##############ECHO OF PROBLEM################# ##############temp/h2sinpostode.ode################# diff ( y , x , 2 ) = sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(2.0 - sin(x)); } double exact_soln_yp (double x) { return(- cos(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.129384878631564e-21 est_needed_step_err = 1.129384878631564e-21 opt_iter = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 2.146019406120075e-21 est_needed_step_err = 2.146019406120075e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.683742500284564e-259 estimated_step_error = 2.683742500284564e-259 Double H and LOOP opt_iter = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 2450000 step_error = 3.034929749250866e-21 est_needed_step_err = 3.034929749250866e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.844254051529349e-248 estimated_step_error = 1.844254051529349e-248 Double H and LOOP opt_iter = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 1225000 step_error = 4.29203881224015e-21 est_needed_step_err = 4.29203881224015e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.267362075281023e-237 estimated_step_error = 1.267362075281023e-237 Double H and LOOP opt_iter = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 6.069859498501731e-21 est_needed_step_err = 6.069859498501731e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.709250556831352e-227 estimated_step_error = 8.709250556831352e-227 Double H and LOOP opt_iter = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 8.584077624480301e-21 est_needed_step_err = 8.584077624480301e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.984957858910476e-216 estimated_step_error = 5.984957858910476e-216 Double H and LOOP opt_iter = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 153125 step_error = 1.213971899700346e-20 est_needed_step_err = 1.213971899700346e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.112840586441048e-205 estimated_step_error = 4.112840586441048e-205 Double H and LOOP opt_iter = 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 1.71681552489606e-20 est_needed_step_err = 1.71681552489606e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.826334711102374e-194 estimated_step_error = 2.826334711102374e-194 Double H and LOOP opt_iter = 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.900166583353172 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.900166583353172 desired_abs_gbl_error = 1.900166583353172e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 2.427943799400693e-20 est_needed_step_err = 2.427943799400693e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.942259165871316e-183 estimated_step_error = 1.942259165871316e-183 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.900166583353172 y[1] (numeric) = 1.900166583353172 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000959999999943 y[1] (closed_form) = 1.801236583729084 y[1] (numeric) = 1.801236583729078 absolute error = 6.661338147750939e-15 relative error = 3.698202783534425e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000639999999968 y[1] (closed_form) = 1.704418652408627 y[1] (numeric) = 1.704418652408624 absolute error = 3.108624468950438e-15 relative error = 1.823862033284742e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.40003200000001 y[1] (closed_form) = 1.610552183938919 y[1] (numeric) = 1.610552183938928 absolute error = 8.659739592076221e-15 relative error = 5.376876128842432e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000000233 y[1] (closed_form) = 1.520574461395777 y[1] (numeric) = 1.520574461395795 absolute error = 1.84297022087776e-14 relative error = 1.212022342652031e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000960000000366 y[1] (closed_form) = 1.435278296987897 y[1] (numeric) = 1.435278296987927 absolute error = 2.930988785010413e-14 relative error = 2.042104859497592e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000640000000499 y[1] (closed_form) = 1.355733364181676 y[1] (numeric) = 1.355733364181712 absolute error = 3.641531520770513e-14 relative error = 2.686023385556017e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000320000000631 y[1] (closed_form) = 1.282621614853024 y[1] (numeric) = 1.282621614853069 absolute error = 4.440892098500626e-14 relative error = 3.462355574765133e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000764 y[1] (closed_form) = 1.216673090372469 y[1] (numeric) = 1.21667309037252 absolute error = 5.129230373768223e-14 relative error = 4.215783528341186e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.00009600000009 y[1] (closed_form) = 1.15847715004827 y[1] (numeric) = 1.158477150048324 absolute error = 5.417888360170764e-14 relative error = 4.676733036939933e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.100064000000016 y[1] (closed_form) = 1.108763611611999 y[1] (numeric) = 1.108763611612014 absolute error = 1.554312234475219e-14 relative error = 1.401842753673572e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200031999999943 y[1] (closed_form) = 1.067949319061857 y[1] (numeric) = 1.067949319061848 absolute error = 9.325873406851315e-15 relative error = 8.732505597778416e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299999999999869 y[1] (closed_form) = 1.036441814582842 y[1] (numeric) = 1.036441814582816 absolute error = 2.575717417130363e-14 relative error = 2.485153899514432e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400095999999796 y[1] (closed_form) = 1.014533957706834 y[1] (numeric) = 1.014533957706809 absolute error = 2.442490654175344e-14 relative error = 2.40750014883301e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.500063999999722 y[1] (closed_form) = 1.002500488257931 y[1] (numeric) = 1.002500488257927 absolute error = 4.218847493575595e-15 relative error = 4.208324627259569e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600031999999649 y[1] (closed_form) = 1.00042733185498 y[1] (numeric) = 1.000427331855006 absolute error = 2.664535259100376e-14 relative error = 2.663397104675088e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.699999999999575 y[1] (closed_form) = 1.008335189547477 y[1] (numeric) = 1.008335189547549 absolute error = 7.283063041541027e-14 relative error = 7.222859141521719e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.800095999999502 y[1] (closed_form) = 1.026174185010238 y[1] (numeric) = 1.02617418501037 absolute error = 1.316724507205436e-13 relative error = 1.283139379687571e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900063999999428 y[1] (closed_form) = 1.053720604782688 y[1] (numeric) = 1.053720604782894 absolute error = 2.05613304160579e-13 relative error = 1.951307616338993e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.000031999999355 y[1] (closed_form) = 1.090715890338378 y[1] (numeric) = 1.090715890338675 absolute error = 2.97539770599542e-13 relative error = 2.727931015172383e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.099999999999455 y[1] (closed_form) = 1.136790633350851 y[1] (numeric) = 1.136790633351162 absolute error = 3.104183576851938e-13 relative error = 2.730655483764778e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200095999999555 y[1] (closed_form) = 1.191560096012869 y[1] (numeric) = 1.191560096013175 absolute error = 3.059774655866931e-13 relative error = 2.567872712509739e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300063999999655 y[1] (closed_form) = 1.254337431015587 y[1] (numeric) = 1.254337431015873 absolute error = 2.853273173286652e-13 relative error = 2.274725367141815e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400031999999755 y[1] (closed_form) = 1.324560416393399 y[1] (numeric) = 1.324560416393651 absolute error = 2.522426711948356e-13 relative error = 1.904350062654436e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999855 y[1] (closed_form) = 1.401527855895928 y[1] (numeric) = 1.401527855896131 absolute error = 2.033928581113287e-13 relative error = 1.451222373181514e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600095999999955 y[1] (closed_form) = 1.484580891874125 y[1] (numeric) = 1.48458089187427 absolute error = 1.447730824111204e-13 relative error = 9.751781341356201e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700064000000055 y[1] (closed_form) = 1.572677981258544 y[1] (numeric) = 1.572677981258618 absolute error = 7.438494264988549e-14 relative error = 4.729826673758003e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800032000000155 y[1] (closed_form) = 1.665042001130652 y[1] (numeric) = 1.665042001130649 absolute error = 2.442490654175344e-15 relative error = 1.46692434936582e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000255 y[1] (closed_form) = 1.760750670786265 y[1] (numeric) = 1.760750670786179 absolute error = 8.615330671091215e-14 relative error = 4.892987300265532e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000096000000355 y[1] (closed_form) = 1.858975031870293 y[1] (numeric) = 1.858975031870116 absolute error = 1.77191594730175e-13 relative error = 9.531682335286911e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100064000000455 y[1] (closed_form) = 1.958483282301895 y[1] (numeric) = 1.958483282301623 absolute error = 2.724487302430134e-13 relative error = 1.391121040986328e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200032000000555 y[1] (closed_form) = 2.058406088831067 y[1] (numeric) = 2.058406088830691 absolute error = 3.75699471533153e-13 relative error = 1.825196075602877e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000655 y[1] (closed_form) = 2.157745694143895 y[1] (numeric) = 2.157745694143425 absolute error = 4.707345624410664e-13 relative error = 2.181603530567278e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400096000000755 y[1] (closed_form) = 2.255633913476373 y[1] (numeric) = 2.255633913475803 absolute error = 5.702105454474804e-13 relative error = 2.527939228261887e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500064000000855 y[1] (closed_form) = 2.350843160199962 y[1] (numeric) = 2.350843160199309 absolute error = 6.532552276894421e-13 relative error = 2.778812465030105e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600032000000955 y[1] (closed_form) = 2.442549139338456 y[1] (numeric) = 2.442549139337722 absolute error = 7.345235530920036e-13 relative error = 3.007200720190804e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000001055 y[1] (closed_form) = 2.529836140909388 y[1] (numeric) = 2.529836140908583 absolute error = 8.055778266680136e-13 relative error = 3.184308318002115e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800096000001155 y[1] (closed_form) = 2.611933821024419 y[1] (numeric) = 2.611933821023558 absolute error = 8.606448886894214e-13 relative error = 3.295048602540284e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900064000001255 y[1] (closed_form) = 2.687812617443777 y[1] (numeric) = 2.687812617442867 absolute error = 9.099387909827783e-13 relative error = 3.385424955137566e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000032000001355 y[1] (closed_form) = 2.756823411517195 y[1] (numeric) = 2.756823411516252 absolute error = 9.43245481721533e-13 relative error = 3.421494020186174e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000001455 y[1] (closed_form) = 2.818277111065247 y[1] (numeric) = 2.81827711106429 absolute error = 9.565681580170349e-13 relative error = 3.394159340333545e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200096000001555 y[1] (closed_form) = 2.871622833436906 y[1] (numeric) = 2.87162283343595 absolute error = 9.556799795973347e-13 relative error = 3.328013583362993e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300064000001655 y[1] (closed_form) = 2.916191586020806 y[1] (numeric) = 2.916191586019868 absolute error = 9.383605004131823e-13 relative error = 3.217760125608179e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.400032000001755 y[1] (closed_form) = 2.951611908054673 y[1] (numeric) = 2.951611908053774 absolute error = 8.992806499463768e-13 relative error = 3.046744212856453e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.500000000001855 y[1] (closed_form) = 2.977530117665488 y[1] (numeric) = 2.977530117664636 absolute error = 8.517631044924201e-13 relative error = 2.860636402765387e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.600096000001956 y[1] (closed_form) = 2.993701765697325 y[1] (numeric) = 2.993701765696547 absolute error = 7.780442956573097e-13 relative error = 2.598937224049368e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.700064000002055 y[1] (closed_form) = 2.999924048390744 y[1] (numeric) = 2.999924048390061 absolute error = 6.834532939592464e-13 relative error = 2.278235325077222e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.800032000002155 y[1] (closed_form) = 2.996161808358146 y[1] (numeric) = 2.99616180835758 absolute error = 5.657696533489798e-13 relative error = 1.888314749125694e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.900000000002255 y[1] (closed_form) = 2.982452612623912 y[1] (numeric) = 2.982452612623486 absolute error = 4.263256414560601e-13 relative error = 1.429446488609876e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 2 ) = sin ( x ) ; Iterations = 38282 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %