157 " " absolute error = 8.5964078640454740000E-4 " " relative error = 7.23678405837264800E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.19000000000000009 " " y2[1] (analytic) = 1.1888588949765007 " " y2[1] (numeric) = 1.1885846125444857 " " absolute error = 2.7428243201499390000E-4 " " relative error = 2.307106698481786500E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1888588949765007 " " y1[1] (numeric) = 1.1897344612887246 " " absolute error = 8.7556631222396320000E-4 " " relative error = 7.36476226004323200E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1910000000000001 " " y2[1] (analytic) = 1.189840804618511 " " y2[1] (numeric) = 1.1895540649966378 " " absolute error = 2.8673962187308890000E-4 " " relative error = 2.40989904498210500E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.189840804618511 " " y1[1] (numeric) = 1.1907324348665338 " " absolute error = 8.9163024802285660000E-4 " " relative error = 7.49369364844343900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1920000000000001 " " y2[1] (analytic) = 1.1908225244197324 " " y2[1] (numeric) = 1.1905229081122504 " " absolute error = 2.99616307481986870000E-4 " " relative error = 2.516045013743629000E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1908225244197324 " " y1[1] (numeric) = 1.1917303569790614 " " absolute error = 9.0783255932902480000E-4 " " relative error = 7.6235756438298500E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1930000000000001 " " y2[1] (analytic) = 1.1918040533984455 " " y2[1] (numeric) = 1.1914911316016195 " " absolute error = 3.12921796826071130000E-4 " " relative error = 2.62561447021236700E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1918040533984455 " " y1[1] (numeric) = 1.1927282266098334 " " absolute error = 9.2417321138782430000E-4 " " relative error = 7.7544056739237600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1940000000000001 " " y2[1] (analytic) = 1.192785390573121 " " y2[1] (numeric) = 1.1924587250733838 " " absolute error = 3.2666549973714430000E-4 " " relative error = 2.73867790734915800E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.192785390573121 " " y1[1] (numeric) = 1.1937260427422849 " " absolute error = 9.4065216916394690000E-4 " " relative error = 7.88618117389896400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1950000000000001 " " y2[1] (analytic) = 1.193766534962422 " " y2[1] (numeric) = 1.1934256780345363 " " absolute error = 3.4085692788576870000E-4 " " relative error = 2.85530644311869860E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.193766534962422 " " y1[1] (numeric) = 1.1947238043597612 " " absolute error = 9.5726939733919990000E-4 " " relative error = 8.01889958633606100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1960000000000001 " " y2[1] (analytic) = 1.1947474855852043 " " y2[1] (numeric) = 1.1943919798904377 " " absolute error = 3.5550569476661130000E-4 " " relative error = 2.975571817943434300E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1947474855852043 " " y1[1] (numeric) = 1.1957215104455186 " " absolute error = 9.740248603142820000E-4 " " relative error = 8.15255836121045100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1970000000000001 " " y2[1] (analytic) = 1.195728241460517 " " y2[1] (numeric) = 1.195357619944829 " " absolute error = 3.7062151568800770000E-4 " " relative error = 3.099546392207929000E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.195728241460517 " " y1[1] (numeric) = 1.1967191599827252 " " absolute error = 9.9091852220811740000E-4 " " relative error = 8.28715495585990600E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1980000000000001 " " y2[1] (analytic) = 1.1967088016076048 " " y2[1] (numeric) = 1.1963225873998449 " " absolute error = 3.86214207759971730000E-4 " " relative error = 3.227303143765208000E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1967088016076048 " " y1[1] (numeric) = 1.1977167519544625 " " absolute error = 1.0079503468576334000E-3 " " relative error = 8.4226868349559900E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.1990000000000001 " " y2[1] (analytic) = 1.1976891650459074 " " y2[1] (numeric) = 1.1972868713560267 " " absolute error = 4.0229368988065060000E-4 " " relative error = 3.35891566544505500E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1976891650459074 " " y1[1] (numeric) = 1.198714285343726 " " absolute error = 1.025120297818649100E-3 " " relative error = 8.55915147048488400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2000000000000001 " " y2[1] (analytic) = 1.1986693307950613 " " y2[1] (numeric) = 1.1982504608123357 " " absolute error = 4.188699827256670000E-4 " " relative error = 3.49445816260132500E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.1986693307950613 " " y1[1] (numeric) = 1.1997117591334263 " " absolute error = 1.0424283383649868000E-3 " " relative error = 8.69654634171342400E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2010000000000001 " " y2[1] (analytic) = 1.199649297874901 " " y2[1] (numeric) = 1.1992133446661664 " " absolute error = 4.3595320873457410000E-4 " " relative error = 3.634005450649921400E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.199649297874901 " " y1[1] (numeric) = 1.2007091723063903 " " absolute error = 1.0598744314893604000E-3 " " relative error = 8.83486893517011700E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2020000000000001 " " y2[1] (analytic) = 1.2006290653054594 " " y2[1] (numeric) = 1.2001755117133601 " " absolute error = 4.53553592099309450000E-4 " " relative error = 3.777632952638191300E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.2006290653054594 " " y1[1] (numeric) = 1.201706523845362 " " absolute error = 1.0774585399024872000E-3 " " relative error = 8.97411674461141100E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2030000000000001 " " y2[1] (analytic) = 1.2016086321069694 " " y2[1] (numeric) = 1.2011369506482186 " " absolute error = 4.7168145875087220000E-4 " " relative error = 3.92541669681416070E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.2016086321069694 " " y1[1] (numeric) = 1.2027038127330032 " " absolute error = 1.0951806260337538000E-3 " " relative error = 9.11428727100105300E-2 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.2040000000000001 " " y2[1] (analytic) = 1.2025879972998639 " " y2[1] (numeric) = 1.2020976500635174 " " absolute error = 4.9034723634644450000E-4 " " relative error = 4.0774333142140695E-2 "%" h = 1.000E-3 " " y1[1] (analytic) = 1.2025879972998639 " " y1[1] (numeric) = 1.2037010379518955 " " absolute error = 1.1130406520316605000E-3 " " relative error = 9.25537802248765700E-2 "%" h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y2 , x , 4 ) = y1 - 1.0;" "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;" Iterations = 104 "Total Elapsed Time "= 15 Minutes 13 Seconds "Elapsed Time(since restart) "= 15 Minutes 13 Seconds "Expected Time Remaining "= 11 Hours 49 Minutes 44 Seconds "Optimized Time Remaining "= 11 Hours 49 Minutes 30 Seconds "Time to Timeout " Unknown Percent Done = 2.100000000000002 "%" (%o55) true (%o55) diffeq.max