(%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_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[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, " ")) (%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_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[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, " ")) (%i4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_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_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2) 1 (%i5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y_higher ! < glob_small_float) ! 1, m! or (!array_y_higher ! < glob_small_float) ! 1, m - 1! or (!array_y_higher ! < glob_small_float)) do m : m - 1, ! 1, m - 2! array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1, glob_h if abs(hdrc) > glob_small_float then (rcs : ------, hdrc convfloat(m - 1) rm0 ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs, hdrc 1, 1 array_real_pole : ord_no) else (array_real_pole : glob_large_float, 1, 2 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 : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y_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_y_higher ! >= glob_large_float) ! 1, m! or (!array_y_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y_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_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_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), found : false, 1, 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")), 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 display_pole()) (%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y_higher ! < glob_small_float) ! 1, m! or (!array_y_higher ! < glob_small_float) ! 1, m - 1! or (!array_y_higher ! < glob_small_float)) do m : m - 1, ! 1, m - 2! array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1, glob_h if abs(hdrc) > glob_small_float then (rcs : ------, hdrc convfloat(m - 1) rm0 ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs, hdrc 1, 1 array_real_pole : ord_no) else (array_real_pole : glob_large_float, 1, 2 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 : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y_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_y_higher ! >= glob_large_float) ! 1, m! or (!array_y_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y_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_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_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), found : false, 1, 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")), 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 display_pole()) (%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_y ! > array_norms ! iii! iii then array_norms : !array_y !, 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_y ! > array_norms ! iii! iii then array_norms : !array_y !, iii : 1 + iii)) iii ! iii! (%i8) atomall() := (array_tmp1 : array_y array_y , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp2 glob_h factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : ats(2, array_y, array_y, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp2 glob_h factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_y, array_y, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp2 glob_h factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_y, array_y, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp2 glob_h factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_y, array_y, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp2 glob_h factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_y, array_y, 1), array_tmp2 : kkk array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk order_d array_tmp2 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) (%o8) atomall() := (array_tmp1 : array_y array_y , 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp2 glob_h factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : ats(2, array_y, array_y, 1), 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 1 then (temporary : array_tmp2 glob_h factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : ats(3, array_y, array_y, 1), 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 1 then (temporary : array_tmp2 glob_h factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : ats(4, array_y, array_y, 1), 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 1 then (temporary : array_tmp2 glob_h factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : ats(5, array_y, array_y, 1), 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 1 then (temporary : array_tmp2 glob_h factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk ats(kkk, array_y, array_y, 1), array_tmp2 : kkk array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk order_d array_tmp2 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) log(x) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i21) mode_declare(ats, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o21) [ats] (%i22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i23) mode_declare(att, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o23) [att] (%i24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i29) log_revs(file, revs) := printf(file, revs) (%o29) log_revs(file, revs) := printf(file, revs) (%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i32) logstart(file) := printf(file, "") (%o32) logstart(file) := printf(file, "") (%i33) logend(file) := printf(file, "~%") (%o33) logend(file) := printf(file, "~%") (%i34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i35) mode_declare(comp_expect_sec, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o35) [comp_expect_sec] (%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i37) mode_declare(comp_percent, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o37) [comp_percent] (%i38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i39) factorial_1(nnn) := (if nnn <= glob_max_terms then (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret) nnn nnn else ret : array_fact_1 ) else ret : nnn!, ret) nnn (%o39) factorial_1(nnn) := (if nnn <= glob_max_terms then (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret) nnn nnn else ret : array_fact_1 ) else ret : nnn!, ret) nnn (%i40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then (if array_fact_2 = 0 mmm, nnn factorial_1(mmm) then (ret : ----------------, array_fact_2 : ret) factorial_1(nnn) mmm, nnn mmm! else ret : array_fact_2 ) else ret : ----, ret) mmm, nnn nnn! (%o40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then (if array_fact_2 = 0 mmm, nnn factorial_1(mmm) then (ret : ----------------, array_fact_2 : ret) factorial_1(nnn) mmm, nnn mmm! else ret : array_fact_2 ) else ret : ----, ret) mmm, nnn nnn! (%i41) convfp(mmm) := mmm (%o41) convfp(mmm) := mmm (%i42) convfloat(mmm) := mmm (%o42) convfloat(mmm) := mmm (%i43) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o43) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i44) arcsin(x) := asin(x) (%o44) arcsin(x) := asin(x) (%i45) arccos(x) := acos(x) (%o45) arccos(x) := acos(x) (%i46) arctan(x) := atan(x) (%o46) arctan(x) := atan(x) 2.0 (%i47) exact_soln_y(x) := ----------- 1.0 - 2.0 x 2.0 (%o47) exact_soln_y(x) := ----------- 1.0 - 2.0 x (%i48) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(min_in_hour, 60.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_start, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(days_in_year, 365.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, 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(years_in_century, 100.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_almost_1, 0.999, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(sec_in_min, 60.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_dump, false, boolean), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, 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/nonlinear2postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.0,"), omniout_str(ALWAYS, "x_end : 0.2 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.01,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 1000000,"), 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_y (x) := ("), omniout_str(ALWAYS, "2.0/(1.0 - 2.0*x) "), 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_1st_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_1st_rel_error : 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_y : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y_init : 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_norms : 0.0, term : 1 + term), ord : 1, term while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_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_y_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 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_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 0.2, array_y_init : exact_soln_y(x_start), glob_h : 0.01, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, 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_y_set_initial : true, array_y_set_initial : false, 1, 1 1, 2 array_y_set_initial : false, array_y_set_initial : false, 1, 3 1, 4 array_y_set_initial : false, array_y_set_initial : false, 1, 5 1, 6 array_y_set_initial : false, array_y_set_initial : false, 1, 7 1, 8 array_y_set_initial : false, array_y_set_initial : false, 1, 9 1, 10 array_y_set_initial : false, array_y_set_initial : false, 1, 11 1, 12 array_y_set_initial : false, array_y_set_initial : false, 1, 13 1, 14 array_y_set_initial : false, array_y_set_initial : false, 1, 15 1, 16 array_y_set_initial : false, array_y_set_initial : false, 1, 17 1, 18 array_y_set_initial : false, array_y_set_initial : false, 1, 19 1, 20 array_y_set_initial : false, array_y_set_initial : false, 1, 21 1, 22 array_y_set_initial : false, array_y_set_initial : false, 1, 23 1, 24 array_y_set_initial : false, array_y_set_initial : false, 1, 25 1, 26 array_y_set_initial : false, array_y_set_initial : false, 1, 27 1, 28 array_y_set_initial : false, array_y_set_initial : false, 1, 29 1, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no term_no - 1 array_y_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_y_init glob_h it array_y_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_y(), if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_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, atomall(), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, ord : 1, calc_term : 2, iii : glob_max_terms, factorial_1(calc_term - 1)! while iii >= calc_term do (array_y_higher_work : 1, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, ord : 1, calc_term : 1, iii : glob_max_terms, factorial_1(calc_term - 1)! while iii >= calc_term do (array_y_higher_work : 1, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1)! while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_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 ( y , x , 1 ) = y * y;"), 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, "2012-06-18T00:46:55-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "nonlinear2"), logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 092 "), logitem_str(html_log_file, "nonlinear2 diffeq.max"), logitem_str(html_log_file, "nonlinear2 maxima results"), logitem_str(html_log_file, "Mostly affecting speed of factorials"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o48) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_warned, false, boolean), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(min_in_hour, 60.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_start, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(days_in_year, 365.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, 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(years_in_century, 100.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_almost_1, 0.999, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(sec_in_min, 60.0, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_dump, false, boolean), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, 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/nonlinear2postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.0,"), omniout_str(ALWAYS, "x_end : 0.2 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.01,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 1000000,"), 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_y (x) := ("), omniout_str(ALWAYS, "2.0/(1.0 - 2.0*x) "), 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_1st_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_1st_rel_error : 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_y : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y_init : 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_norms : 0.0, term : 1 + term), ord : 1, term while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_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_y_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 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_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 0.2, array_y_init : exact_soln_y(x_start), glob_h : 0.01, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, 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_y_set_initial : true, array_y_set_initial : false, 1, 1 1, 2 array_y_set_initial : false, array_y_set_initial : false, 1, 3 1, 4 array_y_set_initial : false, array_y_set_initial : false, 1, 5 1, 6 array_y_set_initial : false, array_y_set_initial : false, 1, 7 1, 8 array_y_set_initial : false, array_y_set_initial : false, 1, 9 1, 10 array_y_set_initial : false, array_y_set_initial : false, 1, 11 1, 12 array_y_set_initial : false, array_y_set_initial : false, 1, 13 1, 14 array_y_set_initial : false, array_y_set_initial : false, 1, 15 1, 16 array_y_set_initial : false, array_y_set_initial : false, 1, 17 1, 18 array_y_set_initial : false, array_y_set_initial : false, 1, 19 1, 20 array_y_set_initial : false, array_y_set_initial : false, 1, 21 1, 22 array_y_set_initial : false, array_y_set_initial : false, 1, 23 1, 24 array_y_set_initial : false, array_y_set_initial : false, 1, 25 1, 26 array_y_set_initial : false, array_y_set_initial : false, 1, 27 1, 28 array_y_set_initial : false, array_y_set_initial : false, 1, 29 1, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no term_no - 1 array_y_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_y_init glob_h it array_y_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_y(), if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_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, atomall(), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, ord : 1, calc_term : 2, iii : glob_max_terms, factorial_1(calc_term - 1)! while iii >= calc_term do (array_y_higher_work : 1, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, ord : 1, calc_term : 1, iii : glob_max_terms, factorial_1(calc_term - 1)! while iii >= calc_term do (array_y_higher_work : 1, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1)! while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_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 ( y , x , 1 ) = y * y;"), 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, "2012-06-18T00:46:55-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "nonlinear2"), logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 092 "), logitem_str(html_log_file, "nonlinear2 diffeq.max"), logitem_str(html_log_file, "nonlinear2 maxima results"), logitem_str(html_log_file, "Mostly affecting speed of factorials"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i49) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/nonlinear2postode.ode#################" "diff ( y , x , 1 ) = y * y;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms : 30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.0," "x_end : 0.2 ," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h : 0.01," "glob_look_poles : true," "glob_max_iter : 1000000," "/* 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_y (x) := (" "2.0/(1.0 - 2.0*x) " ");" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.0 " " y[1] (analytic) = 2. " " y[1] (numeric) = 2. " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.000E-3 " " y[1] (analytic) = 2.004008016032064 " " y[1] (numeric) = 2.004008016032069 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 2.4376056728669940000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.000E-3 " " y[1] (analytic) = 2.0080321285140563 " " y[1] (numeric) = 2.0080321285140657 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.6442849566119550000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.000E-3 " " y[1] (analytic) = 2.0120724346076457 " " y[1] (numeric) = 2.01207243460766 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.0627947934553960000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.000E-3 " " y[1] (analytic) = 2.0161290322580645 " " y[1] (numeric) = 2.0161290322580836 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 9.4715346676821370000000000000E-13 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.000E-3 " " y[1] (analytic) = 2.0202020202020203 " " y[1] (numeric) = 2.0202020202020443 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 1.1870504579292174000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.000E-3 " " y[1] (analytic) = 2.0242914979757085 " " y[1] (numeric) = 2.024291497975738 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.4479084597951442000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.000E-3 " " y[1] (analytic) = 2.028397565922921 " " y[1] (numeric) = 2.028397565922955 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.6858070495118227000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.000E-3 " " y[1] (analytic) = 2.032520325203252 " " y[1] (numeric) = 2.0325203252032917 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 1.944577832091454000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.000000000000001000E-3 " " y[1] (analytic) = 2.0366598778004072 " " y[1] (numeric) = 2.0366598778004525 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 2.2240875807710836000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.000000000000000200E-2 " " y[1] (analytic) = 2.0408163265306123 " " y[1] (numeric) = 2.040816326530663 " " absolute error = 5.06261699229071400000000000000E-14 " " relative error = 2.4806823262224498000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.100000000000000300E-2 " " y[1] (analytic) = 2.044989775051125 " " y[1] (numeric) = 2.0449897750511807 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 2.7362112575701760000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.200000000000000400E-2 " " y[1] (analytic) = 2.0491803278688523 " " y[1] (numeric) = 2.049180327868914 " " absolute error = 6.1728400169158700000000000000E-14 " " relative error = 3.012345928254945300000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.300000000000000600E-2 " " y[1] (analytic) = 2.053388090349076 " " y[1] (numeric) = 2.0533880903491433 " " absolute error = 6.70574706873594600000000000000E-14 " " relative error = 3.265698822474405000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.400000000000000700E-2 " " y[1] (analytic) = 2.05761316872428 " " y[1] (numeric) = 2.057613168724353 " " absolute error = 7.32747196252603300000000000000E-14 " " relative error = 3.561151373787652000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.500000000000000800E-2 " " y[1] (analytic) = 2.061855670103093 " " y[1] (numeric) = 2.061855670103172 " " absolute error = 7.90478793533111500000000000000E-14 " " relative error = 3.83382214863559000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.600000000000001000E-2 " " y[1] (analytic) = 2.066115702479339 " " y[1] (numeric) = 2.0661157024794243 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 4.1268322092946613000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.700000000000001000E-2 " " y[1] (analytic) = 2.070393374741201 " " y[1] (numeric) = 2.0703933747412924 " " absolute error = 9.1482377229112900000000000000E-14 " " relative error = 4.418598820166152500000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.80000000000000100E-2 " " y[1] (analytic) = 2.074688796680498 " " y[1] (numeric) = 2.074688796680596 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 4.709121981250063400000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.90000000000000100E-2 " " y[1] (analytic) = 2.079002079002079 " " y[1] (numeric) = 2.0790020790021835 " " absolute error = 1.04360964314764710000000000000E-13 " " relative error = 5.019762383540183000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.00000000000000120E-2 " " y[1] (analytic) = 2.0833333333333335 " " y[1] (numeric) = 2.0833333333334445 " " absolute error = 1.11022302462515650000000000000E-13 " " relative error = 5.329070518200751000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.10000000000000130E-2 " " y[1] (analytic) = 2.0876826722338206 " " y[1] (numeric) = 2.0876826722339383 " " absolute error = 1.1768364061026660000000000000E-13 " " relative error = 5.637046385231769000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.200000000000001400E-2 " " y[1] (analytic) = 2.092050209205021 " " y[1] (numeric) = 2.0920502092051456 " " absolute error = 1.2478906796786760000000000000E-13 " " relative error = 5.9649174488640710000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.300000000000001500E-2 " " y[1] (analytic) = 2.0964360587002098 " " y[1] (numeric) = 2.096436058700341 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 6.270184371715004000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.400000000000001600E-2 " " y[1] (analytic) = 2.100840336134454 " " y[1] (numeric) = 2.1008403361345924 " " absolute error = 1.38555833473219540000000000000E-13 " " relative error = 6.5952576733252500000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.500000000000001700E-2 " " y[1] (analytic) = 2.1052631578947367 " " y[1] (numeric) = 2.1052631578948824 " " absolute error = 1.45661260830820540000000000000E-13 " " relative error = 6.9189098894639760000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.600000000000002000E-2 " " y[1] (analytic) = 2.109704641350211 " " y[1] (numeric) = 2.1097046413503637 " " absolute error = 1.52766688188421540000000000000E-13 " " relative error = 7.241141020131181000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.700000000000002000E-2 " " y[1] (analytic) = 2.1141649048625792 " " y[1] (numeric) = 2.1141649048627396 " " absolute error = 1.6031620475587260000000000000E-13 " " relative error = 7.582956484952774000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.800000000000002000E-2 " " y[1] (analytic) = 2.1186440677966103 " " y[1] (numeric) = 2.118644067796778 " " absolute error = 1.67865721323323670000000000000E-13 " " relative error = 7.923262046460876000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.90000000000000200E-2 " " y[1] (analytic) = 2.1231422505307855 " " y[1] (numeric) = 2.1231422505309614 " " absolute error = 1.7585932710062480000000000000E-13 " " relative error = 8.282974306439427000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.00000000000000200E-2 " " y[1] (analytic) = 2.127659574468085 " " y[1] (numeric) = 2.127659574468269 " " absolute error = 1.83852932877925920000000000000E-13 " " relative error = 8.641087845262518000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.10000000000000200E-2 " " y[1] (analytic) = 2.1321961620469083 " " y[1] (numeric) = 2.1321961620471 " " absolute error = 1.91846538655227050000000000000E-13 " " relative error = 8.997602662930149000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.20000000000000230E-2 " " y[1] (analytic) = 2.1367521367521367 " " y[1] (numeric) = 2.1367521367523366 " " absolute error = 1.99840144432528180000000000000E-13 " " relative error = 9.352518759442319000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.30000000000000240E-2 " " y[1] (analytic) = 2.1413276231263385 " " y[1] (numeric) = 2.1413276231265463 " " absolute error = 2.0783375020982930000000000000E-13 " " relative error = 9.705836134799027000000000000E-12 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.40000000000000250E-2 " " y[1] (analytic) = 2.145922746781116 " " y[1] (numeric) = 2.1459227467813324 " " absolute error = 2.1627144519698050000000000000E-13 " " relative error = 1.00782493461792900000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.500000000000002600E-2 " " y[1] (analytic) = 2.1505376344086025 " " y[1] (numeric) = 2.150537634408827 " " absolute error = 2.24709140184131680000000000000E-13 " " relative error = 1.044897501856212200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.600000000000002600E-2 " " y[1] (analytic) = 2.1551724137931036 " " y[1] (numeric) = 2.1551724137933372 " " absolute error = 2.33590924381132940000000000000E-13 " " relative error = 1.083861889128456700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.700000000000003000E-2 " " y[1] (analytic) = 2.1598272138228944 " " y[1] (numeric) = 2.159827213823137 " " absolute error = 2.4247270857813420000000000000E-13 " " relative error = 1.122648640716761200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.80000000000000300E-2 " " y[1] (analytic) = 2.1645021645021645 " " y[1] (numeric) = 2.1645021645024163 " " absolute error = 2.5179858198498550000000000000E-13 " " relative error = 1.163309448770633000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.90000000000000300E-2 " " y[1] (analytic) = 2.1691973969631237 " " y[1] (numeric) = 2.1691973969633844 " " absolute error = 2.60680366181986760000000000000E-13 " " relative error = 1.201736488098958800000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.00000000000000300E-2 " " y[1] (analytic) = 2.173913043478261 " " y[1] (numeric) = 2.1739130434785308 " " absolute error = 2.695621503789880000000000000E-13 " " relative error = 1.239985891743344700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.10000000000000300E-2 " " y[1] (analytic) = 2.178649237472767 " " y[1] (numeric) = 2.178649237473046 " " absolute error = 2.7933211299568940000000000000E-13 " " relative error = 1.282134398650214300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.20000000000000300E-2 " " y[1] (analytic) = 2.183406113537118 " " y[1] (numeric) = 2.1834061135374068 " " absolute error = 2.8865798640254070000000000000E-13 " " relative error = 1.322053577723636000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.30000000000000300E-2 " " y[1] (analytic) = 2.188183807439825 " " y[1] (numeric) = 2.1881838074401236 " " absolute error = 2.9842794901924210000000000000E-13 " " relative error = 1.363815727017936300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.40000000000000340E-2 " " y[1] (analytic) = 2.192982456140351 " " y[1] (numeric) = 2.1929824561406597 " " absolute error = 3.0864200084579350000000000000E-13 " " relative error = 1.407407523856818200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.50000000000000340E-2 " " y[1] (analytic) = 2.197802197802198 " " y[1] (numeric) = 2.197802197802517 " " absolute error = 3.18856052672344960000000000000E-13 " " relative error = 1.450795039659169300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.600000000000003500E-2 " " y[1] (analytic) = 2.2026431718061676 " " y[1] (numeric) = 2.2026431718064967 " " absolute error = 3.2907010449889640000000000000E-13 " " relative error = 1.493978274424989400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.700000000000003600E-2 " " y[1] (analytic) = 2.207505518763797 " " y[1] (numeric) = 2.207505518764137 " " absolute error = 3.3972824553529790000000000000E-13 " " relative error = 1.538968952274899500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.800000000000003700E-2 " " y[1] (analytic) = 2.212389380530974 " " y[1] (numeric) = 2.212389380531324 " " absolute error = 3.5038638657169940000000000000E-13 " " relative error = 1.58374646730408100000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.90000000000000400E-2 " " y[1] (analytic) = 2.21729490022173 " " y[1] (numeric) = 2.217294900222091 " " absolute error = 3.6104452760810090000000000000E-13 " " relative error = 1.62831081951253480000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.00000000000000300E-2 " " y[1] (analytic) = 2.2222222222222223 " " y[1] (numeric) = 2.222222222222595 " " absolute error = 3.72590847064202530000000000000E-13 " " relative error = 1.676658811788911400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.10000000000000300E-2 " " y[1] (analytic) = 2.2271714922049 " " y[1] (numeric) = 2.227171492205284 " " absolute error = 3.8369307731045410000000000000E-13 " " relative error = 1.722781917123938600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.20000000000000400E-2 " " y[1] (analytic) = 2.232142857142857 " " y[1] (numeric) = 2.232142857143253 " " absolute error = 3.9568348597640580000000000000E-13 " " relative error = 1.772662017174297700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.30000000000000400E-2 " " y[1] (analytic) = 2.237136465324385 " " y[1] (numeric) = 2.2371364653247925 " " absolute error = 4.0767389464235750000000000000E-13 " " relative error = 1.82230230905133800000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.40000000000000400E-2 " " y[1] (analytic) = 2.2421524663677133 " " y[1] (numeric) = 2.242152466368133 " " absolute error = 4.19664303308309200000000000000E-13 " " relative error = 1.871702792755058600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.50000000000000400E-2 " " y[1] (analytic) = 2.247191011235955 " " y[1] (numeric) = 2.2471910112363873 " " absolute error = 4.32098801184110900000000000000E-13 " " relative error = 1.922839665269293600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.60000000000000400E-2 " " y[1] (analytic) = 2.2522522522522523 " " y[1] (numeric) = 2.252252252252697 " " absolute error = 4.4453329905991270000000000000E-13 " " relative error = 1.973727847826012300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.700000000000004000E-2 " " y[1] (analytic) = 2.2573363431151243 " " y[1] (numeric) = 2.2573363431155813 " " absolute error = 4.5696779693571443000000000000E-13 " " relative error = 2.024367340425215000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.800000000000004000E-2 " " y[1] (analytic) = 2.2624434389140275 " " y[1] (numeric) = 2.2624434389144974 " " absolute error = 4.6984638402136625000000000000E-13 " " relative error = 2.076721017374438500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.900000000000004000E-2 " " y[1] (analytic) = 2.267573696145125 " " y[1] (numeric) = 2.267573696145608 " " absolute error = 4.8272497110701806000000000000E-13 " " relative error = 2.128817122581949000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.000000000000004000E-2 " " y[1] (analytic) = 2.272727272727273 " " y[1] (numeric) = 2.2727272727277694 " " absolute error = 4.96491736612370000000000000E-13 " " relative error = 2.184563641094427700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.10000000000000400E-2 " " y[1] (analytic) = 2.2779043280182236 " " y[1] (numeric) = 2.2779043280187334 " " absolute error = 5.0981441290787190000000000000E-13 " " relative error = 2.23808527266555700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.20000000000000400E-2 " " y[1] (analytic) = 2.2831050228310503 " " y[1] (numeric) = 2.2831050228315743 " " absolute error = 5.2402526762307390000000000000E-13 " " relative error = 2.295230672189063600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.30000000000000400E-2 " " y[1] (analytic) = 2.288329519450801 " " y[1] (numeric) = 2.2883295194513393 " " absolute error = 5.3823612233827590000000000000E-13 " " relative error = 2.352091854618265400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.40000000000000500E-2 " " y[1] (analytic) = 2.2935779816513766 " " y[1] (numeric) = 2.293577981651929 " " absolute error = 5.5244697705347790000000000000E-13 " " relative error = 2.40866881995316300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.50000000000000500E-2 " " y[1] (analytic) = 2.298850574712644 " " y[1] (numeric) = 2.298850574713211 " " absolute error = 5.67101920978530000000000000E-13 " " relative error = 2.46689335625660500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.60000000000000500E-2 " " y[1] (analytic) = 2.3041474654377883 " " y[1] (numeric) = 2.3041474654383705 " " absolute error = 5.8220095411343210000000000000E-13 " " relative error = 2.52675214085229500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.70000000000000500E-2 " " y[1] (analytic) = 2.309468822170901 " " y[1] (numeric) = 2.3094688221714983 " " absolute error = 5.9729998724833420000000000000E-13 " " relative error = 2.58630894478528660000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.80000000000000500E-2 " " y[1] (analytic) = 2.3148148148148153 " " y[1] (numeric) = 2.3148148148154277 " " absolute error = 6.1239902038323630000000000000E-13 " " relative error = 2.645563768055580500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.90000000000000500E-2 " " y[1] (analytic) = 2.3201856148491884 " " y[1] (numeric) = 2.320185614849817 " " absolute error = 6.2838623193783860000000000000E-13 " " relative error = 2.708344659652084000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.00000000000000500E-2 " " y[1] (analytic) = 2.3255813953488373 " " y[1] (numeric) = 2.325581395349482 " " absolute error = 6.4481753270229090000000000000E-13 " " relative error = 2.77271539061985100000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.10000000000000500E-2 " " y[1] (analytic) = 2.3310023310023316 " " y[1] (numeric) = 2.3310023310029924 " " absolute error = 6.6080474425689320000000000000E-13 " " relative error = 2.83485235286207100000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.20000000000000500E-2 " " y[1] (analytic) = 2.3364485981308416 " " y[1] (numeric) = 2.3364485981315193 " " absolute error = 6.7768013423119560000000000000E-13 " " relative error = 2.900470974509516400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.30000000000000500E-2 " " y[1] (analytic) = 2.3419203747072603 " " y[1] (numeric) = 2.341920374707955 " " absolute error = 6.9455552420549790000000000000E-13 " " relative error = 2.965752088357475600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.40000000000000500E-2 " " y[1] (analytic) = 2.3474178403755874 " " y[1] (numeric) = 2.3474178403762993 " " absolute error = 7.1187500338965040000000000000E-13 " " relative error = 3.0325875144399100000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.50000000000000600E-2 " " y[1] (analytic) = 2.3529411764705888 " " y[1] (numeric) = 2.3529411764713184 " " absolute error = 7.2963857178365290000000000000E-13 " " relative error = 3.10096393008052400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.60000000000000600E-2 " " y[1] (analytic) = 2.3584905660377364 " " y[1] (numeric) = 2.358490566038484 " " absolute error = 7.4740214017765540000000000000E-13 " " relative error = 3.16898507435325800000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.70000000000000600E-2 " " y[1] (analytic) = 2.364066193853428 " " y[1] (numeric) = 2.3640661938541943 " " absolute error = 7.660538869913580000000000000E-13 " " relative error = 3.24040794197344400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.80000000000000600E-2 " " y[1] (analytic) = 2.369668246445498 " " y[1] (numeric) = 2.369668246446283 " " absolute error = 7.8470563380506060000000000000E-13 " " relative error = 3.31145777465735500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.90000000000000600E-2 " " y[1] (analytic) = 2.3752969121140146 " " y[1] (numeric) = 2.3752969121148184 " " absolute error = 8.0380146982861330000000000000E-13 " " relative error = 3.384004187978461600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.00000000000000600E-2 " " y[1] (analytic) = 2.3809523809523814 " " y[1] (numeric) = 2.3809523809532043 " " absolute error = 8.228973058521660000000000000E-13 " " relative error = 3.456168684579097000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.10000000000000600E-2 " " y[1] (analytic) = 2.3866348448687353 " " y[1] (numeric) = 2.386634844869578 " " absolute error = 8.4288132029541880000000000000E-13 " " relative error = 3.53167273203780500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.20000000000000600E-2 " " y[1] (analytic) = 2.392344497607656 " " y[1] (numeric) = 2.392344497608519 " " absolute error = 8.6286533473867170000000000000E-13 " " relative error = 3.606777099207646400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.30000000000000600E-2 " " y[1] (analytic) = 2.398081534772183 " " y[1] (numeric) = 2.398081534773066 " " absolute error = 8.8329343839177450000000000000E-13 " " relative error = 3.68333363809369900000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.40000000000000600E-2 " " y[1] (analytic) = 2.403846153846154 " " y[1] (numeric) = 2.403846153847059 " " absolute error = 9.0460972046457750000000000000E-13 " " relative error = 3.76317643713264200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.50000000000000600E-2 " " y[1] (analytic) = 2.409638554216868 " " y[1] (numeric) = 2.4096385542177936 " " absolute error = 9.2548191332753050000000000000E-13 " " relative error = 3.8407499403092504000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.60000000000000700E-2 " " y[1] (analytic) = 2.415458937198068 " " y[1] (numeric) = 2.4154589371990154 " " absolute error = 9.4724228461018360000000000000E-13 " " relative error = 3.92158305828615940000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.70000000000000700E-2 " " y[1] (analytic) = 2.421307506053269 " " y[1] (numeric) = 2.4213075060542386 " " absolute error = 9.6944674510268670000000000000E-13 " " relative error = 4.00381505727409500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.80000000000000700E-2 " " y[1] (analytic) = 2.4271844660194177 " " y[1] (numeric) = 2.42718446602041 " " absolute error = 9.9209529480503990000000000000E-13 " " relative error = 4.08743261459676400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.90000000000000700E-2 " " y[1] (analytic) = 2.433090024330901 " " y[1] (numeric) = 2.4330900243319156 " " absolute error = 1.014743844507393100000000000E-12 " " relative error = 4.17059720092538440000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.00000000000000700E-2 " " y[1] (analytic) = 2.439024390243903 " " y[1] (numeric) = 2.439024390244941 " " absolute error = 1.0382805726294464000000000000E-12 " " relative error = 4.256950347780729700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.10000000000000700E-2 " " y[1] (analytic) = 2.4449877750611253 " " y[1] (numeric) = 2.444987775062187 " " absolute error = 1.0618173007514997000000000000E-12 " " relative error = 4.34283276007363300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.20000000000000700E-2 " " y[1] (analytic) = 2.4509803921568634 " " y[1] (numeric) = 2.450980392157949 " " absolute error = 1.085798118083403100000000000E-12 " " relative error = 4.430056321780283500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.30000000000000700E-2 " " y[1] (analytic) = 2.4570024570024573 " " y[1] (numeric) = 2.457002457003568 " " absolute error = 1.1106671138350066000000000000E-12 " " relative error = 4.52041515330847630000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.40000000000000700E-2 " " y[1] (analytic) = 2.4630541871921188 " " y[1] (numeric) = 2.4630541871932543 " " absolute error = 1.1355361095866101000000000000E-12 " " relative error = 4.61027660492163650000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.50000000000000700E-2 " " y[1] (analytic) = 2.469135802469136 " " y[1] (numeric) = 2.4691358024702974 " " absolute error = 1.1612932837579137000000000000E-12 " " relative error = 4.7032377992195500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.60000000000000700E-2 " " y[1] (analytic) = 2.4752475247524757 " " y[1] (numeric) = 2.475247524753663 " " absolute error = 1.1874945471390674000000000000E-12 " " relative error = 4.797477970441831300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.70000000000000800E-2 " " y[1] (analytic) = 2.481389578163772 " " y[1] (numeric) = 2.481389578164986 " " absolute error = 1.2141398997300712000000000000E-12 " " relative error = 4.89298379591218640000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.80000000000000800E-2 " " y[1] (analytic) = 2.487562189054727 " " y[1] (numeric) = 2.487562189055968 " " absolute error = 1.240785252321075000000000000E-12 " " relative error = 4.9879567143307200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.90000000000000800E-2 " " y[1] (analytic) = 2.4937655860349133 " " y[1] (numeric) = 2.493765586036182 " " absolute error = 1.2687628725416290000000000000E-12 " " relative error = 5.087739118891931000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10000000000000007 " " y[1] (analytic) = 2.5000000000000004 " " y[1] (numeric) = 2.5000000000012976 " " absolute error = 1.297184581972033000000000000E-12 " " relative error = 5.18873832788813000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10100000000000008 " " y[1] (analytic) = 2.5062656641604018 " " y[1] (numeric) = 2.5062656641617274 " " absolute error = 1.325606291402437000000000000E-12 " " relative error = 5.28916910269572200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10200000000000008 " " y[1] (analytic) = 2.5125628140703524 " " y[1] (numeric) = 2.5125628140717073 " " absolute error = 1.354916179252541000000000000E-12 " " relative error = 5.39256639342511200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10300000000000008 " " y[1] (analytic) = 2.5188916876574314 " " y[1] (numeric) = 2.518891687658816 " " absolute error = 1.3846701563124952000000000000E-12 " " relative error = 5.497140520560604000000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10400000000000008 " " y[1] (analytic) = 2.525252525252526 " " y[1] (numeric) = 2.525252525253941 " " absolute error = 1.4148682225822995000000000000E-12 " " relative error = 5.60287816142590400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10500000000000008 " " y[1] (analytic) = 2.5316455696202538 " " y[1] (numeric) = 2.5316455696216997 " " absolute error = 1.4459544672718040000000000000E-12 " " relative error = 5.71152014572362400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10600000000000008 " " y[1] (analytic) = 2.538071065989848 " " y[1] (numeric) = 2.5380710659913257 " " absolute error = 1.4774848011711583000000000000E-12 " " relative error = 5.82129011661436400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10700000000000008 " " y[1] (analytic) = 2.5445292620865145 " " y[1] (numeric) = 2.5445292620880244 " " absolute error = 1.5099033134902130000000000000E-12 " " relative error = 5.93392002201653600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10800000000000008 " " y[1] (analytic) = 2.551020408163266 " " y[1] (numeric) = 2.5510204081648085 " " absolute error = 1.5423218258092675000000000000E-12 " " relative error = 6.04590155717232600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10900000000000008 " " y[1] (analytic) = 2.5575447570332486 " " y[1] (numeric) = 2.5575447570348246 " " absolute error = 1.5760726057578722000000000000E-12 " " relative error = 6.16244388851327900000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11000000000000008 " " y[1] (analytic) = 2.5641025641025648 " " y[1] (numeric) = 2.564102564104175 " " absolute error = 1.610267474916327000000000000E-12 " " relative error = 6.28004315217367400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11100000000000008 " " y[1] (analytic) = 2.5706940874035995 " " y[1] (numeric) = 2.570694087405245 " " absolute error = 1.645350522494482000000000000E-12 " " relative error = 6.40041353250353400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11200000000000009 " " y[1] (analytic) = 2.5773195876288666 " " y[1] (numeric) = 2.5773195876305475 " " absolute error = 1.680877659282487000000000000E-12 " " relative error = 6.52180531801604800000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11300000000000009 " " y[1] (analytic) = 2.5839793281653756 " " y[1] (numeric) = 2.5839793281670924 " " absolute error = 1.716848885280342000000000000E-12 " " relative error = 6.64420518603492200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11400000000000009 " " y[1] (analytic) = 2.5906735751295344 " " y[1] (numeric) = 2.590673575131288 " " absolute error = 1.7537082896978973000000000000E-12 " " relative error = 6.76931399823388200000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11500000000000009 " " y[1] (analytic) = 2.5974025974025983 " " y[1] (numeric) = 2.5974025974043897 " " absolute error = 1.7914558725351526000000000000E-12 " " relative error = 6.89710510926033500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11600000000000009 " " y[1] (analytic) = 2.6041666666666674 " " y[1] (numeric) = 2.6041666666684975 " " absolute error = 1.830091633792108000000000000E-12 " " relative error = 7.02755187376169400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11700000000000009 " " y[1] (analytic) = 2.610966057441254 " " y[1] (numeric) = 2.6109660574431235 " " absolute error = 1.8696155734687636000000000000E-12 " " relative error = 7.16062764638536400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11800000000000009 " " y[1] (analytic) = 2.6178010471204196 " " y[1] (numeric) = 2.617801047122329 " " absolute error = 1.9095836023552692000000000000E-12 " " relative error = 7.29460936099712600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11900000000000009 " " y[1] (analytic) = 2.624671916010499 " " y[1] (numeric) = 2.6246719160124496 " " absolute error = 1.950439809661475000000000000E-12 " " relative error = 7.43117567481021800000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12000000000000009 " " y[1] (analytic) = 2.6315789473684217 " " y[1] (numeric) = 2.6315789473704134 " " absolute error = 1.991740106177530800000000000E-12 " " relative error = 7.56861240347461600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1210000000000001 " " y[1] (analytic) = 2.638522427440634 " " y[1] (numeric) = 2.638522427442668 " " absolute error = 2.0339285811132868000000000000E-12 " " relative error = 7.70858932241935500000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1220000000000001 " " y[1] (analytic) = 2.6455026455026465 " " y[1] (numeric) = 2.6455026455047235 " " absolute error = 2.077005234468742900000000000E-12 " " relative error = 7.85107978629184600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1230000000000001 " " y[1] (analytic) = 2.652519893899205 " " y[1] (numeric) = 2.652519893901326 " " absolute error = 2.120970066243899000000000000E-12 " " relative error = 7.99605714973949600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1240000000000001 " " y[1] (analytic) = 2.6595744680851072 " " y[1] (numeric) = 2.6595744680872735 " " absolute error = 2.1662671656486054000000000000E-12 " " relative error = 8.14516454283875300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12500000000000008 " " y[1] (analytic) = 2.6666666666666674 " " y[1] (numeric) = 2.66666666666888 " " absolute error = 2.212452443473012000000000000E-12 " " relative error = 8.29669666302379300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12600000000000008 " " y[1] (analytic) = 2.673796791443851 " " y[1] (numeric) = 2.6737967914461103 " " absolute error = 2.2590818105072685000000000000E-12 " " relative error = 8.44896597129718100000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12700000000000009 " " y[1] (analytic) = 2.680965147453084 " " y[1] (numeric) = 2.680965147455391 " " absolute error = 2.3070434451710753000000000000E-12 " " relative error = 8.60527205048810900000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12800000000000009 " " y[1] (analytic) = 2.6881720430107534 " " y[1] (numeric) = 2.6881720430131093 " " absolute error = 2.355893258254582200000000000E-12 " " relative error = 8.76392292070704300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1290000000000001 " " y[1] (analytic) = 2.695417789757413 " " y[1] (numeric) = 2.695417789759819 " " absolute error = 2.405631249757789200000000000E-12 " " relative error = 8.92489193660139600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1300000000000001 " " y[1] (analytic) = 2.7027027027027035 " " y[1] (numeric) = 2.7027027027051598 " " absolute error = 2.4562574196806963000000000000E-12 " " relative error = 9.08815245281857400000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1310000000000001 " " y[1] (analytic) = 2.7100271002710037 " " y[1] (numeric) = 2.7100271002735115 " " absolute error = 2.5077717680233036000000000000E-12 " " relative error = 9.25367782400598700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1320000000000001 " " y[1] (analytic) = 2.717391304347827 " " y[1] (numeric) = 2.7173913043503877 " " absolute error = 2.560618383995461000000000000E-12 " " relative error = 9.42307565310329300000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1330000000000001 " " y[1] (analytic) = 2.724795640326976 " " y[1] (numeric) = 2.724795640329591 " " absolute error = 2.6147972675971687000000000000E-12 " " relative error = 9.59630597208160700000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1340000000000001 " " y[1] (analytic) = 2.7322404371584708 " " y[1] (numeric) = 2.7322404371611406 " " absolute error = 2.6698643296185764000000000000E-12 " " relative error = 9.77170344640398600000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1350000000000001 " " y[1] (analytic) = 2.739726027397261 " " y[1] (numeric) = 2.7397260273999873 " " absolute error = 2.7262636592695344000000000000E-12 " " relative error = 9.95086235633379800000000000E-11 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1360000000000001 " " y[1] (analytic) = 2.747252747252748 " " y[1] (numeric) = 2.7472527472555317 " " absolute error = 2.7835511673401925000000000000E-12 " " relative error = 1.01321262491182980000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1370000000000001 " " y[1] (analytic) = 2.754820936639119 " " y[1] (numeric) = 2.7548209366419614 " " absolute error = 2.8421709430404010000000000000E-12 " " relative error = 1.03170805232366520000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1380000000000001 " " y[1] (analytic) = 2.7624309392265203 " " y[1] (numeric) = 2.762430939229422 " " absolute error = 2.901678897160309000000000000E-12 " " relative error = 1.05040776077203160000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1390000000000001 " " y[1] (analytic) = 2.770083102493076 " " y[1] (numeric) = 2.7700831024960384 " " absolute error = 2.9625191189097677000000000000E-12 " " relative error = 1.06946940192642570000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1400000000000001 " " y[1] (analytic) = 2.7777777777777786 " " y[1] (numeric) = 2.7777777777808037 " " absolute error = 3.0251356974986265000000000000E-12 " " relative error = 1.08904885109950530000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1410000000000001 " " y[1] (analytic) = 2.785515320334263 " " y[1] (numeric) = 2.7855153203373515 " " absolute error = 3.0886404545071855000000000000E-12 " " relative error = 1.10882192316807920000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1420000000000001 " " y[1] (analytic) = 2.7932960893854757 " " y[1] (numeric) = 2.7932960893886296 " " absolute error = 3.1539215683551447000000000000E-12 " " relative error = 1.12910392147114140000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1430000000000001 " " y[1] (analytic) = 2.801120448179273 " " y[1] (numeric) = 2.8011204481824925 " " absolute error = 3.219646771412954000000000000E-12 " " relative error = 1.1494138973944240000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1440000000000001 " " y[1] (analytic) = 2.808988764044945 " " y[1] (numeric) = 2.808988764048232 " " absolute error = 3.2871483313101635000000000000E-12 " " relative error = 1.17022480594641780000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1450000000000001 " " y[1] (analytic) = 2.8169014084507054 " " y[1] (numeric) = 2.8169014084540613 " " absolute error = 3.355982158836923000000000000E-12 " " relative error = 1.19137366638710720000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1460000000000001 " " y[1] (analytic) = 2.824858757062148 " " y[1] (numeric) = 2.8248587570655745 " " absolute error = 3.426592343203083000000000000E-12 " " relative error = 1.2130136894938910000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1470000000000001 " " y[1] (analytic) = 2.832861189801701 " " y[1] (numeric) = 2.8328611898051994 " " absolute error = 3.4985347951987933000000000000E-12 " " relative error = 1.23498278270517360000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1480000000000001 " " y[1] (analytic) = 2.840909090909092 " " y[1] (numeric) = 2.840909090912664 " " absolute error = 3.5718095148240536000000000000E-12 " " relative error = 1.25727694921806630000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1490000000000001 " " y[1] (analytic) = 2.8490028490028503 " " y[1] (numeric) = 2.849002849006497 " " absolute error = 3.646860591288714000000000000E-12 " " relative error = 1.28004806754233800000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1500000000000001 " " y[1] (analytic) = 2.857142857142858 " " y[1] (numeric) = 2.857142857146582 " " absolute error = 3.723688024592775000000000000E-12 " " relative error = 1.30329080860747070000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1510000000000001 " " y[1] (analytic) = 2.8653295128939837 " " y[1] (numeric) = 2.8653295128977856 " " absolute error = 3.801847725526386000000000000E-12 " " relative error = 1.32684485620870850000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1520000000000001 " " y[1] (analytic) = 2.8735632183908058 " " y[1] (numeric) = 2.8735632183946875 " " absolute error = 3.881783783299397300000000000E-12 " " relative error = 1.35086075658818970000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1530000000000001 " " y[1] (analytic) = 2.8818443804034595 " " y[1] (numeric) = 2.881844380407423 " " absolute error = 3.963496197911809000000000000E-12 " " relative error = 1.37533318067539700000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1540000000000001 " " y[1] (analytic) = 2.8901734104046253 " " y[1] (numeric) = 2.8901734104086723 " " absolute error = 4.046984969363620600000000000E-12 " " relative error = 1.40025679939981220000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1550000000000001 " " y[1] (analytic) = 2.8985507246376825 " " y[1] (numeric) = 2.8985507246418143 " " absolute error = 4.1318060084449826000000000000E-12 " " relative error = 1.42547307291351820000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1560000000000001 " " y[1] (analytic) = 2.9069767441860477 " " y[1] (numeric) = 2.9069767441902665 " " absolute error = 4.218847493575595000000000000E-12 " " relative error = 1.4512835377900040000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1570000000000001 " " y[1] (analytic) = 2.915451895043733 " " y[1] (numeric) = 2.9154518950480406 " " absolute error = 4.307665335545607400000000000E-12 " " relative error = 1.47752921009214280000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1580000000000001 " " y[1] (analytic) = 2.923976608187136 " " y[1] (numeric) = 2.923976608191534 " " absolute error = 4.39825953435502000000000000E-12 " " relative error = 1.5042047607494160000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1590000000000001 " " y[1] (analytic) = 2.9325513196480952 " " y[1] (numeric) = 2.9325513196525863 " " absolute error = 4.491074179213683000000000000E-12 " " relative error = 1.53145629511186520000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16000000000000011 " " y[1] (analytic) = 2.9411764705882364 " " y[1] (numeric) = 2.9411764705928225 " " absolute error = 4.586109270121596600000000000E-12 " " relative error = 1.55927715184134230000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16100000000000012 " " y[1] (analytic) = 2.9498525073746324 " " y[1] (numeric) = 2.9498525073793154 " " absolute error = 4.68292071786891030000000000E-12 " " relative error = 1.587510123357560000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16200000000000012 " " y[1] (analytic) = 2.958579881656806 " " y[1] (numeric) = 2.958579881661588 " " absolute error = 4.781952611665474000000000000E-12 " " relative error = 1.61629998274292970000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16300000000000012 " " y[1] (analytic) = 2.967359050445105 " " y[1] (numeric) = 2.9673590504499883 " " absolute error = 4.8832049515112885000000000000E-12 " " relative error = 1.64564006865930340000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16400000000000012 " " y[1] (analytic) = 2.9761904761904776 " " y[1] (numeric) = 2.976190476195464 " " absolute error = 4.986233648196503000000000000E-12 " " relative error = 1.67537450579402420000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16500000000000012 " " y[1] (analytic) = 2.985074626865673 " " y[1] (numeric) = 2.985074626870765 " " absolute error = 5.091926880140818000000000000E-12 " " relative error = 1.70579550484717320000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16600000000000012 " " y[1] (analytic) = 2.9940119760479056 " " y[1] (numeric) = 2.994011976053106 " " absolute error = 5.200284647344233000000000000E-12 " " relative error = 1.7368950722129730000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16700000000000012 " " y[1] (analytic) = 3.003003003003004 " " y[1] (numeric) = 3.003003003008315 " " absolute error = 5.310862860596899000000000000E-12 " " relative error = 1.76851733257876650000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16800000000000012 " " y[1] (analytic) = 3.012048192771086 " " y[1] (numeric) = 3.012048192776509 " " absolute error = 5.423217430688965000000000000E-12 " " relative error = 1.80050818698873540000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16900000000000012 " " y[1] (analytic) = 3.021148036253778 " " y[1] (numeric) = 3.0211480362593166 " " absolute error = 5.538680625249981000000000000E-12 " " relative error = 1.83330328695774260000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17000000000000012 " " y[1] (analytic) = 3.0303030303030316 " " y[1] (numeric) = 3.0303030303086884 " " absolute error = 5.656808355070098000000000000E-12 " " relative error = 1.86674675717313140000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17100000000000012 " " y[1] (analytic) = 3.0395136778115517 " " y[1] (numeric) = 3.039513677817329 " " absolute error = 5.7771565309394650000000000000E-12 " " relative error = 1.9006844986790830000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17200000000000013 " " y[1] (analytic) = 3.0487804878048794 " " y[1] (numeric) = 3.04878048781078 " " absolute error = 5.900613331277782000000000000E-12 " " relative error = 1.93540117265911170000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17300000000000013 " " y[1] (analytic) = 3.0581039755351695 " " y[1] (numeric) = 3.0581039755411963 " " absolute error = 6.0267346668752000000000000E-12 " " relative error = 1.97074223606818920000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17400000000000013 " " y[1] (analytic) = 3.0674846625766885 " " y[1] (numeric) = 3.067484662582844 " " absolute error = 6.155520537731718000000000000E-12 " " relative error = 2.00669969530053920000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17500000000000013 " " y[1] (analytic) = 3.0769230769230784 " " y[1] (numeric) = 3.076923076929366 " " absolute error = 6.2874150330571870000000000000E-12 " " relative error = 2.04340988574358450000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17600000000000013 " " y[1] (analytic) = 3.086419753086421 " " y[1] (numeric) = 3.0864197530928434 " " absolute error = 6.4224181528516060000000000000E-12 " " relative error = 2.08086348152391940000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17700000000000013 " " y[1] (analytic) = 3.095975232198144 " " y[1] (numeric) = 3.095975232204704 " " absolute error = 6.560085807905125000000000000E-12 " " relative error = 2.11890771595335430000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17800000000000013 " " y[1] (analytic) = 3.1055900621118027 " " y[1] (numeric) = 3.105590062118504 " " absolute error = 6.701306176637445000000000000E-12 " " relative error = 2.15782058887725610000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17900000000000013 " " y[1] (analytic) = 3.11526479750779 " " y[1] (numeric) = 3.115264797514635 " " absolute error = 6.845191080628865000000000000E-12 " " relative error = 2.19730633688186460000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18000000000000013 " " y[1] (analytic) = 3.1250000000000018 " " y[1] (numeric) = 3.1250000000069944 " " absolute error = 6.992628698299086000000000000E-12 " " relative error = 2.23764118345570600000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18100000000000013 " " y[1] (analytic) = 3.134796238244516 " " y[1] (numeric) = 3.1347962382516594 " " absolute error = 7.143619029648107000000000000E-12 " " relative error = 2.2788144704577450000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18200000000000013 " " y[1] (analytic) = 3.144654088050316 " " y[1] (numeric) = 3.144654088057614 " " absolute error = 7.298162074675929000000000000E-12 " " relative error = 2.32081553974694430000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18300000000000013 " " y[1] (analytic) = 3.1545741324921153 " " y[1] (numeric) = 3.154574132499571 " " absolute error = 7.455813744172701000000000000E-12 " " relative error = 2.3634929569027450000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18400000000000014 " " y[1] (analytic) = 3.164556962025318 " " y[1] (numeric) = 3.1645569620329357 " " absolute error = 7.617462216558124000000000000E-12 " " relative error = 2.4071180604323658000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18500000000000014 " " y[1] (analytic) = 3.174603174603176 " " y[1] (numeric) = 3.1746031746109593 " " absolute error = 7.783107491832197000000000000E-12 " " relative error = 2.4516788599271410000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18600000000000014 " " y[1] (analytic) = 3.18471337579618 " " y[1] (numeric) = 3.184713375804132 " " absolute error = 7.952305480785071000000000000E-12 " " relative error = 2.4970239209665110000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18700000000000014 " " y[1] (analytic) = 3.1948881789137396 " " y[1] (numeric) = 3.194888178921865 " " absolute error = 8.125500272626596000000000000E-12 " " relative error = 2.54328158533212330000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18800000000000014 " " y[1] (analytic) = 3.205128205128207 " " y[1] (numeric) = 3.2051282051365093 " " absolute error = 8.30224777814692100000000000E-12 " " relative error = 2.59030130678183760000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18900000000000014 " " y[1] (analytic) = 3.215434083601288 " " y[1] (numeric) = 3.2154340836097717 " " absolute error = 8.483880264975596000000000000E-12 " " relative error = 2.6384867624074090000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19000000000000014 " " y[1] (analytic) = 3.225806451612905 " " y[1] (numeric) = 3.2258064516215743 " " absolute error = 8.669509554692922000000000000E-12 " " relative error = 2.68754796195480400000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19100000000000014 " " y[1] (analytic) = 3.2362459546925586 " " y[1] (numeric) = 3.2362459547014177 " " absolute error = 8.859135647298899000000000000E-12 " " relative error = 2.7374729150153580000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19200000000000014 " " y[1] (analytic) = 3.2467532467532485 " " y[1] (numeric) = 3.2467532467623026 " " absolute error = 9.054090810423077000000000000E-12 " " relative error = 2.7886599696103060000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19300000000000014 " " y[1] (analytic) = 3.257328990228015 " " y[1] (numeric) = 3.257328990237268 " " absolute error = 9.253042776435905000000000000E-12 " " relative error = 2.8406841323658210000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19400000000000014 " " y[1] (analytic) = 3.267973856209152 " " y[1] (numeric) = 3.2679738562186094 " " absolute error = 9.457323812966933000000000000E-12 " " relative error = 2.893941086767880000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19500000000000015 " " y[1] (analytic) = 3.278688524590166 " " y[1] (numeric) = 3.278688524599832 " " absolute error = 9.666045741596463000000000000E-12 " " relative error = 2.94814395118691950000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19600000000000015 " " y[1] (analytic) = 3.2894736842105283 " " y[1] (numeric) = 3.289473684220408 " " absolute error = 9.879652651534343000000000000E-12 " " relative error = 3.00341440606643860000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19700000000000015 " " y[1] (analytic) = 3.300330033003302 " " y[1] (numeric) = 3.300330033013401 " " absolute error = 1.009903272120027400000000000E-11 " " relative error = 3.0600069145236813000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19800000000000015 " " y[1] (analytic) = 3.311258278145697 " " y[1] (numeric) = 3.3112582781560205 " " absolute error = 1.032329777217455600000000000E-11 " " relative error = 3.1176359271967140000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19900000000000015 " " y[1] (analytic) = 3.3222591362126264 " " y[1] (numeric) = 3.3222591362231793 " " absolute error = 1.055289189366703800000000000E-11 " " relative error = 3.17642045999377700000000000E-10 "%" h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.20000000000000015 " " y[1] (analytic) = 3.3333333333333353 " " y[1] (numeric) = 3.3333333333441235 " " absolute error = 1.078825917488757100000000000E-11 " " relative error = 3.23647775246626900000000000E-10 "%" h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = y * y;" Iterations = 200 "Total Elapsed Time "= 1 Minutes 53 Seconds "Elapsed Time(since restart) "= 1 Minutes 52 Seconds "Time to Timeout "= 13 Minutes 6 Seconds Percent Done = 100.50000000000007 "%" (%o49) true (%o49) diffeq.max