##############ECHO OF PROBLEM################# ##############temp/expt_sin_linpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( x ) , ( 0.2 * x + 0.3 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=0.2; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(0.0); } // 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 = 0.1 estimated_steps = 100000 step_error = 1.05409255338946e-20 est_needed_step_err = 1.05409255338946e-20 opt_iter = 1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9994 NO COMPLEX POLE (six term test) for Equation 1 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 = 0.1 estimated_steps = 100000 step_error = 1.05409255338946e-20 est_needed_step_err = 1.05409255338946e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1483916146355e-137 estimated_step_error = 1.1483916146355e-137 Double H and LOOP opt_iter = 2 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 50000.00000000001 step_error = 1.49071198499986e-20 est_needed_step_err = 1.49071198499986e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.598389669015201e-130 estimated_step_error = 6.598389669015201e-130 Double H and LOOP opt_iter = 3 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 25000 step_error = 2.108185106778919e-20 est_needed_step_err = 2.108185106778919e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.428063340634194e-122 estimated_step_error = 4.428063340634194e-122 Double H and LOOP opt_iter = 4 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 12500 step_error = 2.98142396999972e-20 est_needed_step_err = 2.98142396999972e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.97156796590924e-114 estimated_step_error = 2.97156796590924e-114 Double H and LOOP opt_iter = 5 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 6250.000000000001 step_error = 4.216370213557839e-20 est_needed_step_err = 4.216370213557839e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.994111636674374e-106 estimated_step_error = 1.994111636674374e-106 Double H and LOOP opt_iter = 6 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 3125 step_error = 5.962847939999439e-20 est_needed_step_err = 5.962847939999439e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.338126533044851e-98 estimated_step_error = 1.338126533044851e-98 Double H and LOOP opt_iter = 7 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 1562.5 step_error = 8.432740427115678e-20 est_needed_step_err = 8.432740427115678e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.97868490503329e-91 estimated_step_error = 8.97868490503329e-91 Double H and LOOP opt_iter = 8 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 781.2500000000001 step_error = 1.192569587999888e-19 est_needed_step_err = 1.192569587999888e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.023708809993655e-83 estimated_step_error = 6.023708809993655e-83 Double H and LOOP opt_iter = 9 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 390.6250000000001 step_error = 1.686548085423136e-19 est_needed_step_err = 1.686548085423136e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.040049393720842e-75 estimated_step_error = 4.040049393720842e-75 Double H and LOOP opt_iter = 10 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 195.3125 step_error = 2.385139175999776e-19 est_needed_step_err = 2.385139175999776e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.708024923037729e-67 estimated_step_error = 2.708024923037729e-67 Double H and LOOP opt_iter = 11 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 97.65625000000001 step_error = 3.373096170846271e-19 est_needed_step_err = 3.373096170846271e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.813036573272479e-59 estimated_step_error = 1.813036573272479e-59 Double H and LOOP opt_iter = 12 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 48.82812500000001 step_error = 4.770278351999551e-19 est_needed_step_err = 4.770278351999551e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.210993393776305e-51 estimated_step_error = 1.210993393776305e-51 Double H and LOOP opt_iter = 13 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 24.4140625 step_error = 6.746192341692542e-19 est_needed_step_err = 6.746192341692542e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.051208448329741e-44 estimated_step_error = 8.051208448329741e-44 Double H and LOOP opt_iter = 14 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 12.20703125 step_error = 9.540556703999103e-19 est_needed_step_err = 9.540556703999103e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.304345214403527e-36 estimated_step_error = 5.304345214403527e-36 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06106 Order of pole (three term test) = 0.9859 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Desired digits = 16 Estimated correct digits = -16 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.112211528922896 y[1] (closed_form) = 0 y[1] (numeric) = 0.005986330755261182 absolute error = 0.005986330755261182 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1244230578457921 y[1] (closed_form) = 0 y[1] (numeric) = 0.01210206389115059 absolute error = 0.01210206389115059 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1305288223072401 y[1] (closed_form) = 0 y[1] (numeric) = 0.01522258671886632 absolute error = 0.01522258671886632 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1427403512301362 y[1] (closed_form) = 0 y[1] (numeric) = 0.02158167232923096 absolute error = 0.02158167232923096 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1549518801530322 y[1] (closed_form) = 0 y[1] (numeric) = 0.02808976883572647 absolute error = 0.02808976883572647 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1610576446144803 y[1] (closed_form) = 0 y[1] (numeric) = 0.03139690406986431 absolute error = 0.03139690406986431 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1732691735373763 y[1] (closed_form) = 0 y[1] (numeric) = 0.03811244261055112 absolute error = 0.03811244261055112 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1854807024602724 y[1] (closed_form) = 0 y[1] (numeric) = 0.04495720968034473 absolute error = 0.04495720968034473 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1915864669217204 y[1] (closed_form) = 0 y[1] (numeric) = 0.04842608438771286 absolute error = 0.04842608438771286 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.006105764461448019 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( sin ( x ) , ( 0.2 * x + 0.3 ) ) ; Iterations = 17 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 109.9 %