(%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 : arctan(array_x ), 1 1 array_tmp1_a1 : sin(array_tmp1 ), array_tmp1_a2 : cos(array_tmp1 ), 1 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 : (- att(1, array_tmp1_a2, array_tmp1, 2) 2 - array_x att(1, array_tmp1_a1, array_tmp1, 2) 1 + ats(2, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(1, array_tmp1_a2, array_tmp1, 1), 1 2 array_tmp1_a2 : - att(1, array_tmp1_a1, array_tmp1, 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 : (- att(2, array_tmp1_a2, array_tmp1, 2) 3 - array_x att(2, array_tmp1_a1, array_tmp1, 2) 1 + ats(3, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(2, array_tmp1_a2, array_tmp1, 1), 1 3 array_tmp1_a2 : - att(2, array_tmp1_a1, array_tmp1, 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 : (- att(3, array_tmp1_a2, array_tmp1, 2) 4 - array_x att(3, array_tmp1_a1, array_tmp1, 2) 1 + ats(4, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(3, array_tmp1_a2, array_tmp1, 1), 1 4 array_tmp1_a2 : - att(3, array_tmp1_a1, array_tmp1, 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 : (- att(4, array_tmp1_a2, array_tmp1, 2) 5 - array_x att(4, array_tmp1_a1, array_tmp1, 2) 1 + ats(5, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(4, array_tmp1_a2, array_tmp1, 1), 1 5 array_tmp1_a2 : - att(4, array_tmp1_a1, array_tmp1, 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 (- att(kkk - 1, array_tmp1_a2, array_tmp1, 2) - array_x att(kkk - 1, array_tmp1_a1, array_tmp1, 2) 1 + ats(kkk, array_x, array_tmp1_a2, 2)) /(array_x array_tmp1_a1 + array_tmp1_a2 ), 1 1 1 array_tmp1_a1 : att(kkk - 1, array_tmp1_a2, array_tmp1, 1), kkk array_tmp1_a2 : - att(kkk - 1, array_tmp1_a1, array_tmp1, 1), kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk 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 : arctan(array_x ), 1 1 array_tmp1_a1 : sin(array_tmp1 ), array_tmp1_a2 : cos(array_tmp1 ), 1 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 : (- att(1, array_tmp1_a2, array_tmp1, 2) 2 - array_x att(1, array_tmp1_a1, array_tmp1, 2) 1 + ats(2, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(1, array_tmp1_a2, array_tmp1, 1), 1 2 array_tmp1_a2 : - att(1, array_tmp1_a1, array_tmp1, 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 : (- att(2, array_tmp1_a2, array_tmp1, 2) 3 - array_x att(2, array_tmp1_a1, array_tmp1, 2) 1 + ats(3, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(2, array_tmp1_a2, array_tmp1, 1), 1 3 array_tmp1_a2 : - att(2, array_tmp1_a1, array_tmp1, 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 : (- att(3, array_tmp1_a2, array_tmp1, 2) 4 - array_x att(3, array_tmp1_a1, array_tmp1, 2) 1 + ats(4, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(3, array_tmp1_a2, array_tmp1, 1), 1 4 array_tmp1_a2 : - att(3, array_tmp1_a1, array_tmp1, 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 : (- att(4, array_tmp1_a2, array_tmp1, 2) 5 - array_x att(4, array_tmp1_a1, array_tmp1, 2) 1 + ats(5, array_x, array_tmp1_a2, 2))/(array_x array_tmp1_a1 1 1 + array_tmp1_a2 ), array_tmp1_a1 : att(4, array_tmp1_a2, array_tmp1, 1), 1 5 array_tmp1_a2 : - att(4, array_tmp1_a1, array_tmp1, 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 (- att(kkk - 1, array_tmp1_a2, array_tmp1, 2) - array_x att(kkk - 1, array_tmp1_a1, array_tmp1, 2) 1 + ats(kkk, array_x, array_tmp1_a2, 2)) /(array_x array_tmp1_a1 + array_tmp1_a2 ), 1 1 1 array_tmp1_a1 : att(kkk - 1, array_tmp1_a2, array_tmp1, 1), kkk array_tmp1_a2 : - att(kkk - 1, array_tmp1_a1, array_tmp1, 1), kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk 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) mode_declare(factorial_1, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o39) [factorial_1] (%i40) factorial_1(nnn) := nnn! (%o40) factorial_1(nnn) := nnn! (%i41) mode_declare(factorial_3, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o41) [factorial_3] mmm2! (%i42) factorial_3(mmm2, nnn2) := ----- nnn2! mmm2! (%o42) factorial_3(mmm2, nnn2) := ----- nnn2! (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) - log(1.0 + x x) (%i49) exact_soln_y(x) := ---------------- + x arctan(x) + 2.0 2.0 - log(1.0 + x x) (%o49) exact_soln_y(x) := ---------------- + x arctan(x) + 2.0 2.0 (%i50) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(hours_in_day, 24.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_look_poles, false, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(years_in_century, 100.0, float), define_variable(days_in_year, 365.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(sec_in_min, 60.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_disp_incr, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(min_in_hour, 60.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 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/arctanpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arctan ( x ) ;"), 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 : -1.0,"), omniout_str(ALWAYS, "x_end : 5.00 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), 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 + x * arctan(x) - log(x * x + 1.0)/2.0"), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_tmp1_a1, 1 + max_terms), array(array_tmp1_a2, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_tmp1_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1_a2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_norms : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, 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_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_tmp1_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_a2 : 0.0, term : 1 + term), term array(array_tmp1_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_a1 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_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_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : - 1.0, x_end : 5.0, 1 array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100, 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, convfp(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, convfp(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, convfp(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 ) = arctan ( x ) ;"), 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, "2012-06-13T01:28:18-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "arctan"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arctan ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "arctan diffeq.max"), logitem_str(html_log_file, "\ arctan maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o50) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(hours_in_day, 24.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_done, false, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_look_poles, false, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(years_in_century, 100.0, float), define_variable(days_in_year, 365.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(sec_in_min, 60.0, float), define_variable(glob_html_log, true, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_disp_incr, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(min_in_hour, 60.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 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/arctanpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arctan ( x ) ;"), 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 : -1.0,"), omniout_str(ALWAYS, "x_end : 5.00 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), 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 + x * arctan(x) - log(x * x + 1.0)/2.0"), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_tmp1_a1, 1 + max_terms), array(array_tmp1_a2, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_tmp1_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1_a2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_norms : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, 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_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_tmp1_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_a2 : 0.0, term : 1 + term), term array(array_tmp1_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_a1 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_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_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : - 1.0, x_end : 5.0, 1 array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100, 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, convfp(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, convfp(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, convfp(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 ) = arctan ( x ) ;"), 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, "2012-06-13T01:28:18-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "arctan"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arctan ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "arctan diffeq.max"), logitem_str(html_log_file, "\ arctan maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i51) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/arctanpostode.ode#################" "diff ( y , x , 1 ) = arctan ( x ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms : 30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : -1.0," "x_end : 5.00 ," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 100," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.0001 ," "glob_look_poles : true," "glob_max_iter : 100," "glob_max_minutes : 15," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (" "2.0 + x * arctan(x) - log(x * x + 1.0)/2.0" ");" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = -1. " " y[1] (analytic) = 2.4388245731174756 " " y[1] (numeric) = 2.4388245731174756 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.9999 " " y[1] (analytic) = 2.4387460358012194 " " y[1] (numeric) = 2.438746035801219 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.820973579580469300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4113142499232674 " " Order of pole = 0.9048861590865833 " " x[1] = -0.9998 " " y[1] (analytic) = 2.438667503485463 " " y[1] (numeric) = 2.438667503485463 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4112440169163014 " " Order of pole = 0.9048923553774291 " " x[1] = -0.9997 " " y[1] (analytic) = 2.4385889761707067 " " y[1] (numeric) = 2.4385889761707067 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4111737879381823 " " Order of pole = 0.9048985603665098 " " x[1] = -0.9996 " " y[1] (analytic) = 2.4385104538574507 " " y[1] (numeric) = 2.4385104538574507 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4111035629878523 " " Order of pole = 0.9049047740255141 " " x[1] = -0.9995 " " y[1] (analytic) = 2.438431936546195 " " y[1] (numeric) = 2.438431936546195 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4110333420619452 " " Order of pole = 0.9049109962840056 " " x[1] = -0.9994000000000001 " " y[1] (analytic) = 2.4383534242374396 " " y[1] (numeric) = 2.4383534242374396 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4109631251607297 " " Order of pole = 0.9049172271379504 " " x[1] = -0.9993000000000001 " " y[1] (analytic) = 2.438274916931686 " " y[1] (numeric) = 2.4382749169316855 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.821325424652698600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4108929122825618 " " Order of pole = 0.9049234665483468 " " x[1] = -0.9992000000000001 " " y[1] (analytic) = 2.4381964146294335 " " y[1] (numeric) = 2.4381964146294326 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.64276813127507650000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4108227034262493 " " Order of pole = 0.9049297144844584 " " x[1] = -0.9991000000000001 " " y[1] (analytic) = 2.4381179173311818 " " y[1] (numeric) = 2.4381179173311813 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.821442706660277600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4107524985915658 " " Order of pole = 0.9049359709331348 " " x[1] = -0.9990000000000001 " " y[1] (analytic) = 2.4380394250374327 " " y[1] (numeric) = 2.438039425037432 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.82150134772018380000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4106822977751539 " " Order of pole = 0.9049422358241266 " " x[1] = -0.9989000000000001 " " y[1] (analytic) = 2.4379609377486857 " " y[1] (numeric) = 2.4379609377486853 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.821559988816527400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4106121009778851 " " Order of pole = 0.9049485091643916 " " x[1] = -0.9988000000000001 " " y[1] (analytic) = 2.4378824554654424 " " y[1] (numeric) = 2.4378824554654415 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.643237259897149600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.410541908196491 " " Order of pole = 0.9049547908851512 " " x[1] = -0.9987000000000001 " " y[1] (analytic) = 2.4378039781882017 " " y[1] (numeric) = 2.4378039781882013 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.821677271115595400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.410471719431071 " " Order of pole = 0.9049610809793087 " " x[1] = -0.9986000000000002 " " y[1] (analytic) = 2.437725505917466 " " y[1] (numeric) = 2.437725505917465 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.64347182463371330000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.410401534679799 " " Order of pole = 0.9049673794045656 " " x[1] = -0.9985000000000002 " " y[1] (analytic) = 2.437647038653735 " " y[1] (numeric) = 2.437647038653734 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.643589107103253300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.410331353941081 " " Order of pole = 0.9049736861227249 " " x[1] = -0.9984000000000002 " " y[1] (analytic) = 2.43756857639751 " " y[1] (numeric) = 2.4375685763975086 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.46555958445751800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.410261177214411 " " Order of pole = 0.9049800011155931 " " x[1] = -0.9983000000000002 " " y[1] (analytic) = 2.437490119149291 " " y[1] (numeric) = 2.4374901191492895 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.46573550835628900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4101910044969461 " " Order of pole = 0.9049863243223513 " " x[1] = -0.9982000000000002 " " y[1] (analytic) = 2.437411666909579 " " y[1] (numeric) = 2.437411666909578 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.46591143234899100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.410120835788988 " " Order of pole = 0.9049926557393917 " " x[1] = -0.9981000000000002 " " y[1] (analytic) = 2.4373332196788753 " " y[1] (numeric) = 2.437333219678874 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.46608735643342800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4100506710885727 " " Order of pole = 0.9049989953218809 " " x[1] = -0.9980000000000002 " " y[1] (analytic) = 2.4372547774576807 " " y[1] (numeric) = 2.4372547774576794 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.46626328060740000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4099805103942655 " " Order of pole = 0.9050053430346061 " " x[1] = -0.9979000000000002 " " y[1] (analytic) = 2.4371763402464968 " " y[1] (numeric) = 2.437176340246495 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.28858560649160500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4099103537048931 " " Order of pole = 0.9050116988471455 " " x[1] = -0.9978000000000002 " " y[1] (analytic) = 2.437097908045823 " " y[1] (numeric) = 2.4370979080458213 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.28882017228686100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4098402010190652 " " Order of pole = 0.9050180627251319 " " x[1] = -0.9977000000000003 " " y[1] (analytic) = 2.437019480856161 " " y[1] (numeric) = 2.43701948085616 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.64452736909634800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4097700523348948 " " Order of pole = 0.9050244346250551 " " x[1] = -0.9976000000000003 " " y[1] (analytic) = 2.4369410586780136 " " y[1] (numeric) = 2.436941058678012 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.28928930420616900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4096999076521084 " " Order of pole = 0.9050308145328909 " " x[1] = -0.9975000000000003 " " y[1] (analytic) = 2.4368626415118793 " " y[1] (numeric) = 2.436862641511878 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.46714290274326600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4096297669690478 " " Order of pole = 0.9050372024093534 " " x[1] = -0.9974000000000003 " " y[1] (analytic) = 2.436784229358261 " " y[1] (numeric) = 2.43678422935826 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.467318827408232000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.40955963028377 " " Order of pole = 0.9050435982099891 " " x[1] = -0.9973000000000003 " " y[1] (analytic) = 2.43670582221766 " " y[1] (numeric) = 2.4367058222176583 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.28999300286309400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.409489497595092 " " Order of pole = 0.9050500019041259 " " x[1] = -0.9972000000000003 " " y[1] (analytic) = 2.436627420090577 " " y[1] (numeric) = 2.4366274200905753 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29022756927777600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4094193689022387 " " Order of pole = 0.9050564134686052 " " x[1] = -0.9971000000000003 " " y[1] (analytic) = 2.4365490229775135 " " y[1] (numeric) = 2.4365490229775117 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29046213578541400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.409349244203071 " " Order of pole = 0.9050628328552914 " " x[1] = -0.9970000000000003 " " y[1] (analytic) = 2.436470630878971 " " y[1] (numeric) = 2.4364706308789694 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29069670238306700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4092791234968858 " " Order of pole = 0.9050692600423798 " " x[1] = -0.9969000000000003 " " y[1] (analytic) = 2.436392243795451 " " y[1] (numeric) = 2.4363922437954497 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.468198451800848000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.409209006782241 " " Order of pole = 0.905075694994439 " " x[1] = -0.9968000000000004 " " y[1] (analytic) = 2.4363138617274553 " " y[1] (numeric) = 2.436313861727454 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.468374376877495000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.409138894057256 " " Order of pole = 0.9050821376681562 " " x[1] = -0.9967000000000004 " " y[1] (analytic) = 2.4362354846754855 " " y[1] (numeric) = 2.4362354846754837 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29140040268671700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4090687853210735 " " Order of pole = 0.9050885880387778 " " x[1] = -0.9966000000000004 " " y[1] (analytic) = 2.4361571126400423 " " y[1] (numeric) = 2.4361571126400405 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29163496961502600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4089986805718648 " " Order of pole = 0.9050950460639147 " " x[1] = -0.9965000000000004 " " y[1] (analytic) = 2.436078745621628 " " y[1] (numeric) = 2.4360787456216264 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29186953661864300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4089285798087166 " " Order of pole = 0.9051015117178327 " " x[1] = -0.9964000000000004 " " y[1] (analytic) = 2.4360003836207444 " " y[1] (numeric) = 2.4360003836207427 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29210410369462200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.40885848302997 " " Order of pole = 0.9051079849611465 " " x[1] = -0.9963000000000004 " " y[1] (analytic) = 2.435922026637893 " " y[1] (numeric) = 2.4359220266378916 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.469254003130016000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4087883902345166 " " Order of pole = 0.9051144657646262 " " x[1] = -0.9962000000000004 " " y[1] (analytic) = 2.435843674673576 " " y[1] (numeric) = 2.4358436746735745 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.46942992853892000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.408718301420804 " " Order of pole = 0.9051209540908403 " " x[1] = -0.9961000000000004 " " y[1] (analytic) = 2.435765327728296 " " y[1] (numeric) = 2.435765327728294 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.11600975665911500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.40864821658721 " " Order of pole = 0.9051274499011317 " " x[1] = -0.9960000000000004 " " y[1] (analytic) = 2.435686985802553 " " y[1] (numeric) = 2.435686985802551 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29304237266327200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4085781357329987 " " Order of pole = 0.9051339531729479 " " x[1] = -0.9959000000000005 " " y[1] (analytic) = 2.4356086488968502 " " y[1] (numeric) = 2.4356086488968485 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29327694005688500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4085080588554426 " " Order of pole = 0.9051404638475482 " " x[1] = -0.9958000000000005 " " y[1] (analytic) = 2.4355303170116893 " " y[1] (numeric) = 2.4355303170116875 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29351150750518400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4084379859550118 " " Order of pole = 0.9051469819242932 " " x[1] = -0.9957000000000005 " " y[1] (analytic) = 2.435451990147573 " " y[1] (numeric) = 2.435451990147571 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29374607500521700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4083679170286298 " " Order of pole = 0.9051535073380599 " " x[1] = -0.9956000000000005 " " y[1] (analytic) = 2.4353736683050022 " " y[1] (numeric) = 2.435373668305001 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.470485481915528000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4082978520762022 " " Order of pole = 0.9051600400779698 " " x[1] = -0.9955000000000005 " " y[1] (analytic) = 2.4352953514844806 " " y[1] (numeric) = 2.435295351484479 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29421521014869200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4082277910952106 " " Order of pole = 0.9051665800890731 " " x[1] = -0.9954000000000005 " " y[1] (analytic) = 2.435217039686509 " " y[1] (numeric) = 2.4352170396865076 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.47083733333967500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4081577340850522 " " Order of pole = 0.9051731273511532 " " x[1] = -0.9953000000000005 " " y[1] (analytic) = 2.4351387329115908 " " y[1] (numeric) = 2.435138732911589 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29468434546370400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4080876810436764 " " Order of pole = 0.9051796818178026 " " x[1] = -0.9952000000000005 " " y[1] (analytic) = 2.4350604311602275 " " y[1] (numeric) = 2.4350604311602257 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29491891317815800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.408017631970339 " " Order of pole = 0.9051862434662539 " " x[1] = -0.9951000000000005 " " y[1] (analytic) = 2.4349821344329214 " " y[1] (numeric) = 2.43498213443292 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.47136511069497900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4079475868633289 " " Order of pole = 0.9051928122562316 " " x[1] = -0.9950000000000006 " " y[1] (analytic) = 2.4349038427301766 " " y[1] (numeric) = 2.4349038427301744 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.11923506088273700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4078775457210493 " " Order of pole = 0.9051993881494997 " " x[1] = -0.9949000000000006 " " y[1] (analytic) = 2.434825556052493 " " y[1] (numeric) = 2.434825556052491 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29562261651386200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4078075085421642 " " Order of pole = 0.905205971112542 " " x[1] = -0.9948000000000006 " " y[1] (analytic) = 2.434747274400375 " " y[1] (numeric) = 2.4347472744003733 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29585718434669200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.407737475325674 " " Order of pole = 0.9052125611180095 " " x[1] = -0.9947000000000006 " " y[1] (analytic) = 2.4346689977743248 " " y[1] (numeric) = 2.434668997774323 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29609175220173100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4076674460693916 " " Order of pole = 0.9052191581169371 " " x[1] = -0.9946000000000006 " " y[1] (analytic) = 2.4345907261748447 " " y[1] (numeric) = 2.434590726174843 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29632632007601800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.407597420772418 " " Order of pole = 0.9052257620837398 " " x[1] = -0.9945000000000006 " " y[1] (analytic) = 2.4345124596024377 " " y[1] (numeric) = 2.4345124596024355 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12070110995824600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.407527399433472 " " Order of pole = 0.9052323729859051 " " x[1] = -0.9944000000000006 " " y[1] (analytic) = 2.4344341980576054 " " y[1] (numeric) = 2.4344341980576036 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.2967954558705100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4074573820504033 " " Order of pole = 0.9052389907751532 " " x[1] = -0.9943000000000006 " " y[1] (analytic) = 2.434355941540853 " " y[1] (numeric) = 2.43435594154085 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.09455450356771910000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4073873686225553 " " Order of pole = 0.9052456154302924 " " x[1] = -0.9942000000000006 " " y[1] (analytic) = 2.4342776900526797 " " y[1] (numeric) = 2.4342776900526784 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.47294844377987400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4073173591479338 " " Order of pole = 0.9052522469059099 " " x[1] = -0.9941000000000006 " " y[1] (analytic) = 2.4341994435935925 " " y[1] (numeric) = 2.4341994435935903 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12187394954081200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4072473536254217 " " Order of pole = 0.9052588851723709 " " x[1] = -0.9940000000000007 " " y[1] (analytic) = 2.4341212021640914 " " y[1] (numeric) = 2.4341212021640892 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.1221671594503700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4071773520533126 " " Order of pole = 0.9052655301894781 " " x[1] = -0.9939000000000007 " " y[1] (analytic) = 2.4340429657646805 " " y[1] (numeric) = 2.4340429657646783 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12246036935809100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.407107354430302 " " Order of pole = 0.9052721819242766 " " x[1] = -0.9938000000000007 " " y[1] (analytic) = 2.4339647343958624 " " y[1] (numeric) = 2.4339647343958606 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29820286340821700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.407037360755139 " " Order of pole = 0.9052788403447884 " " x[1] = -0.9937000000000007 " " y[1] (analytic) = 2.4338865080581407 " " y[1] (numeric) = 2.433886508058139 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29843743132256500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4069673710258825 " " Order of pole = 0.9052855054064803 " " x[1] = -0.9936000000000007 " " y[1] (analytic) = 2.4338082867520185 " " y[1] (numeric) = 2.4338082867520163 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.1233399990331900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.406897385241449 " " Order of pole = 0.9052921770803923 " " x[1] = -0.9935000000000007 " " y[1] (analytic) = 2.433730070477998 " " y[1] (numeric) = 2.433730070477996 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29890656711721700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4068274034003605 " " Order of pole = 0.9052988553304271 " " x[1] = -0.9934000000000007 " " y[1] (analytic) = 2.4336518592365834 " " y[1] (numeric) = 2.4336518592365817 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.29914113499158800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4067574255010624 " " Order of pole = 0.9053055401190786 " " x[1] = -0.9933000000000007 " " y[1] (analytic) = 2.433573653028278 " " y[1] (numeric) = 2.433573653028276 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12421962855837900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.40668745154222 " " Order of pole = 0.9053122314128004 " " x[1] = -0.9932000000000007 " " y[1] (analytic) = 2.4334954518535845 " " y[1] (numeric) = 2.4334954518535823 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12451283834949200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.406617481522173 " " Order of pole = 0.905318929172175 " " x[1] = -0.9931000000000008 " " y[1] (analytic) = 2.4334172557130067 " " y[1] (numeric) = 2.4334172557130045 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12480604810911600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4065475154397198 " " Order of pole = 0.9053256333660773 " " x[1] = -0.9930000000000008 " " y[1] (analytic) = 2.433339064607048 " " y[1] (numeric) = 2.4333390646070456 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12509925783353900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4064775532929572 " " Order of pole = 0.9053323439506773 " " x[1] = -0.9929000000000008 " " y[1] (analytic) = 2.4332608785362115 " " y[1] (numeric) = 2.4332608785362093 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.1253924675190490000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4064075950803545 " " Order of pole = 0.9053390608888776 " " x[1] = -0.9928000000000008 " " y[1] (analytic) = 2.4331826975010014 " " y[1] (numeric) = 2.433182697500999 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12568567716193500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4063376408012969 " " Order of pole = 0.9053457841601684 " " x[1] = -0.9927000000000008 " " y[1] (analytic) = 2.433104521501921 " " y[1] (numeric) = 2.4331045215019187 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12597888675848200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4062676904533207 " " Order of pole = 0.9053525137105609 " " x[1] = -0.9926000000000008 " " y[1] (analytic) = 2.433026350539473 " " y[1] (numeric) = 2.433026350539471 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.30101767704398500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4061977440357913 " " Order of pole = 0.9053592495191829 " " x[1] = -0.9925000000000008 " " y[1] (analytic) = 2.4329481846141627 " " y[1] (numeric) = 2.4329481846141605 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12656530579770700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.406127801546448 " " Order of pole = 0.9053659915357422 " " x[1] = -0.9924000000000008 " " y[1] (analytic) = 2.4328700237264926 " " y[1] (numeric) = 2.4328700237264904 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12685851523295200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.406057862984493 " " Order of pole = 0.9053727397363467 " " x[1] = -0.9923000000000008 " " y[1] (analytic) = 2.4327918678769676 " " y[1] (numeric) = 2.432791867876965 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.09525820695283910000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4059879283478327 " " Order of pole = 0.9053794940737365 " " x[1] = -0.9922000000000009 " " y[1] (analytic) = 2.4327137170660897 " " y[1] (numeric) = 2.4327137170660875 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12744493391611900000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.405917997635346 " " Order of pole = 0.9053862545181612 " " x[1] = -0.9921000000000009 " " y[1] (analytic) = 2.4326355712943646 " " y[1] (numeric) = 2.4326355712943624 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12773814315660500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.40584807084548 " " Order of pole = 0.905393021032161 " " x[1] = -0.9920000000000009 " " y[1] (analytic) = 2.4325574305622957 " " y[1] (numeric) = 2.432557430562293 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.0953637622789680000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4057781479765223 " " Order of pole = 0.90539979357529 " " x[1] = -0.9919000000000009 " " y[1] (analytic) = 2.432479294870386 " " y[1] (numeric) = 2.432479294870384 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.12832456141678600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.405708229027173 " " Order of pole = 0.9054065721146163 " " x[1] = -0.9918000000000009 " " y[1] (analytic) = 2.4324011642191414 " " y[1] (numeric) = 2.4324011642191388 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.09543413245148440000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4056383139958457 " " Order of pole = 0.905413356611982 " " x[1] = -0.9917000000000009 " " y[1] (analytic) = 2.432323038609064 " " y[1] (numeric) = 2.4323230386090615 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.0954693175229320000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4055684028812292 " " Order of pole = 0.9054201470342633 " " x[1] = -0.9916000000000009 " " y[1] (analytic) = 2.43224491804066 " " y[1] (numeric) = 2.4322449180406567 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27808858634789500000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4054984956820213 " " Order of pole = 0.9054269433484592 " " x[1] = -0.9915000000000009 " " y[1] (analytic) = 2.4321668025144314 " " y[1] (numeric) = 2.4321668025144283 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.2781296355729670000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4054285923957917 " " Order of pole = 0.9054337455011101 " " x[1] = -0.991400000000001 " " y[1] (analytic) = 2.4320886920308835 " " y[1] (numeric) = 2.4320886920308804 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27817068478478180000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.405358693021715 " " Order of pole = 0.9054405534678409 " " x[1] = -0.991300000000001 " " y[1] (analytic) = 2.4320105865905206 " " y[1] (numeric) = 2.4320105865905175 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27821173398281750000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.405288797558298 " " Order of pole = 0.9054473672122505 " " x[1] = -0.991200000000001 " " y[1] (analytic) = 2.4319324861938467 " " y[1] (numeric) = 2.4319324861938436 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27825278316655240000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.405218906003732 " " Order of pole = 0.9054541866920705 " " x[1] = -0.991100000000001 " " y[1] (analytic) = 2.431854390841367 " " y[1] (numeric) = 2.4318543908413637 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27829383233546480000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.405149018356854 " " Order of pole = 0.9054610118768789 " " x[1] = -0.991000000000001 " " y[1] (analytic) = 2.431776300533585 " " y[1] (numeric) = 2.4317763005335817 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27833488148903270000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4050791346158342 " " Order of pole = 0.9054678427240557 " " x[1] = -0.990900000000001 " " y[1] (analytic) = 2.431698215271005 " " y[1] (numeric) = 2.4316982152710023 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.09575079768005730000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4050092547791897 " " Order of pole = 0.9054746791973187 " " x[1] = -0.990800000000001 " " y[1] (analytic) = 2.431620135054133 " " y[1] (numeric) = 2.4316201350541298 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27841697974804520000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4049393788456797 " " Order of pole = 0.9054815212647753 " " x[1] = -0.990700000000001 " " y[1] (analytic) = 2.431542059883472 " " y[1] (numeric) = 2.4315420598834687 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27845802885244550000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.404869506813308 " " Order of pole = 0.9054883688807944 " " x[1] = -0.990600000000001 " " y[1] (analytic) = 2.431463989759527 " " y[1] (numeric) = 2.431463989759524 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.27849907793941150000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.40479963868095 " " Order of pole = 0.905495222015599 " " x[1] = -0.990500000000001 " " y[1] (analytic) = 2.431385924682803 " " y[1] (numeric) = 2.4313859246828002 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.09589153743578940000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4047297744469256 " " Order of pole = 0.9055020806292848 " " x[1] = -0.9904000000000011 " " y[1] (analytic) = 2.431307864653805 " " y[1] (numeric) = 2.431307864653802 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.09592672233624360000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.404659914109735 " " Order of pole = 0.9055089446852307 " " x[1] = -0.9903000000000011 " " y[1] (analytic) = 2.4312298096730367 " " y[1] (numeric) = 2.4312298096730345 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.13301589350341700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4045900576673551 " " Order of pole = 0.9055158141373365 " " x[1] = -0.9902000000000011 " " y[1] (analytic) = 2.431151759741004 " " y[1] (numeric) = 2.431151759741002 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.13330910073200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.4045202051193055 " " Order of pole = 0.9055226889674515 " " x[1] = -0.9901000000000011 " " y[1] (analytic) = 2.431073714858212 " " y[1] (numeric) = 2.4310737148582096 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.09603227693808520000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "Complex estimate of poles used" Radius of convergence = 1.404450356462861 " " Order of pole = 0.9055295691167426 " " x[1] = -0.9900000000000011 " " y[1] (analytic) = 2.430995675025164 " " y[1] (numeric) = 2.4309956750251622 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.30711641180465300000000000000E-14 "%" h = 1.0000E-4 " " "Finished!" "Maximum Iterations Reached before Solution Completed!" "diff ( y , x , 1 ) = arctan ( x ) ;" Iterations = 100 "Total Elapsed Time "= 1 Minutes 31 Seconds "Elapsed Time(since restart) "= 1 Minutes 31 Seconds "Expected Time Remaining "= 15 Hours 6 Minutes 19 Seconds "Optimized Time Remaining "= 15 Hours 4 Minutes 45 Seconds "Time to Timeout "= 13 Minutes 28 Seconds Percent Done = 0.1683333333333148 "%" (%o51) true (%o51) diffeq.max