|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"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 := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "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 := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > 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[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; 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[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > 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(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,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(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > 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 # if number 2 > 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,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; 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(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), 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(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; 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, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult FULL CONST $eq_no = 1 i = 1 > array_tmp1[1] := array_m1[1] * array_const_5D0[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp1[1] / array_tmp2[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp3[1] / array_tmp4[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp6[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp5[1] / array_tmp6[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp8[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp9[1] := array_tmp7[1] / array_tmp8[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp10[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp11[1] := array_tmp9[1] / array_tmp10[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp12[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp13[1] := array_tmp11[1] / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp14[1] := array_const_0D0[1] + array_tmp13[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp14[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult FULL CONST $eq_no = 1 i = 2 > array_tmp1[2] := array_m1[2] * array_const_5D0[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := (array_tmp1[2] - array_tmp3[1] * array_tmp2[2]) / array_tmp2[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp6[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp8[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp9[2] := (array_tmp7[2] - array_tmp9[1] * array_tmp8[2]) / array_tmp8[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp10[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp11[2] := (array_tmp9[2] - array_tmp11[1] * array_tmp10[2]) / array_tmp10[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp12[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp13[2] := (array_tmp11[2] - array_tmp13[1] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp14[2] := array_tmp13[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp14[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre mult FULL CONST $eq_no = 1 i = 3 > array_tmp1[3] := array_m1[3] * array_const_5D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp3[3] := (array_tmp1[3] - array_tmp3[2] * array_tmp2[2]) / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp9[3] := (array_tmp7[3] - array_tmp9[2] * array_tmp8[2]) / array_tmp8[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp11[3] := (array_tmp9[3] - array_tmp11[2] * array_tmp10[2]) / array_tmp10[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp13[3] := (array_tmp11[3] - array_tmp13[2] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp14[3] := array_tmp13[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp14[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre mult FULL CONST $eq_no = 1 i = 4 > array_tmp1[4] := array_m1[4] * array_const_5D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp3[4] := (array_tmp1[4] - array_tmp3[3] * array_tmp2[2]) / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp9[4] := (array_tmp7[4] - array_tmp9[3] * array_tmp8[2]) / array_tmp8[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp11[4] := (array_tmp9[4] - array_tmp11[3] * array_tmp10[2]) / array_tmp10[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp13[4] := (array_tmp11[4] - array_tmp13[3] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp14[4] := array_tmp13[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp14[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre mult FULL CONST $eq_no = 1 i = 5 > array_tmp1[5] := array_m1[5] * array_const_5D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp3[5] := (array_tmp1[5] - array_tmp3[4] * array_tmp2[2]) / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp9[5] := (array_tmp7[5] - array_tmp9[4] * array_tmp8[2]) / array_tmp8[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp11[5] := (array_tmp9[5] - array_tmp11[4] * array_tmp10[2]) / array_tmp10[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp13[5] := (array_tmp11[5] - array_tmp13[4] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp14[5] := array_tmp13[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp14[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult FULL CONST $eq_no = 1 i = 1 > array_tmp1[kkk] := array_m1[kkk] * array_const_5D0[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp3[kkk] := -ats(kkk,array_tmp2,array_tmp3,2) / array_tmp2[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp5[kkk] := -ats(kkk,array_tmp4,array_tmp5,2) / array_tmp4[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp7[kkk] := -ats(kkk,array_tmp6,array_tmp7,2) / array_tmp6[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp9[kkk] := -ats(kkk,array_tmp8,array_tmp9,2) / array_tmp8[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp11[kkk] := -ats(kkk,array_tmp10,array_tmp11,2) / array_tmp10[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp13[kkk] := -ats(kkk,array_tmp12,array_tmp13,2) / array_tmp12[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp14[kkk] := array_tmp13[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp14[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_m1[1]*array_const_5D0[1]; array_tmp2[1] := array_x[1] - array_const_6D0[1]; array_tmp3[1] := array_tmp1[1]/array_tmp2[1]; array_tmp4[1] := array_x[1] - array_const_6D0[1]; array_tmp5[1] := array_tmp3[1]/array_tmp4[1]; array_tmp6[1] := array_x[1] - array_const_6D0[1]; array_tmp7[1] := array_tmp5[1]/array_tmp6[1]; array_tmp8[1] := array_x[1] - array_const_6D0[1]; array_tmp9[1] := array_tmp7[1]/array_tmp8[1]; array_tmp10[1] := array_x[1] - array_const_6D0[1]; array_tmp11[1] := array_tmp9[1]/array_tmp10[1]; array_tmp12[1] := array_x[1] - array_const_6D0[1]; array_tmp13[1] := array_tmp11[1]/array_tmp12[1]; array_tmp14[1] := array_const_0D0[1] + array_tmp13[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp14[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_m1[2]*array_const_5D0[1]; array_tmp2[2] := array_x[2]; array_tmp3[2] := (array_tmp1[2] - array_tmp3[1]*array_tmp2[2])/array_tmp2[1]; array_tmp4[2] := array_x[2]; array_tmp5[2] := (array_tmp3[2] - array_tmp5[1]*array_tmp4[2])/array_tmp4[1]; array_tmp6[2] := array_x[2]; array_tmp7[2] := (array_tmp5[2] - array_tmp7[1]*array_tmp6[2])/array_tmp6[1]; array_tmp8[2] := array_x[2]; array_tmp9[2] := (array_tmp7[2] - array_tmp9[1]*array_tmp8[2])/array_tmp8[1]; array_tmp10[2] := array_x[2]; array_tmp11[2] := (array_tmp9[2] - array_tmp11[1]*array_tmp10[2])/array_tmp10[1]; array_tmp12[2] := array_x[2]; array_tmp13[2] := (array_tmp11[2] - array_tmp13[1]*array_tmp12[2])/array_tmp12[1]; array_tmp14[2] := array_tmp13[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp14[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_m1[3]*array_const_5D0[1]; array_tmp3[3] := (array_tmp1[3] - array_tmp3[2]*array_tmp2[2])/array_tmp2[1]; array_tmp5[3] := (array_tmp3[3] - array_tmp5[2]*array_tmp4[2])/array_tmp4[1]; array_tmp7[3] := (array_tmp5[3] - array_tmp7[2]*array_tmp6[2])/array_tmp6[1]; array_tmp9[3] := (array_tmp7[3] - array_tmp9[2]*array_tmp8[2])/array_tmp8[1]; array_tmp11[3] := (array_tmp9[3] - array_tmp11[2]*array_tmp10[2])/array_tmp10[1]; array_tmp13[3] := (array_tmp11[3] - array_tmp13[2]*array_tmp12[2])/array_tmp12[1]; array_tmp14[3] := array_tmp13[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp14[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_m1[4]*array_const_5D0[1]; array_tmp3[4] := (array_tmp1[4] - array_tmp3[3]*array_tmp2[2])/array_tmp2[1]; array_tmp5[4] := (array_tmp3[4] - array_tmp5[3]*array_tmp4[2])/array_tmp4[1]; array_tmp7[4] := (array_tmp5[4] - array_tmp7[3]*array_tmp6[2])/array_tmp6[1]; array_tmp9[4] := (array_tmp7[4] - array_tmp9[3]*array_tmp8[2])/array_tmp8[1]; array_tmp11[4] := (array_tmp9[4] - array_tmp11[3]*array_tmp10[2])/array_tmp10[1]; array_tmp13[4] := (array_tmp11[4] - array_tmp13[3]*array_tmp12[2])/array_tmp12[1]; array_tmp14[4] := array_tmp13[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp14[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_m1[5]*array_const_5D0[1]; array_tmp3[5] := (array_tmp1[5] - array_tmp3[4]*array_tmp2[2])/array_tmp2[1]; array_tmp5[5] := (array_tmp3[5] - array_tmp5[4]*array_tmp4[2])/array_tmp4[1]; array_tmp7[5] := (array_tmp5[5] - array_tmp7[4]*array_tmp6[2])/array_tmp6[1]; array_tmp9[5] := (array_tmp7[5] - array_tmp9[4]*array_tmp8[2])/array_tmp8[1]; array_tmp11[5] := (array_tmp9[5] - array_tmp11[4]*array_tmp10[2])/array_tmp10[1]; array_tmp13[5] := (array_tmp11[5] - array_tmp13[4]*array_tmp12[2])/array_tmp12[1]; array_tmp14[5] := array_tmp13[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp14[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_m1[kkk]*array_const_5D0[1]; array_tmp3[kkk] := -ats(kkk, array_tmp2, array_tmp3, 2)/array_tmp2[1]; array_tmp5[kkk] := -ats(kkk, array_tmp4, array_tmp5, 2)/array_tmp4[1]; array_tmp7[kkk] := -ats(kkk, array_tmp6, array_tmp7, 2)/array_tmp6[1]; array_tmp9[kkk] := -ats(kkk, array_tmp8, array_tmp9, 2)/array_tmp8[1]; array_tmp11[kkk] := -ats(kkk, array_tmp10, array_tmp11, 2)/array_tmp10[1]; array_tmp13[kkk] := -ats(kkk, array_tmp12, array_tmp13, 2)/array_tmp12[1]; array_tmp14[kkk] := array_tmp13[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp14[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; 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 := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) ; > end; exact_soln_y := proc(x) return 1.0/((x - 6.0)*(x - 6.0)*(x - 6.0)*(x - 6.0)*(x - 6.0)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5D0, > array_const_6D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > 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/sing7postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x - 6.0) / ( x - 6.0) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=64;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 2.0;"); > omniout_str(ALWAYS,"x_end := 3.0;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"## Not Given = 0"); > omniout_str(ALWAYS,"## No Pole = 3"); > omniout_str(ALWAYS,"## Pole = 4"); > omniout_str(ALWAYS,"glob_type_given_pole := 4;"); > omniout_str(ALWAYS,"array_given_rad_poles[1][1] = 6.0; # Real Part"); > omniout_str(ALWAYS,"array_given_rad_poles[1][2] = 0.0; # Imag Part"); > omniout_str(ALWAYS,"array_given_ord_poles[1][1] = 6.0; # Order"); > omniout_str(ALWAYS,"array_given_ord_poles[1][2] = 0.0; # Not Used"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"## Real Part"); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := 6.0;"); > omniout_str(ALWAYS,"## Imag Part"); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := 0.0;"); > omniout_str(ALWAYS,"## Order"); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := 6.0;"); > omniout_str(ALWAYS,"## Not Used"); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := 0.0;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) ;"); > omniout_str(ALWAYS,"end;"); > 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 := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=64; > max_terms:=40; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_tmp7:= Array(0..(max_terms + 1),[]); > array_tmp8:= Array(0..(max_terms + 1),[]); > array_tmp9:= Array(0..(max_terms + 1),[]); > array_tmp10:= Array(0..(max_terms + 1),[]); > array_tmp11:= Array(0..(max_terms + 1),[]); > array_tmp12:= Array(0..(max_terms + 1),[]); > array_tmp13:= Array(0..(max_terms + 1),[]); > array_tmp14:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_5D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_5D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_5D0[1] := 5.0; > array_const_6D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_6D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_6D0[1] := 6.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 2.0; > x_end := 3.0; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 100; > ## Not Given = 0 > ## No Pole = 3 > ## Pole = 4 > glob_type_given_pole := 4; > array_given_rad_poles[1][1] = 6.0; # Real Part > array_given_rad_poles[1][2] = 0.0; # Imag Part > array_given_ord_poles[1][1] = 6.0; # Order > array_given_ord_poles[1][2] = 0.0; # Not Used > ## Real Part > array_given_rad_poles[1,1] := 6.0; > ## Imag Part > array_given_rad_poles[1,2] := 0.0; > ## Order > array_given_ord_poles[1,1] := 6.0; > ## Not Used > array_given_ord_poles[1,2] := 0.0; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > 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 ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x - 6.0) / ( x - 6.0) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T04:52:52-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing7") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x - 6.0) / ( x - 6.0) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > 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_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"sing7 diffeq.mxt") > ; > logitem_str(html_log_file,"sing7 maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_5D0, array_const_6D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; 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.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sing7postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( \ x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x - 6.0) / ( x - 6.0) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=64;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 2.0;"); omniout_str(ALWAYS, "x_end := 3.0;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "## Not Given = 0"); omniout_str(ALWAYS, "## No Pole = 3"); omniout_str(ALWAYS, "## Pole = 4"); omniout_str(ALWAYS, "glob_type_given_pole := 4;"); omniout_str(ALWAYS, "array_given_rad_poles[1][1] = 6.0; # Real Part"); omniout_str(ALWAYS, "array_given_rad_poles[1][2] = 0.0; # Imag Part"); omniout_str(ALWAYS, "array_given_ord_poles[1][1] = 6.0; # Order"); omniout_str(ALWAYS, "array_given_ord_poles[1][2] = 0.0; # Not Used"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "## Real Part"); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := 6.0;"); omniout_str(ALWAYS, "## Imag Part"); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := 0.0;"); omniout_str(ALWAYS, "## Order"); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := 6.0;"); omniout_str(ALWAYS, "## Not Used"); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := 0.0;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0\ )/ ( x - 6.0 )/ ( x - 6.0 )) ;"); omniout_str(ALWAYS, "end;"); 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 := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 64; max_terms := 40; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_tmp7 := Array(0 .. max_terms + 1, []); array_tmp8 := Array(0 .. max_terms + 1, []); array_tmp9 := Array(0 .. max_terms + 1, []); array_tmp10 := Array(0 .. max_terms + 1, []); array_tmp11 := Array(0 .. max_terms + 1, []); array_tmp12 := Array(0 .. max_terms + 1, []); array_tmp13 := Array(0 .. max_terms + 1, []); array_tmp14 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_5D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5D0[term] := 0.; term := term + 1 end do; array_const_5D0[1] := 5.0; array_const_6D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_6D0[term] := 0.; term := term + 1 end do; array_const_6D0[1] := 6.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 2.0; x_end := 3.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 100; glob_type_given_pole := 4; array_given_rad_poles[1][1] = 6.0; array_given_rad_poles[1][2] = 0.; array_given_ord_poles[1][1] = 6.0; array_given_ord_poles[1][2] = 0.; array_given_rad_poles[1, 1] := 6.0; array_given_rad_poles[1, 2] := 0.; array_given_ord_poles[1, 1] := 6.0; array_given_ord_poles[1, 2] := 0.; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 40] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); 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 glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / \ ( x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x - 6.0) / ( x - 6.\ 0) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T04:52:52-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing7") ; logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 5.0 / (\ x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x \ - 6.0) / ( x - 6.0) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); 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_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "sing7 diffeq.mxt"); logitem_str(html_log_file, "sing7 maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/sing7postode.ode################# diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x - 6.0) / ( x - 6.0) ; ! #BEGIN FIRST INPUT BLOCK Digits:=64; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 2.0; x_end := 3.0; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 100; ## Not Given = 0 ## No Pole = 3 ## Pole = 4 glob_type_given_pole := 4; array_given_rad_poles[1][1] = 6.0; # Real Part array_given_rad_poles[1][2] = 0.0; # Imag Part array_given_ord_poles[1][1] = 6.0; # Order array_given_ord_poles[1][2] = 0.0; # Not Used ## Real Part array_given_rad_poles[1,1] := 6.0; ## Imag Part array_given_rad_poles[1,2] := 0.0; ## Order array_given_ord_poles[1,1] := 6.0; ## Not Used array_given_ord_poles[1,2] := 0.0; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) ; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 1 estimated_steps = 1000000 step_error = 1.0000000000000000000000000000000e-16 est_needed_step_err = 1.0000000000000000000000000000000e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.6189156200578823399422219450783e-240 estimated_step_error = 3.6189156200578823399422219450783e-240 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.4869001800820161834291302330579e-229 estimated_step_error = 2.4869001800820161834291302330579e-229 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.7089852063982088135112908961593e-218 estimated_step_error = 1.7089852063982088135112908961593e-218 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1744062626655536754052916073969e-207 estimated_step_error = 1.1744062626655536754052916073969e-207 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.0704662369390067770704845781059e-197 estimated_step_error = 8.0704662369390067770704845781059e-197 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.5459929604035997949742158837407e-186 estimated_step_error = 5.5459929604035997949742158837407e-186 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.8111921750105265151263442656941e-175 estimated_step_error = 3.8111921750105265151263442656941e-175 best_h = 0.000128 opt_iter = 8 bytes used=4000056, alloc=3341724, time=0.20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.6190517063618338552351601897346e-164 estimated_step_error = 2.6190517063618338552351601897346e-164 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.7998266474171772580660063640856e-153 estimated_step_error = 1.7998266474171772580660063640856e-153 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2368699655751214021720193900027e-142 estimated_step_error = 1.2368699655751214021720193900027e-142 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.5002350274325366183598976486466e-132 estimated_step_error = 8.5002350274325366183598976486466e-132 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.8420446943289851711399124024276e-121 estimated_step_error = 5.8420446943289851711399124024276e-121 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.0156230096550909721325416778252e-110 estimated_step_error = 4.0156230096550909721325416778252e-110 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.7608911760546872732741722532032e-99 estimated_step_error = 2.7608911760546872732741722532032e-99 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.8991640308490030348651102833585e-88 estimated_step_error = 1.8991640308490030348651102833585e-88 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.3077065258387760865108215987094e-77 estimated_step_error = 1.3077065258387760865108215987094e-77 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.0225887203103737203503662992089e-67 estimated_step_error = 9.0225887203103737203503662992089e-67 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.2504749138554123847238959605934e-56 estimated_step_error = 6.2504749138554123847238959605934e-56 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = -0.0009765625 y[1] (numeric) = -0.0009765625 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.125 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.997 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = -0.00098886162072434683516143825299956 y[1] (numeric) = -0.00098886162072432165753681271470627 absolute error = 2.5177624625538293287206959648141e-17 relative error = 2.5461221365933423699312237716617e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.115 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.987 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 bytes used=8001876, alloc=4455632, time=0.44 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = -0.0010013470890107980722809588508551 y[1] (numeric) = -0.0010013470890107470137760042989406 absolute error = 5.1058504954551914503726126086242e-17 relative error = 5.0989817132230483542894113688853e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.104 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.977 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 12.04 Order of pole (six term test) = -9.203e-58 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = -0.0010140222071652686107927623032123 y[1] (numeric) = -0.0010140222071651909466684145294491 absolute error = 7.7664124347773763214816898547608e-17 relative error = 7.6590161240044532541762243366998e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.094 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.967 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 7.813 Order of pole (six term test) = -7.677e-59 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = -0.0010268903445442873292464297948487 y[1] (numeric) = -0.0010268903445441823125674798125233 absolute error = 1.0501667894998232536157816542216e-16 relative error = 1.0226669235709539450851866119943e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.084 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.957 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = -0.0010399549390904745649415053181806 y[1] (numeric) = -0.0010399549390903414258382820781523 absolute error = 1.3313910322324002824738629280327e-16 relative error = 1.2802391547818507950986273352975e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.073 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.947 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = -0.0010532194989071890145372531522954 y[1] (numeric) = -0.0010532194989070269594407905324298 absolute error = 1.6205509646261986561710444907155e-16 relative error = 1.5386640356617662484208337613108e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.063 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.937 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 2.364 Order of pole (six term test) = 5.572e-59 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = -0.0010666876038734459802255441204606 y[1] (numeric) = -0.0010666876038732541910752092713786 absolute error = 1.9178915033484908197483067282796e-16 relative error = 1.7979879923457265822748438321170e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.053 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.927 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = -0.0010803629073002427904754232113271 y[1] (numeric) = -0.0010803629073000204238979411404776 absolute error = 2.2236657748207084945377231609026e-16 relative error = 2.0582581647286519803116207792752e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.042 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.917 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = -0.0010942491376294622617967576607378 y[1] (numeric) = -0.0010942491376292084482555228812619 absolute error = 2.5381354123477947595465143178302e-16 relative error = 2.3195224241586428851323980381276e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.032 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.907 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = -0.0011083501001765612793082263883551 y[1] (numeric) = -0.0011083501001762751222217464625444 absolute error = 2.8615708647992581063098212083105e-16 relative error = 2.5818293915825035843606046435303e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.022 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.897 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = -0.0011226696789182890015970272274391 y[1] (numeric) = -0.0011226696789179695764252950060052 absolute error = 3.1942517173222143388154273090471e-16 relative error = 2.8452284561563373233780107063098e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.012 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.887 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=12003092, alloc=4586680, time=0.68 x[1] = 2.12 y[1] (analytic) = -0.0011372118383267178835394317600521 y[1] (numeric) = -0.001137211838326364236836972962624 absolute error = 3.5364670245879742815607540771027e-16 relative error = 3.1097697943344456075394371868243e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 4.001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.877 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 1.218 Order of pole (six term test) = 1.043e-58 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = -0.0011519806252509107052468133904904 y[1] (numeric) = -0.0011519806252505218536811037897381 absolute error = 3.8885156570960075222556616310550e-16 relative error = 3.3755043894501761566823258735210e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.991 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.867 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = -0.0011669801708475881437354483669233 y[1] (numeric) = -0.0011669801708471630730693401234614 absolute error = 4.2507066610824346195437567154158e-16 relative error = 3.6424840518027896939244952629146e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.981 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.857 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = -0.0011822146925622041757797978717813 y[1] (numeric) = -0.0011822146925617418398165374093081 absolute error = 4.6233596326046247324293257399067e-16 relative error = 3.9107614392648558970843946984286e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.97 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.847 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = -0.0011976884961618808071309156378601 y[1] (numeric) = -0.0011976884961613801266202757320984 absolute error = 5.0068051063990576170548645039785e-16 relative error = 4.1803900784251439424674331011189e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.837 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = -0.0012134059778216993383217235722777 y[1] (numeric) = -0.0012134059778211591998257099316337 absolute error = 5.4013849601364064392934230347829e-16 relative error = 4.4514243862824436758942671913340e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.827 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 2.483 Order of pole (six term test) = 2.246e-58 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = -0.00122937162626589265620688466897 y[1] (numeric) = -0.0012293716262653119109234120817708 absolute error = 5.8074528347258719923413563425856e-16 relative error = 4.7239196925062401249798019149629e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.939 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.817 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = -0.0012455900249655319409637754838593 y[1] (numeric) = -0.0012455900249649094035066404624537 absolute error = 6.2253745713502140552225909809193e-16 relative error = 4.9979322622806674126167092400744e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.929 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.807 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = -0.0012620658543943517605717703532856 y[1] (numeric) = -0.0012620658543936862077051759783281 absolute error = 6.6555286659437495742705234270907e-16 relative error = 5.2735193197486887606725340119347e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.919 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.797 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = -0.0012788038943444098512383805317325 y[1] (numeric) = -0.0012788038943437000205641947425819 absolute error = 7.0983067418578915058874027804224e-16 relative error = 5.5507390720739878258545045068770e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.908 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.787 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 2.91 Order of pole (six term test) = 1.435e-58 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = -0.0012958090263033320177926394270087 y[1] (numeric) = -0.0012958090263025766063884901608331 absolute error = 7.5541140414926617562603175759830e-16 relative error = 5.8296507341386137528322094672491e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.78 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.898 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.777 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16003856, alloc=4586680, time=0.92 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = -0.0013130862358949486002558852864376 y[1] (numeric) = -0.0013130862358941462632621144758417 absolute error = 8.0233699377081059589054352452169e-16 relative error = 6.1103145538949987559453336069241e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.888 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.767 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 1.814 Order of pole (six term test) = 2.594e-58 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = -0.0013306406153851869118737780064251 y[1] (numeric) = -0.0013306406153843362610271913313876 absolute error = 8.5065084658667503741012976356593e-16 relative error = 6.3927918383915634708169186507469e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.878 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.757 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = -0.0013484773662551440329218106995885 y[1] (numeric) = -0.0013484773662542436350340709735874 absolute error = 9.0039788773972600105923977922348e-16 relative error = 6.6771449804917425005308613998812e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.867 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.747 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = -0.001366601801843326419596845213703 y[1] (numeric) = -0.0013666018018423747949752641762074 absolute error = 9.5162462158103749552792948316464e-16 relative error = 6.9634374863069012974801720540349e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.857 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.737 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = -0.0013850193500591070373697710706107 y[1] (numeric) = -0.0013850193500581026581781569589428 absolute error = 1.0043791916141116678647978804192e-15 relative error = 7.2517340033642765827896100783911e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.73 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.847 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.727 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 3.165 Order of pole (six term test) = 5.285e-59 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = -0.0014037355561695172355959638435772 y[1] (numeric) = -0.0014037355561684585241530802164863 absolute error = 1.0587114428836270909185459717392e-15 relative error = 7.5421003495317567544363631227525e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.836 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.717 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = -0.0014227560856615594306027724443357 y[1] (numeric) = -0.0014227560856604447576158571066048 absolute error = 1.1146729869153377309300409903477e-15 relative error = 7.8346035427220270511644038487571e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.826 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.707 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = -0.0014420867271822979470294722292816 y[1] (numeric) = -0.0014420867271811256297601535289461 absolute error = 1.1723172693187003355004965691721e-15 relative error = 8.1293118313993375360832007571321e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.816 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.697 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = -0.0014617333955590591746605429194726 y[1] (numeric) = -0.0014617333955578274750203739123198 absolute error = 1.2316996401690071527142141887998e-15 relative error = 8.4262947259129111928285554712999e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.805 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.687 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = -0.0014817021349021486269454564494155 y[1] (numeric) = -0.0014817021349008557495181651921334 absolute error = 1.2928774272912572820191576571021e-15 relative error = 8.7256230306817955786370908182918e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.795 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.677 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 8.326 Order of pole (six term test) = -6.170e-58 TOP MAIN SOLVE Loop bytes used=20004968, alloc=4652204, time=1.16 x[1] = 2.33 y[1] (analytic) = -0.0015019991217925716383838698489519 y[1] (numeric) = -0.001501999121791215728371296121916 absolute error = 1.3559100125737270359159376942808e-15 relative error = 9.0273688772567755835700110536845e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.785 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.667 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = -0.0015226306685573264156639274267743 y[1] (numeric) = -0.0015226306685559055567524822151019 absolute error = 1.4208589114452116724215726884614e-15 relative error = 9.3316057582858079767518724250349e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.66 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.774 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.657 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = -0.0015436032266349230708888499057254 y[1] (numeric) = -0.001543603226633435283033193682982 absolute error = 1.4877878556562227433279233048797e-15 relative error = 9.6384085624103116964801502719647e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.65 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.764 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.647 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = -0.001564923390033870227945730227095 y[1] (numeric) = -0.0015649233900323134650662191741671 absolute error = 1.5567628795110529279351852466453e-15 relative error = 9.9478536101205524252572606794747e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.754 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.637 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 2.398 Order of pole (six term test) = -1.362e-58 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = -0.001586597898886961923310303063699 y[1] (numeric) = -0.0015865978988853340709005984833947 absolute error = 1.6278524097045803042728774531984e-15 relative error = 1.0260018690599297095321857488410e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.743 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.627 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 8.555 Order of pole (six term test) = -4.650e-59 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = -0.0016086336431042919435191221236229 y[1] (numeric) = -0.0016086336431025908161601971294206 absolute error = 1.7011273589249942022797556999633e-15 relative error = 1.0574983099583884857653747001988e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.733 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.617 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = -0.0016310376661280205814992313031562 y[1] (numeric) = -0.0016310376661262439202758399994284 absolute error = 1.7766612233913037278347851716293e-15 relative error = 1.0892827678277867032902597322616e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.723 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.607 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 5.883 Order of pole (six term test) = 3.819e-58 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = -0.0016538171687920201866246676489018 y[1] (numeric) = -0.0016538171687901656564401650914692 absolute error = 1.8545301845025574325161948353554e-15 relative error = 1.1213634853344411016463235976489e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.712 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.597 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = -0.0016769795132896309680860015359303 y[1] (numeric) = -0.0016769795132876961548712173566994 absolute error = 1.9348132147841792308932206827483e-15 relative error = 1.1537488678014743459682035253281e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.59 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.702 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.587 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = -0.0017005322272528674331004751153346 y[1] (numeric) = -0.0017005322272508498409121493818245 absolute error = 2.0175921883257335100436267544033e-15 relative error = 1.1864474874346027782674479984140e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.58 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.692 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.577 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = -0.0017244830079465287519774189209293 y[1] (numeric) = -0.0017244830079444257999815051262739 absolute error = 2.1029519959137946554676609229739e-15 relative error = 1.2194680876664231741962718620803e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.682 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.567 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 bytes used=24005768, alloc=4652204, time=1.41 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = -0.0017488397265807833988194347391519 y[1] (numeric) = -0.0017488397265785924181543613016777 absolute error = 2.1909806650734374742193066680493e-15 relative error = 1.2528195876228743994188813617100e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.671 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.557 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = -0.0017736104327459197841195079859889 y[1] (numeric) = -0.0017736104327436380146342657748194 absolute error = 2.2817694852422111694447137848905e-15 relative error = 1.2865110867156746050163084320293e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.55 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.661 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.547 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = -0.0017988033589730804451498179722466 y[1] (numeric) = -0.0017988033589707050320115066342135 absolute error = 2.3754131383113380330899946681394e-15 relative error = 1.3205518693646639457770031610051e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.651 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.537 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = -0.0018244269254249278705978859954526 y[1] (numeric) = -0.0018244269254224558607631056775826 absolute error = 2.4720098347803178700105135933645e-15 relative error = 1.3549514098541169319004652391274e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.53 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.527 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = -0.0018504897447203253938193491502692 y[1] (numeric) = -0.0018504897447177537323635659992603 absolute error = 2.5716614557831510089033567101007e-15 relative error = 1.3897193773272276245221604378374e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.517 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = -0.0018770006268972569887859682439247 y[1] (numeric) = -0.0018770006268945825150847111949014 absolute error = 2.6744737012570490232817306334502e-15 relative error = 1.4248656409231151577050500364861e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.51 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.507 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = -0.0019039685845183554471351222704825 y[1] (numeric) = -0.0019039685845155748908905844531981 absolute error = 2.7805562445378172844275662293123e-15 relative error = 1.4604002750608467218554408005016e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.609 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.497 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 9.566 Order of pole (six term test) = -8.976e-58 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = -0.0019314028379235595152628301814016 y[1] (numeric) = -0.0019314028379206694923691500779088 absolute error = 2.8900228936801034928430193885707e-15 relative error = 1.4963335648751303925911346817257e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.49 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.599 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.487 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = -0.0019593128206345773479086629358654 y[1] (numeric) = -0.0019593128206315743561488474860741 absolute error = 3.0029917598154497912684032890076e-15 relative error = 1.5326760118084912609777872774411e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.589 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.477 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = -0.0019877081849159963195180985857177 y[1] (numeric) = -0.0019877081849128767340852219821203 absolute error = 3.1195854328766035974012200402064e-15 relative error = 1.5694383393649114516260222676428e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.578 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.467 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 5.857 Order of pole (six term test) = 1.602e-58 TOP MAIN SOLVE Loop bytes used=28006864, alloc=4652204, time=1.65 x[1] = 2.54 y[1] (analytic) = -0.0020165988074980480672406029254004 y[1] (numeric) = -0.0020165988074948081360755700484677 absolute error = 3.2399311650328769326939222197568e-15 relative error = 1.6066314990300880505450553173098e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.46 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.568 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.457 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = -0.002045994795466212870647517948184 y[1] (numeric) = -0.0020459947954628487095853194068697 absolute error = 3.3641610621985413142991165827788e-15 relative error = 1.6442666763636429617610875932724e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.45 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.558 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.447 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = -0.0020759064923230293650549036833211 y[1] (numeric) = -0.0020759064923195369527709093298708 absolute error = 3.4924122839943534502631900754335e-15 relative error = 1.6823552972688055386599244208620e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.44 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.548 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.437 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = -0.0021063444842276644111559866596517 y[1] (numeric) = -0.0021063444842240395839034252825416 absolute error = 3.6248272525613771100894211360333e-15 relative error = 1.7209090344452827727059569948337e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.43 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.537 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.427 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 12.07 Order of pole (six term test) = -6.285e-58 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = -0.002137319606418993989012126121163 y[1] (numeric) = -0.0021373196064152324351414797684289 absolute error = 3.7615538706463527341508171838902e-15 relative error = 1.7599398140312331608530668144775e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.42 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.527 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.417 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = -0.0021688429498281495474589718482034 y[1] (numeric) = -0.0021688429498242468017095728222947 absolute error = 3.9027457493990259086951899177507e-15 relative error = 1.7994598224404694187336075912824e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.41 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.517 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.407 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = -0.0022009258678866956320249151851208 y[1] (numeric) = -0.0022009258678826470695785710456268 absolute error = 4.0485624463441394939835621611623e-15 relative error = 1.8394815134012322782428859582276e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.506 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.397 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = -0.0022335799835368241607597125433998 y[1] (numeric) = -0.0022335799835326249910456982570956 absolute error = 4.1991697140142863041934586605618e-15 relative error = 1.8800176152031030382396548718457e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.39 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.496 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.387 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 7.454 Order of pole (six term test) = 1.738e-59 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = -0.0022668171964501787576783952664261 y[1] (numeric) = -0.0022668171964458240179186406884189 absolute error = 4.3547397597545780071377890729623e-15 relative error = 1.9210811381588566733998065879515e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.38 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.486 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.377 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = -0.0023006496904621594427971834380461 y[1] (numeric) = -0.0023006496904576439912799472544 absolute error = 4.5154515172361836461553674073953e-15 relative error = 1.9626853822883005119700902742822e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.37 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.475 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.367 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = -0.0023350899412288040868724842994823 y[1] (numeric) = -0.0023350899412241225959422409949321 absolute error = 4.6814909302433045501638867026508e-15 relative error = 2.0048439452313961477312484313591e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.36 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.465 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.357 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=32007724, alloc=4717728, time=1.89 x[1] = 2.65 y[1] (analytic) = -0.0023701507241135987555559175302411 y[1] (numeric) = -0.0023701507241087457043065903675514 absolute error = 4.8530512493271626897712601771002e-15 relative error = 2.0475707303982247514168220162913e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.35 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.455 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.347 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = -0.0024058451223118347968638425096333 y[1] (numeric) = -0.0024058451223068044635218913366473 absolute error = 5.0303333419511729860163230384007e-15 relative error = 2.0908799553636287065484782219872e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.34 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.444 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.337 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = -0.0024421865352204066911031045898858 y[1] (numeric) = -0.0024421865352151931450863208517291 absolute error = 5.2135460167837381566142859697631e-15 relative error = 2.1347861605146459472894242895786e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.33 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.434 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.328 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = -0.0024791886870612317264176042674054 y[1] (numeric) = -0.0024791886870558288200547751229597 absolute error = 5.4029063628291444456603783630150e-15 relative error = 2.1793042179591479742846909794994e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.32 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.424 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.318 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = -0.0025168656357667709488286790759282 y[1] (numeric) = -0.0025168656357611723087245561249096 absolute error = 5.5986401041229510185625352716236e-15 relative error = 2.2244493407043987419571938477276e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.31 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.413 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.308 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = -0.0025552317821364410471104761871179 y[1] (numeric) = -0.0025552317821306400651397200228898 absolute error = 5.8009819707561642280612321324827e-15 relative error = 2.2702370921145699423771794756894e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.403 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.298 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = -0.0025943018792730293763479477428771 y[1] (numeric) = -0.0025943018792670192002609152564638 absolute error = 6.0101760870324864133111260448256e-15 relative error = 2.3166833956565791743002335327269e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.29 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.393 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.288 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = -0.0026340910423085597291421630509013 y[1] (numeric) = -0.0026340910423023332527645579003088 absolute error = 6.2264763776051505925595620119037e-15 relative error = 2.3638045449439616227306691655207e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.28 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.382 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.278 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 3.723 Order of pole (six term test) = -2.354e-58 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = -0.0026746147584294052841682381921137 y[1] (numeric) = -0.0026746147584229551371757537639195 absolute error = 6.4501469924844281941964878983891e-15 relative error = 2.4116172140888437508111787014120e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.27 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.372 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.268 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = -0.0027158888972108079778157439371467 y[1] (numeric) = -0.0027158888972041265150638899713318 absolute error = 6.6814627518539658149552698433839e-15 relative error = 2.4601384683724597145370450285883e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.26 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.362 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.258 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=36008616, alloc=4717728, time=2.13 x[1] = 2.75 y[1] (analytic) = -0.0027579297212713409625282458866717 y[1] (numeric) = -0.0027579297212644202529165620701368 absolute error = 6.9207096116838165349312703629856e-15 relative error = 2.5093857752450383717814806317227e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.25 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.352 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.248 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = -0.0028007538972582434700412668273836 y[1] (numeric) = -0.0028007538972510752848900862889578 absolute error = 7.1681851511805384257864464320352e-15 relative error = 2.5593770156662915192640796238277e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.24 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.341 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.238 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = -0.0028443785071749659534936723420131 y[1] (numeric) = -0.0028443785071675417544105021377434 absolute error = 7.4241990831702042697989931376817e-15 relative error = 2.6101304957981530335261943257646e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.23 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.331 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.228 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 15.4 Order of pole (six term test) = 6.906e-57 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = -0.0028888210600626885350002211539505 y[1] (numeric) = -0.0028888210600549994612116523745884 absolute error = 7.6890737885687793620302473352312e-15 relative error = 2.6616649590618546255977641123431e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.22 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.321 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.218 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = -0.0029340995040480182630756016535392 y[1] (numeric) = -0.0029340995040400551181994453865595 absolute error = 7.9631448761562669797611224818531e-15 relative error = 2.7139995985718776881159994829080e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.21 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.31 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.208 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = -0.00298023223876953125 y[1] (numeric) = -0.0029802322387612844882310635060147 absolute error = 8.2467617689364939853335956820916e-15 relative error = 2.7671540699597929974928513363024e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.198 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = -0.0030272381281963052116087973105244 y[1] (numeric) = -0.0030272381281877649232903636854064 absolute error = 8.5402883184336251179922504871668e-15 relative error = 2.8211485046014916484352011887764e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.19 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.188 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = -0.0030751365138520871077855962541089 y[1] (numeric) = -0.0030751365138432430043372465736683 absolute error = 8.8441034483496804405836392480691e-15 relative error = 2.8760035232618223984732375366673e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.18 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.279 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.178 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = -0.0031239472284592603576909530533877 y[1] (numeric) = -0.0031239472284501017558618683261491 absolute error = 9.1586018290847272386082893134482e-15 relative error = 2.9317402501711834815468615845021e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.17 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.269 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.168 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = -0.0031736906100173173978927774602678 y[1] (numeric) = -0.0031736906100078332033080741782823 absolute error = 9.4841945847032819855249645886147e-15 relative error = 2.9883803275491718502257682085525e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.16 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.259 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.158 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = -0.0032243875163311071265137805390143 y[1] (numeric) = -0.0032243875163212858164797634761541 absolute error = 9.8213100340170628602187197428587e-15 relative error = 3.0459459305909707087528620142152e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.15 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.248 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.148 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=40009548, alloc=4717728, time=2.37 x[1] = 2.86 y[1] (analytic) = -0.0032760593400047140409804758097651 y[1] (numeric) = -0.0032760593399945436465129299403378 absolute error = 1.0170394467545869427242613775931e-14 relative error = 3.1044597829327581339242865232177e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.14 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.238 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.138 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = -0.0033287280239174376882996439937289 y[1] (numeric) = -0.0033287280239069057753374286507393 absolute error = 1.0531912962215342989634342161049e-14 relative error = 3.1639451726130466275602386686678e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.13 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.228 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.128 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 2.081 Order of pole (six term test) = 1.233e-58 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = -0.0033824160771989785135138744761813 y[1] (numeric) = -0.0033824160771880721632781214677528 absolute error = 1.0906350235753008428462751541767e-14 relative error = 3.2244259685475167348270712723601e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.12 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.217 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.118 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = -0.003437146591721600476418145266291 y[1] (numeric) = -0.0034371465917103062648752925991225 absolute error = 1.1294211542852667168509563931639e-14 relative error = 3.2859266375355885836260537524129e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.11 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.207 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.108 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = -0.0034929432591277331276781487512501 y[1] (numeric) = -0.0034929432591160371040628564759184 absolute error = 1.1696023615292275331631316065515e-14 relative error = 3.3484722618176845960284802396835e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.197 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.098 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = -0.0035498303884121974716552090878715 y[1] (numeric) = -0.0035498303884000851360068967880953 absolute error = 1.2112335648312299776278849651561e-14 relative error = 3.4120885572028759983492918084212e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.09 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.187 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.088 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = -0.0036078329240789922356561214348795 y[1] (numeric) = -0.0036078329240664485153204308124502 absolute error = 1.2543720335690622429360537908370e-14 relative error = 3.4768018917873764807948242587008e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.08 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.176 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.078 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = -0.0036669764648933615210872345593818 y[1] (numeric) = -0.0036669764648803707461311477463732 absolute error = 1.2990774956086813008569466740040e-14 relative error = 3.5426393052851498667640484036414e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.07 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.166 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.068 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = -0.0037272872832506827076240328966126 y[1] (numeric) = -0.0037272872832372285851106594017802 absolute error = 1.3454122513373494832354530817556e-14 relative error = 3.6096285289927364526115806549262e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.06 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.156 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.058 Order of pole (three term test) = 1225 Radius of convergence (six term test) for eq 1 = 2.564 Order of pole (six term test) = -1.283e-58 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = -0.003788792345184566466624863894591 y[1] (numeric) = -0.003788792345170632053691037791643 absolute error = 1.3934412933826102947980437199189e-14 relative error = 3.6777980064112763522217102121244e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.05 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.145 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.048 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = -0.0038515193310374504411980296425951 y[1] (numeric) = -0.0038515193310230181168748245149398 absolute error = 1.4432324323205127655266587204484e-14 relative error = 3.7471769145496193867005759387532e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.135 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.038 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 bytes used=44010456, alloc=4717728, time=2.62 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = -0.0039154966568178962752069814904192 y[1] (numeric) = -0.0039154966568029477109200439546083 absolute error = 1.4948564286937535810822240644834e-14 relative error = 3.8177951859333615400089870247440e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.03 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.125 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.028 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = -0.0039807534962697680150772373911478 y[1] (numeric) = -0.003980753496254284143760450298578 absolute error = 1.5483871316787092569866140707231e-14 relative error = 3.8896835313456395855003246423056e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.114 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.018 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = -0.0040473198036794803495043186704984 y[1] (numeric) = -0.0040473198036634413332567212353903 absolute error = 1.6039016247597435108094694455327e-14 relative error = 3.9628734633265500967362475601863e-10 % Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 3.01 Order of pole (given) = 6 Radius of convergence (ratio test) for eq 1 = 3.104 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.008 Order of pole (three term test) = 1225 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) / ( x- 6.0) / ( x - 6.0) / ( x - 6.0) ; Iterations = 100 Total Elapsed Time = 2 Seconds Elapsed Time(since restart) = 2 Seconds Time to Timeout = 2 Minutes 57 Seconds Percent Done = 101 % > quit bytes used=45238064, alloc=4717728, time=2.68