##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.5; 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); 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_y1 (double x) { return( - cos(x)); } double exact_soln_y2 (double x) { return( - sin(x)); } double exact_soln_y2p (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 = 4.5 estimated_steps = 4500000 step_error = 1.571348402636772e-21 est_needed_step_err = 1.571348402636772e-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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 4500000 step_error = 1.571348402636772e-21 est_needed_step_err = 1.571348402636772e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 2250000 step_error = 2.222222222222222e-21 est_needed_step_err = 2.222222222222222e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 1125000 step_error = 3.142696805273544e-21 est_needed_step_err = 3.142696805273544e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 562500 step_error = 4.444444444444444e-21 est_needed_step_err = 4.444444444444444e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 281250 step_error = 6.285393610547089e-21 est_needed_step_err = 6.285393610547089e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 140625 step_error = 8.888888888888888e-21 est_needed_step_err = 8.888888888888888e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 70312.5 step_error = 1.257078722109418e-20 est_needed_step_err = 1.257078722109418e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 35156.25 step_error = 1.777777777777778e-20 est_needed_step_err = 1.777777777777778e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 9 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 17578.125 step_error = 2.514157444218836e-20 est_needed_step_err = 2.514157444218836e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 10 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 8789.0625 step_error = 3.555555555555555e-20 est_needed_step_err = 3.555555555555555e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 11 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 4394.53125 step_error = 5.028314888437671e-20 est_needed_step_err = 5.028314888437671e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 12 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 2197.265625 step_error = 7.11111111111111e-20 est_needed_step_err = 7.11111111111111e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 13 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 1098.6328125 step_error = 1.005662977687534e-19 est_needed_step_err = 1.005662977687534e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 14 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 549.31640625 step_error = 1.422222222222222e-19 est_needed_step_err = 1.422222222222222e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 15 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 274.658203125 step_error = 2.011325955375068e-19 est_needed_step_err = 2.011325955375068e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 16 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 137.3291015625 step_error = 2.844444444444444e-19 est_needed_step_err = 2.844444444444444e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 17 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 = 0.8775825618903728 min_size = 0.479425538604203 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.5 estimated_steps = 68.66455078125 step_error = 4.022651910750137e-19 est_needed_step_err = 4.022651910750137e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (closed_form) = -0.8775825618903728 y1[1] (numeric) = -0.8775825618903728 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 y2[1] (closed_form) = -0.479425538604203 y2[1] (numeric) = -0.479425538604203 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.6 y1[1] (closed_form) = -0.8253356149096783 y1[1] (numeric) = -0.8253356149094621 absolute error = 2.162714451969805e-13 relative error = 2.620406066211603e-11 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 13 h = 0.1 y2[1] (closed_form) = -0.5646424733950354 y2[1] (numeric) = -0.5646424734123264 absolute error = 1.729105747472204e-11 relative error = 3.062301950251068e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.7 y1[1] (closed_form) = -0.7648421872844885 y1[1] (numeric) = -0.7648421872763022 absolute error = 8.186340494376054e-12 relative error = 1.070330668270406e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.1 y2[1] (closed_form) = -0.644217687237691 y2[1] (numeric) = -0.6442176873918414 absolute error = 1.541503591440119e-10 relative error = 2.392830283890303e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y1[1] (closed_form) = -0.6967067093471655 y1[1] (numeric) = -0.6967067093117303 absolute error = 3.543521032156605e-11 relative error = 5.086101489501927e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.1 y2[1] (closed_form) = -0.7173560908995227 y2[1] (numeric) = -0.7173560913011536 absolute error = 4.016309507193228e-10 relative error = 5.59876685811228e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y1[1] (closed_form) = -0.6216099682706645 y1[1] (numeric) = -0.6216099681781837 absolute error = 9.24808007951583e-11 relative error = 1.487762512117403e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.1 y2[1] (closed_form) = -0.7833269096274833 y2[1] (numeric) = -0.7833269103760433 absolute error = 7.48559991770037e-10 relative error = 9.556163366403689e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y1[1] (closed_form) = -0.5403023058681398 y1[1] (numeric) = -0.540302305679519 absolute error = 1.886207856571787e-10 relative error = 3.491023147756312e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.1 y2[1] (closed_form) = -0.8414709848078964 y2[1] (numeric) = -0.8414709859896337 absolute error = 1.181737263600269e-09 relative error = 1.404370780378189e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.1 y1[1] (closed_form) = -0.4535961214255775 y1[1] (numeric) = -0.4535961210938362 absolute error = 3.317412455849933e-10 relative error = 7.313582059352392e-08 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 10 h = 0.1 y2[1] (closed_form) = -0.8912073600614353 y2[1] (numeric) = -0.8912073617475995 absolute error = 1.686164208258845e-09 relative error = 1.891999868742791e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.2 y1[1] (closed_form) = -0.3623577544766736 y1[1] (numeric) = -0.3623577539485244 absolute error = 5.28149191048044e-10 relative error = 1.457535224576084e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.9320390859672263 y2[1] (numeric) = -0.932039088212527 absolute error = 2.245300723124899e-09 relative error = 2.40901991872458e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.3 y1[1] (closed_form) = -0.2674988286245873 y1[1] (numeric) = -0.2674988278421547 absolute error = 7.824326186955943e-10 relative error = 2.924994560606747e-07 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.963558185417193 y2[1] (numeric) = -0.9635581882585377 absolute error = 2.841344715065475e-09 relative error = 2.948804501967107e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.4 y1[1] (closed_form) = -0.1699671429002408 y1[1] (numeric) = -0.1699671418028917 absolute error = 1.097349128231784e-09 relative error = 6.456242715545635e-07 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.9854497299884603 y2[1] (numeric) = -0.985449733443993 absolute error = 3.455532748830592e-09 relative error = 3.506554057172512e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.5 y1[1] (closed_form) = -0.07073720166770268 y1[1] (numeric) = -0.07073720019395752 absolute error = 1.473745167568374e-09 relative error = 2.083408917547356e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = -0.9974949866040544 y2[1] (numeric) = -0.9974949906725096 absolute error = 4.068455128347637e-09 relative error = 4.078672256989066e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.6 y1[1] (closed_form) = 0.02919952230128904 y1[1] (numeric) = 0.029199524211797 absolute error = 1.910507963637231e-09 relative error = 6.542942531470422e-06 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 8 h = 0.1 y2[1] (closed_form) = -0.9995736030415051 y2[1] (numeric) = -0.9995736077018873 absolute error = 4.660382191268297e-09 relative error = 4.662370211745963e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.7 y1[1] (closed_form) = 0.1288444942955251 y1[1] (numeric) = 0.1288444967000751 absolute error = 2.404550003554107e-09 relative error = 1.866241950578729e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = -0.9916648104524686 y2[1] (numeric) = -0.9916648156640663 absolute error = 5.211597708942861e-09 relative error = 5.255402484802255e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.8 y1[1] (closed_form) = 0.2272020946930875 y1[1] (numeric) = 0.2272020976439148 absolute error = 2.950827276970713e-09 relative error = 1.298767637224821e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = -0.973847630878195 y2[1] (numeric) = -0.9738476365809292 absolute error = 5.702734173773649e-09 relative error = 5.855879290511848e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y1[1] (closed_form) = 0.323289566863504 y1[1] (numeric) = 0.3232895704058946 absolute error = 3.542390603072931e-09 relative error = 1.095733041260983e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = -0.9463000876874142 y2[1] (numeric) = -0.946300093802518 absolute error = 6.115103756698659e-09 relative error = 6.462118979237192e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2 y1[1] (closed_form) = 0.4161468365471428 y1[1] (numeric) = 0.4161468407176131 absolute error = 4.170470302433671e-09 relative error = 1.002163163617182e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 y2[1] (closed_form) = -0.9092974268256815 y2[1] (numeric) = -0.9092974332567051 absolute error = 6.431023602537778e-09 relative error = 7.072519302059621e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y1[1] (closed_form) = 0.5048461045998579 y1[1] (numeric) = 0.5048461094244494 absolute error = 4.824591504082321e-09 relative error = 9.556558840651653e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.8632093666488735 y2[1] (numeric) = -0.8632093732830015 absolute error = 6.634128024707309e-09 relative error = 7.685421730839331e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y1[1] (closed_form) = 0.5885011172553463 y1[1] (numeric) = 0.5885011227480681 absolute error = 5.492721832922598e-09 relative error = 9.333409354496343e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.8084964038195899 y2[1] (numeric) = -0.8084964105292531 absolute error = 6.709663269433008e-09 relative error = 8.298940153270269e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y1[1] (closed_form) = 0.6662760212798248 y1[1] (numeric) = 0.6662760274412709 absolute error = 6.16144613108105e-09 relative error = 9.247587988001966e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.7457052121767197 y2[1] (numeric) = -0.7457052188214827 absolute error = 6.644762962082496e-09 relative error = 8.910710095060724e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y1[1] (closed_form) = 0.737393715541246 y1[1] (numeric) = 0.7373937223574138 absolute error = 6.816167852363719e-09 relative error = 9.243593630792827e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.6754631805511503 y2[1] (numeric) = -0.6754631869798472 absolute error = 6.428696908145071e-09 relative error = 9.517464597995581e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y1[1] (closed_form) = 0.8011436155469343 y1[1] (numeric) = 0.8011436229882678 absolute error = 7.441333549351725e-09 relative error = 9.288389004100828e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.5984721441039558 y2[1] (numeric) = -0.5984721501570481 absolute error = 6.053092360680523e-09 relative error = 1.011424244271775e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y1[1] (closed_form) = 0.8568887533689478 y1[1] (numeric) = 0.8568887613896268 absolute error = 8.020679009845821e-09 relative error = 9.360233727320709e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.5155013718214634 y2[1] (numeric) = -0.5155013773335865 absolute error = 5.512123091300225e-09 relative error = 1.069274184823949e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y1[1] (closed_form) = 0.9040721420170617 y1[1] (numeric) = 0.9040721505545533 absolute error = 8.537491602567115e-09 relative error = 9.443374268251699e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.4273798802338289 y2[1] (numeric) = -0.4273798850364919 absolute error = 4.802662989522588e-09 relative error = 1.123745691279371e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y1[1] (closed_form) = 0.9422223406686585 y1[1] (numeric) = 0.9422223496435449 absolute error = 8.974886389623293e-09 relative error = 9.525231999120468e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.3349881501559038 y2[1] (numeric) = -0.3349881540803065 absolute error = 3.924402636190649e-09 relative error = 1.171504912745191e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y1[1] (closed_form) = 0.9709581651495908 y1[1] (numeric) = 0.9709581744656823 absolute error = 9.31609156484825e-09 relative error = 9.594740431904154e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.2392493292139811 y2[1] (numeric) = -0.2392493320939076 absolute error = 2.879926463972282e-09 relative error = 1.203734394338267e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y1[1] (closed_form) = 0.9899924966004456 y1[1] (numeric) = 0.9899925061451863 absolute error = 9.544740664502172e-09 relative error = 9.641225259058065e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.1411200080598659 y2[1] (numeric) = -0.1411200097346144 absolute error = 1.674748534297166e-09 relative error = 1.186754845979533e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y1[1] (closed_form) = 0.9991351502732795 y1[1] (numeric) = 0.9991351599184447 absolute error = 9.645165222060825e-09 relative error = 9.653514061058425e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = -0.04158066243328916 y2[1] (numeric) = -0.04158066275059596 absolute error = 3.173068058304196e-10 relative error = 7.631114736074676e-07 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 9 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y1[1] (closed_form) = 0.998294775794753 y1[1] (numeric) = 0.9982947853974378 absolute error = 9.602684758469593e-09 relative error = 9.619087459237471e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.05837414342758142 y2[1] (numeric) = 0.05837414460866666 absolute error = 1.181085243495694e-09 relative error = 2.023302054891719e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y1[1] (closed_form) = 0.9874797699088647 y1[1] (numeric) = 0.9874797793127553 absolute error = 9.403890666170867e-09 relative error = 9.52312234916849e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.15774569414325 y2[1] (numeric) = 0.1577456969495791 absolute error = 2.806329113536066e-09 relative error = 1.779021055869594e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y1[1] (closed_form) = 0.9667981925794605 y1[1] (numeric) = 0.9667982016163786 absolute error = 9.03691810272278e-09 relative error = 9.347264167521746e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.2555411020268329 y2[1] (numeric) = 0.2555411065685064 absolute error = 4.541673481739394e-09 relative error = 1.777277097780731e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y1[1] (closed_form) = 0.9364566872907957 y1[1] (numeric) = 0.9364566957824983 absolute error = 8.4917026743625e-09 relative error = 9.067907560070199e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.3507832276896215 y2[1] (numeric) = 0.3507832340575082 absolute error = 6.367886717928428e-09 relative error = 1.815333862986983e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y1[1] (closed_form) = 0.8967584163341462 y1[1] (numeric) = 0.8967584240943649 absolute error = 7.760218689867315e-09 relative error = 8.65363351881354e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.4425204432948541 y2[1] (numeric) = 0.442520451558322 absolute error = 8.263467909941369e-09 relative error = 1.867364103772121e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y1[1] (closed_form) = 0.8481000317104072 y1[1] (numeric) = 0.8481000385471011 absolute error = 6.836693988709897e-09 relative error = 8.061188224367806e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.5298361409084948 y2[1] (numeric) = 0.5298361511133891 absolute error = 1.020489426295512e-08 relative error = 1.926047220081492e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y1[1] (closed_form) = 0.7909677119144155 y1[1] (numeric) = 0.7909677176322132 absolute error = 5.717797679771763e-09 relative error = 7.228863572613747e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.6118578909427207 y2[1] (numeric) = 0.6118579031096223 absolute error = 1.216690159733247e-08 relative error = 1.988517558968849e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y1[1] (closed_form) = 0.7259323042001387 y1[1] (numeric) = 0.7259323086029382 absolute error = 4.40279956936962e-09 relative error = 6.06502774968914e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.6877661591839753 y2[1] (numeric) = 0.6877661733067715 absolute error = 1.412279615475853e-08 relative error = 2.053429929078661e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y1[1] (closed_form) = 0.6536436208636106 y1[1] (numeric) = 0.6536436237573062 absolute error = 2.893695616457137e-09 relative error = 4.427023417797473e-07 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.7568024953079294 y2[1] (numeric) = 0.7568025113527208 absolute error = 1.60447913843953e-08 relative error = 2.120076437891098e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y1[1] (closed_form) = 0.5748239465332677 y1[1] (numeric) = 0.5748239477285687 absolute error = 1.195300969314417e-09 relative error = 2.079420971452586e-07 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.8182771110644114 y2[1] (numeric) = 0.8182771289687795 absolute error = 1.790436809923079e-08 relative error = 2.18805681561114e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y1[1] (closed_form) = 0.4902608213406986 y1[1] (numeric) = 0.4902608206560012 absolute error = 6.846974653917925e-10 relative error = 1.396598372921938e-07 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.8715757724135886 y2[1] (numeric) = 0.8715757920862414 absolute error = 1.96726527290636e-08 relative error = 2.257136252719097e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y1[1] (closed_form) = 0.4007991720799746 y1[1] (numeric) = 0.4007991693442507 absolute error = 2.735723869662365e-09 relative error = 6.82567245701916e-07 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 9 h = 0.1 y2[1] (closed_form) = 0.9161659367494552 y2[1] (numeric) = 0.9161659580702639 absolute error = 2.132080867411901e-08 relative error = 2.327177623495254e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.4 y1[1] (closed_form) = 0.3073328699784194 y1[1] (numeric) = 0.3073328650340815 absolute error = 4.944337828050038e-09 relative error = 1.608789137457775e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = 0.951602073889516 y2[1] (numeric) = 0.9516020967099517 absolute error = 2.282043565227099e-08 relative error = 2.398106969123789e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.5 y1[1] (closed_form) = 0.2107957994307797 y1[1] (numeric) = 0.210795792136482 absolute error = 7.294297721394116e-09 relative error = 3.460361990652185e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = 0.977530117665097 y2[1] (numeric) = 0.9775301418090703 absolute error = 2.414397326511164e-08 relative error = 2.469895589793316e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.6 y1[1] (closed_form) = 0.1121525269350549 y1[1] (numeric) = 0.1121525171683898 absolute error = 9.766665046151424e-09 relative error = 8.708377165507016e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = 0.9936910036334644 y2[1] (numeric) = 0.993691028898566 absolute error = 2.526510156641848e-08 relative error = 2.54255110230804e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y1[1] (closed_form) = 0.01238866346289145 y1[1] (numeric) = 0.01238865112294331 absolute error = 1.233994813797101e-08 relative error = 9.960677497563515e-05 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 7 h = 0.1 y2[1] (closed_form) = 0.9999232575641008 y2[1] (numeric) = 0.999923283723236 absolute error = 2.615913519132818e-08 relative error = 2.616114286115725e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y1[1] (closed_form) = -0.08749898343944551 y1[1] (numeric) = -0.0874989984297304 absolute error = 1.499028488838317e-08 relative error = 1.713195319435606e-05 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 7 h = 0.1 y2[1] (closed_form) = 0.9961646088358408 y2[1] (numeric) = 0.9961646356392452 absolute error = 2.68034043848786e-08 relative error = 2.690660172740143e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y1[1] (closed_form) = -0.186512369422574 y1[1] (numeric) = -0.1865123871142367 absolute error = 1.769166266263333e-08 relative error = 9.485517082542662e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = 0.9824526126243328 y2[1] (numeric) = 0.982452639801952 absolute error = 2.717761915516093e-08 relative error = 2.766303311318387e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y1[1] (closed_form) = -0.2836621854632246 y1[1] (numeric) = -0.2836622058793981 absolute error = 2.041617352954717e-08 relative error = 7.19735466192198e-06 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 8 h = 0.1 y2[1] (closed_form) = 0.958924274663139 y2[1] (numeric) = 0.9589243019273491 absolute error = 2.726421011178815e-08 relative error = 2.843207835297089e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 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 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; Iterations = 46 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.4 %