##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos ( x ) ; diff ( y1 , x , 1 ) = m1 * y2 ; ! // 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_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); 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_y2 (double x) { return(sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y1 (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 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 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.674790358513323e-258 estimated_step_error = 2.674790358513323e-258 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 2450000 step_error = 1.59719141249985e-21 est_needed_step_err = 1.59719141249985e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.838101935663099e-247 estimated_step_error = 1.838101935663099e-247 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 1225000 step_error = 2.258769757263128e-21 est_needed_step_err = 2.258769757263128e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.263134028636665e-236 estimated_step_error = 1.263134028636665e-236 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 3.194382824999699e-21 est_needed_step_err = 3.194382824999699e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.680190902457671e-226 estimated_step_error = 8.680190902457671e-226 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 4.517539514526256e-21 est_needed_step_err = 4.517539514526256e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.964981703152478e-215 estimated_step_error = 5.964981703152478e-215 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 153125 step_error = 6.388765649999399e-21 est_needed_step_err = 6.388765649999399e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.099104124878064e-204 estimated_step_error = 4.099104124878064e-204 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 9.035079029052512e-21 est_needed_step_err = 9.035079029052512e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.816882783259633e-193 estimated_step_error = 2.816882783259633e-193 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.09983341664682815 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 1.27775312999988e-20 est_needed_step_err = 1.27775312999988e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.935746940941988e-182 estimated_step_error = 1.935746940941988e-182 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 0.09983341664682815 y2[1] (numeric) = 0.09983341664682815 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.000128 y1[1] (closed_form) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000959999999943 y2[1] (closed_form) = 0.1987634162709156 y2[1] (numeric) = 0.1987634162709209 absolute error = 5.329070518200751e-15 relative error = 2.681112358693413e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.980047501069369 y1[1] (numeric) = 0.9800475010693684 absolute error = 5.551115123125783e-16 relative error = 5.664128643834854e-14 % Desired digits = 16 Estimated correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000639999999968 y2[1] (closed_form) = 0.2955813475913734 y2[1] (numeric) = 0.2955813475913767 absolute error = 3.33066907387547e-15 relative error = 1.126819774324852e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.9553175738758645 y1[1] (numeric) = 0.955317573875865 absolute error = 5.551115123125783e-16 relative error = 5.810753695866903e-14 % Desired digits = 16 Estimated correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.40003200000001 y2[1] (closed_form) = 0.3894478160610806 y2[1] (numeric) = 0.3894478160610709 absolute error = 9.769962616701378e-15 relative error = 2.508670536534493e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.9210485321443462 y1[1] (numeric) = 0.921048532144352 absolute error = 5.773159728050814e-15 relative error = 6.268029888294798e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000233 y2[1] (closed_form) = 0.4794255386042234 y2[1] (numeric) = 0.4794255386042027 absolute error = 2.076117056049043e-14 relative error = 4.330426497706715e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.8775825618903615 y1[1] (numeric) = 0.8775825618903754 absolute error = 1.387778780781446e-14 relative error = 1.581365493170344e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000960000000366 y2[1] (closed_form) = 0.5647217030121027 y2[1] (numeric) = 0.5647217030120735 absolute error = 2.919886554764162e-14 relative error = 5.170487585637531e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.8252814054291484 y1[1] (numeric) = 0.8252814054291694 absolute error = 2.098321516541546e-14 relative error = 2.542552761685468e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000640000000499 y2[1] (closed_form) = 0.6442666358183241 y2[1] (numeric) = 0.6442666358182869 absolute error = 3.719247132494274e-14 relative error = 5.772838333883644e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.7648009557861044 y1[1] (numeric) = 0.7648009557861374 absolute error = 3.297362383136715e-14 relative error = 4.311399401622746e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000320000000631 y2[1] (closed_form) = 0.7173783851469757 y2[1] (numeric) = 0.7173783851469342 absolute error = 4.152234112098085e-14 relative error = 5.78806693659634e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.6966837535955014 y1[1] (numeric) = 0.6966837535955481 absolute error = 4.674038933671909e-14 relative error = 6.708982245602476e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000764 y2[1] (closed_form) = 0.7833269096275309 y2[1] (numeric) = 0.7833269096274866 absolute error = 4.429789868254375e-14 relative error = 5.655097270130453e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.6216099682706046 y1[1] (numeric) = 0.6216099682706662 absolute error = 6.161737786669619e-14 relative error = 9.912546614740319e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.00009600000009 y2[1] (closed_form) = 0.8415228499517303 y2[1] (numeric) = 0.8415228499516865 absolute error = 4.385380947269368e-14 relative error = 5.211244052993823e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.5402215221639338 y1[1] (numeric) = 0.5402215221640109 absolute error = 7.704947790898586e-14 relative error = 1.426257095429173e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100064000000016 y2[1] (closed_form) = 0.8912363883880015 y2[1] (numeric) = 0.8912363883880007 absolute error = 7.771561172376096e-16 relative error = 8.719977408499542e-14 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 16 h = 0.000128 y1[1] (closed_form) = 0.4535390832255932 y1[1] (numeric) = 0.4535390832256088 absolute error = 1.565414464721471e-14 relative error = 3.451553620446915e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200031999999943 y2[1] (closed_form) = 0.9320506809381428 y2[1] (numeric) = 0.9320506809381703 absolute error = 2.753353101070388e-14 relative error = 2.954080885707887e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.362327929040454 y1[1] (numeric) = 0.362327929040402 absolute error = 5.195843755245733e-14 relative error = 1.434016905350295e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.299999999999869 y2[1] (closed_form) = 0.963558185417158 y2[1] (numeric) = 0.9635581854172003 absolute error = 4.229949723821846e-14 relative error = 4.389926615579062e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.2674988286247134 y1[1] (numeric) = 0.2674988286245888 absolute error = 1.245670233629426e-13 relative error = 4.656731545456727e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.400095999999796 y2[1] (closed_form) = 0.9854660422931665 y2[1] (numeric) = 0.985466042293211 absolute error = 4.451994328746878e-14 relative error = 4.517653716800982e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.1698725389433001 y1[1] (numeric) = 0.1698725389430991 absolute error = 2.00978123032769e-13 relative error = 1.183111315595579e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.500063999999722 y2[1] (closed_form) = 0.9974995117420687 y2[1] (numeric) = 0.9974995117421006 absolute error = 3.186340080674199e-14 relative error = 3.19432745897736e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.07067336184401106 y1[1] (numeric) = 0.07067336184373328 absolute error = 2.777778007612142e-13 relative error = 3.930445552799939e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.600031999999649 y2[1] (closed_form) = 0.9995726681450202 y2[1] (numeric) = 0.9995726681450239 absolute error = 3.663735981263017e-15 relative error = 3.665302281686111e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = -0.02923150864127944 y1[1] (numeric) = -0.0292315086416325 absolute error = 3.530647996186076e-13 relative error = 1.207822709225569e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.699999999999575 y2[1] (closed_form) = 0.9916648104525233 y2[1] (numeric) = 0.9916648104524836 absolute error = 3.97459842815806e-14 relative error = 4.008005917185207e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = -0.1288444942951036 y1[1] (numeric) = -0.1288444942955281 absolute error = 4.244937734654286e-13 relative error = 3.294620975368757e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.800095999999502 y2[1] (closed_form) = 0.9738258149897615 y2[1] (numeric) = 0.9738258149896619 absolute error = 9.958700530887654e-14 relative error = 1.022636736220877e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.2272955830180754 y1[1] (numeric) = -0.2272955830185652 absolute error = 4.898026428890034e-13 relative error = 2.15491491909041e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.900063999999428 y2[1] (closed_form) = 0.9462793952173116 y2[1] (numeric) = 0.9462793952171374 absolute error = 1.741939925636871e-13 relative error = 1.840830450753751e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.3233501294064362 y1[1] (numeric) = -0.3233501294069832 absolute error = 5.469513730815834e-13 relative error = 1.691514316340634e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.000031999999355 y2[1] (closed_form) = 0.9092841096616225 y2[1] (numeric) = 0.9092841096613612 absolute error = 2.613464999967618e-13 relative error = 2.874200673032968e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.4161759338511424 y1[1] (numeric) = -0.4161759338517353 absolute error = 5.929146063010649e-13 relative error = 1.4246729761965e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.099999999999455 y2[1] (closed_form) = 0.8632093666491488 y2[1] (numeric) = 0.8632093666488744 absolute error = 2.744471316873387e-13 relative error = 3.179380834949717e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.5048461045993872 y1[1] (numeric) = -0.5048461045998642 absolute error = 4.770628336814298e-13 relative error = 9.449668509574727e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.200095999999555 y2[1] (closed_form) = 0.8084399039871307 y2[1] (numeric) = 0.8084399039868593 absolute error = 2.714495295208508e-13 relative error = 3.3576958309714e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.5885787301978205 y1[1] (numeric) = -0.5885787301981876 absolute error = 3.671507542435393e-13 relative error = 6.237920866086011e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.300063999999655 y2[1] (closed_form) = 0.7456625689844129 y2[1] (numeric) = 0.7456625689841601 absolute error = 2.527977827071481e-13 relative error = 3.390243700330257e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.6663237450485806 y1[1] (numeric) = -0.666323745048844 absolute error = 2.633449014410871e-13 relative error = 3.952206467171406e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.400031999999755 y2[1] (closed_form) = 0.6754395836066009 y2[1] (numeric) = 0.6754395836063811 absolute error = 2.19824158875781e-13 relative error = 3.254534738725264e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.7374153299853086 y1[1] (numeric) = -0.7374153299854772 absolute error = 1.686428774405613e-13 relative error = 2.286945640849657e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.499999999999855 y2[1] (closed_form) = 0.5984721441040725 y2[1] (numeric) = 0.5984721441038956 absolute error = 1.768585278227874e-13 relative error = 2.955167246548275e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.8011436155468471 y1[1] (numeric) = -0.8011436155469304 absolute error = 8.326672684688674e-14 relative error = 1.039348316968741e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.600095999999955 y2[1] (closed_form) = 0.5154191081258751 y2[1] (numeric) = 0.5154191081257499 absolute error = 1.252331571777177e-13 relative error = 2.429734466637844e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.8569382375519997 y1[1] (numeric) = -0.8569382375520103 absolute error = 1.054711873393899e-14 relative error = 1.230791003569727e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.700064000000055 y2[1] (closed_form) = 0.4273220187414564 y2[1] (numeric) = 0.4273220187413895 absolute error = 6.689093723366568e-14 relative error = 1.565351989833617e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.9040994924778614 y1[1] (numeric) = -0.9040994924778154 absolute error = 4.596323321948148e-14 relative error = 5.083868932777548e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.800032000000155 y2[1] (closed_form) = 0.3349579988693484 y2[1] (numeric) = 0.3349579988693439 absolute error = 4.496403249731884e-15 relative error = 1.34237822798963e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = -0.9422330598070955 y1[1] (numeric) = -0.9422330598070089 absolute error = 8.659739592076221e-14 relative error = 9.190655647180476e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.900000000000255 y2[1] (closed_form) = 0.2392493292137345 y2[1] (numeric) = 0.2392493292137935 absolute error = 5.898059818321144e-14 relative error = 2.465235675980552e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.9709581651496516 y1[1] (numeric) = -0.970958165149539 absolute error = 1.125766146969909e-13 relative error = 1.159438364470005e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.000096000000355 y2[1] (closed_form) = 0.1410249681297067 y2[1] (numeric) = 0.1410249681298272 absolute error = 1.204591981718295e-13 relative error = 8.541692990211347e-11 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.9900060395593631 y1[1] (numeric) = -0.9900060395592398 absolute error = 1.232347557333924e-13 relative error = 1.244787918548884e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.100064000000455 y2[1] (closed_form) = 0.0415167176981046 y2[1] (numeric) = 0.04151671769828193 absolute error = 1.77337311502157e-13 relative error = 4.271467527652197e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = -0.9991378093894635 y1[1] (numeric) = -0.9991378093893464 absolute error = 1.17128529097954e-13 relative error = 1.17229603361249e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.200032000000555 y2[1] (closed_form) = -0.0584060888310667 y2[1] (numeric) = -0.05840608883084066 absolute error = 2.260483467075858e-13 relative error = 3.870287349002365e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = -0.9982929073110044 y1[1] (numeric) = -0.9982929073109079 absolute error = 9.64783808399261e-14 relative error = 9.664336001324469e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.300000000000655 y2[1] (closed_form) = -0.1577456941438955 y2[1] (numeric) = -0.1577456941436318 absolute error = 2.637057239240903e-13 relative error = 1.671714244596358e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = -0.9874797699087615 y1[1] (numeric) = -0.9874797699087012 absolute error = 6.0285110237146e-14 relative error = 6.104946356796358e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.400096000000755 y2[1] (closed_form) = -0.2556339134763733 y2[1] (numeric) = -0.255633913476086 absolute error = 2.872702076217593e-13 relative error = 1.123756248594574e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = -0.966773656178505 y1[1] (numeric) = -0.9667736561784949 absolute error = 1.010302952408892e-14 relative error = 1.045025323096258e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.500064000000855 y2[1] (closed_form) = -0.3508431601999625 y2[1] (numeric) = -0.3508431601996682 absolute error = 2.942646126768977e-13 relative error = 8.387354979620583e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.9364342352460762 y1[1] (numeric) = -0.9364342352461249 absolute error = 4.873879078104437e-14 relative error = 5.204721158900902e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.600032000000955 y2[1] (closed_form) = -0.4425491393384564 y2[1] (numeric) = -0.4425491393381753 absolute error = 2.811084698350896e-13 relative error = 6.352028392944205e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.8967442552204009 y1[1] (numeric) = -0.8967442552205174 absolute error = 1.164623952831789e-13 relative error = 1.298724743483915e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.700000000001055 y2[1] (closed_form) = -0.5298361409093882 y2[1] (numeric) = -0.5298361409091427 absolute error = 2.455813330470846e-13 relative error = 4.635043064929079e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.848100031709849 y1[1] (numeric) = -0.8481000317100394 absolute error = 1.904032487232143e-13 relative error = 2.245056498103692e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.800096000001155 y2[1] (closed_form) = -0.611933821024419 y2[1] (numeric) = -0.6119338210242332 absolute error = 1.857403120197887e-13 relative error = 3.035300642622543e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.7909089699114902 y1[1] (numeric) = -0.7909089699117596 absolute error = 2.694511280765255e-13 relative error = 3.406853864695446e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.900064000001255 y2[1] (closed_form) = -0.6878126174437771 y2[1] (numeric) = -0.6878126174436798 absolute error = 9.725553695716371e-14 relative error = 1.413983030997734e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.7258882856784096 y1[1] (numeric) = -0.725888285678757 absolute error = 3.473887844052115e-13 relative error = 4.785705889723025e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.000032000001355 y2[1] (closed_form) = -0.7568234115171953 y2[1] (numeric) = -0.756823411517215 absolute error = 1.965094753586527e-14 relative error = 2.596503654197382e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = -0.6536194028480748 y1[1] (numeric) = -0.6536194028485004 absolute error = 4.255484853388225e-13 relative error = 6.510646463133464e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.100000000001455 y2[1] (closed_form) = -0.818277111065247 y2[1] (numeric) = -0.8182771110654172 absolute error = 1.701971896750365e-13 relative error = 2.079945624453199e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.574823946532078 y1[1] (numeric) = -0.5748239465325737 absolute error = 4.957145804951324e-13 relative error = 8.623763562492243e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.200096000001555 y2[1] (closed_form) = -0.8716228334369058 y2[1] (numeric) = -0.871622833437259 absolute error = 3.531619441332623e-13 relative error = 4.05177481113827e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.4901771478061988 y1[1] (numeric) = -0.4901771478067531 absolute error = 5.543343561953407e-13 relative error = 1.130885759722336e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.300064000001655 y2[1] (closed_form) = -0.9161915860208062 y2[1] (numeric) = -0.916191586021378 absolute error = 5.717648576819556e-13 relative error = 6.240669161405846e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.4007405366377099 y1[1] (numeric) = -0.400740536638308 absolute error = 5.980771433655718e-13 relative error = 1.492429860935841e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.400032000001755 y2[1] (closed_form) = -0.9516119080546728 y2[1] (numeric) = -0.9516119080555002 absolute error = 8.274492202531292e-13 relative error = 8.695238187431235e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 0.000128 y1[1] (closed_form) = -0.3073024185530355 y1[1] (numeric) = -0.3073024185536576 absolute error = 6.221134718487065e-13 relative error = 2.024434024235769e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.500000000001855 y2[1] (closed_form) = -0.9775301176654881 y2[1] (numeric) = -0.9775301176666092 absolute error = 1.121103210266483e-12 relative error = 1.146873318792338e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = -0.210795799428966 y1[1] (numeric) = -0.2107957994295871 absolute error = 6.211697822777751e-13 relative error = 2.946784442386847e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.600096000001956 y2[1] (closed_form) = -0.9937017656973247 y2[1] (numeric) = -0.9937017656987772 absolute error = 1.452504783117092e-12 relative error = 1.461710981360494e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = -0.1120571320801102 y1[1] (numeric) = -0.1120571320807017 absolute error = 5.914990719446678e-13 relative error = 5.278549084424204e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.700064000002055 y2[1] (closed_form) = -0.9999240483907444 y2[1] (numeric) = -0.9999240483925665 absolute error = 1.822098028014807e-12 relative error = 1.822236429804095e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = -0.01232466834702301 y1[1] (numeric) = -0.01232466834755107 absolute error = 5.2805849970472e-13 relative error = 4.28456559508371e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.800032000002155 y2[1] (closed_form) = -0.9961618083581462 y2[1] (numeric) = -0.996161808360377 absolute error = 2.23088214568179e-12 relative error = 2.239477690234566e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = 0.08753086066427158 y1[1] (numeric) = 0.08753086066384602 absolute error = 4.255623631266303e-13 relative error = 4.861855120548776e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.900000000002255 y2[1] (closed_form) = -0.9824526126239118 y2[1] (numeric) = -0.9824526126265888 absolute error = 2.676969756976177e-12 relative error = 2.724782572287724e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 y1[1] (closed_form) = 0.1865123694247913 y1[1] (numeric) = 0.1865123694245121 absolute error = 2.791933351176112e-13 relative error = 1.496915920261216e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 3 ) = m1 * cos ( x ) ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations = 38282 Total Elapsed Time = 22.0 Seconds Elapsed Time(since restart) = 22.0 Seconds Time to Timeout = 2 Minutes 38.0 Seconds Percent Done = 100 %