##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=64; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=0.7; 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); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); array_y2_init[4 + 1] = exact_soln_y2pppp(x_start); glob_look_poles=true; glob_max_h=0.1; 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) + 10.0 * x + 10.0); } double exact_soln_y2p (double x) { return( cos(x) + 10.0); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(x)); } double exact_soln_y2pppp (double x) { return( sin(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 = 0.6 estimated_steps = 600000 step_error = 3.227486121839514e-21 est_needed_step_err = 3.227486121839514e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 600000 step_error = 3.227486121839514e-21 est_needed_step_err = 3.227486121839514e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.674790362139999e-258 estimated_step_error = 2.674790362139999e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 300000 step_error = 4.564354645876384e-21 est_needed_step_err = 4.564354645876384e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.838101940647567e-247 estimated_step_error = 1.838101940647567e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 150000 step_error = 6.454972243679028e-21 est_needed_step_err = 6.454972243679028e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.263134035487269e-236 estimated_step_error = 1.263134035487269e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 75000 step_error = 9.128709291752767e-21 est_needed_step_err = 9.128709291752767e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.680190996611721e-226 estimated_step_error = 8.680190996611721e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 37500 step_error = 1.290994448735806e-20 est_needed_step_err = 1.290994448735806e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.964981832556958e-215 estimated_step_error = 5.964981832556958e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 18750 step_error = 1.825741858350553e-20 est_needed_step_err = 1.825741858350553e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.099104302730605e-204 estimated_step_error = 4.099104302730605e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 9375 step_error = 2.581988897471611e-20 est_needed_step_err = 2.581988897471611e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.816883027699333e-193 estimated_step_error = 2.816883027699333e-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 = 11.09983341664683 min_size = 0.9950041652780258 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.6 estimated_steps = 4687.5 step_error = 3.651483716701107e-20 est_needed_step_err = 3.651483716701107e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.935747276900176e-182 estimated_step_error = 1.935747276900176e-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) = 11.09983341664683 y2[1] (numeric) = 11.09983341664683 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] = 0.1600319999999977 y2[1] (closed_form) = 11.75966979780571 y2[1] (numeric) = 11.75966979780574 absolute error = 2.842170943040401e-14 relative error = 2.416879888558379e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 0.9872221846875562 y1[1] (numeric) = 0.9872221846875561 absolute error = 1.110223024625157e-16 relative error = 1.124592864550069e-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] = 0.2200639999999926 y2[1] (closed_form) = 12.41893208007057 y2[1] (numeric) = 12.41893208007065 absolute error = 7.993605777301127e-14 relative error = 6.436628951477207e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 0.9758834806361015 y1[1] (numeric) = 0.9758834806361013 absolute error = 2.220446049250313e-16 relative error = 2.275318819622789e-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] = 0.2800959999999941 y2[1] (closed_form) = 13.07740790861254 y2[1] (numeric) = 13.07740790861262 absolute error = 7.638334409421077e-14 relative error = 5.840862702149568e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.000128 y1[1] (closed_form) = 0.9610289037400077 y1[1] (numeric) = 0.9610289037400073 absolute error = 4.440892098500626e-16 relative error = 4.620976623302523e-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] = 0.3400000000000021 y2[1] (closed_form) = 13.73348709214084 y2[1] (numeric) = 13.73348709214083 absolute error = 5.329070518200751e-15 relative error = 3.880347709541577e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.000128 y1[1] (closed_form) = 0.9427546655283455 y1[1] (numeric) = 0.9427546655283474 absolute error = 1.887379141862766e-15 relative error = 2.001983348239414e-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] = 0.40003200000001 y2[1] (closed_form) = 14.38976781606118 y2[1] (numeric) = 14.3897678160611 absolute error = 7.815970093361102e-14 relative error = 5.43161654397042e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 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] = 0.460064000000018 y2[1] (closed_form) = 15.04464545341631 y2[1] (numeric) = 15.04464545341615 absolute error = 1.580957587066223e-13 relative error = 1.050844030829069e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.8960240830115753 y1[1] (numeric) = 0.8960240830115859 absolute error = 1.054711873393899e-14 relative error = 1.177102148693333e-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] = 0.520096000000026 y2[1] (closed_form) = 15.69792344619552 y2[1] (numeric) = 15.69792344619528 absolute error = 2.415845301584341e-13 relative error = 1.538958518854183e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.8677714751855665 y1[1] (numeric) = 0.8677714751855811 absolute error = 1.454392162258955e-14 relative error = 1.676008262368781e-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] = 0.5800000000000339 y2[1] (closed_form) = 16.34802393679224 y2[1] (numeric) = 16.34802393679194 absolute error = 2.984279490192421e-13 relative error = 1.825468020924605e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.8364626499151684 y1[1] (numeric) = 0.8364626499151869 absolute error = 1.854072451124011e-14 relative error = 2.216563347224226e-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] = 0.6400320000000419 y2[1] (closed_form) = 16.99754110812133 y2[1] (numeric) = 16.99754110812097 absolute error = 3.552713678800501e-13 relative error = 2.090133894191928e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.000128 y1[1] (closed_form) = 0.8020766472194742 y1[1] (numeric) = 0.8020766472194995 absolute error = 2.520206265899105e-14 relative error = 3.142101536849127e-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 Finished! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ; Iterations = 4688 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Time to Timeout = 2 Minutes 58.0 Seconds Percent Done = 100 %