##############ECHO OF PROBLEM################# ##############temp/expt_sin_cpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // 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; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(-2.5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)+0.50000000000000000000000000000000*x+0.75000000000000000000000000000000); } // 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 = 7.905694150420948e-21 est_needed_step_err = 7.905694150420948e-21 opt_iter = 1 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 min_size = 0.05350569829701002 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 = 7.905694150420948e-21 est_needed_step_err = 7.905694150420948e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.224391489014967e-229 estimated_step_error = 4.224391489014967e-229 Double H and LOOP opt_iter = 2 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 min_size = 0.05350569829701002 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 = 1.118033988749895e-20 est_needed_step_err = 1.118033988749895e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.902978870871578e-218 estimated_step_error = 2.902978870871578e-218 Double H and LOOP opt_iter = 3 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 min_size = 0.05350569829701002 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 = 1.58113883008419e-20 est_needed_step_err = 1.58113883008419e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.994910713810994e-207 estimated_step_error = 1.994910713810994e-207 Double H and LOOP opt_iter = 4 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 min_size = 0.05350569829701002 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 = 2.23606797749979e-20 est_needed_step_err = 2.23606797749979e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.370890587590276e-196 estimated_step_error = 1.370890587590276e-196 Double H and LOOP opt_iter = 5 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 min_size = 0.05350569829701002 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 = 3.162277660168379e-20 est_needed_step_err = 3.162277660168379e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.420666170094891e-186 estimated_step_error = 9.420666170094891e-186 Double H and LOOP opt_iter = 6 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 min_size = 0.05350569829701002 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 = 4.472135954999579e-20 est_needed_step_err = 4.472135954999579e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.473801966584477e-175 estimated_step_error = 6.473801966584477e-175 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 = 1.6 Order of pole (three term test) = 1.101 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.05350569829701002 y[1] (numeric) = 0.05350569829701002 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 3.2e-05 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] = 0.1100160000000013 y[1] (closed_form) = 0.05450280455948553 y[1] (numeric) = 0.05450280455936239 absolute error = 1.231376112187377e-13 relative error = 2.259289447836444e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 3.2e-05 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] = 0.1200000000000027 y[1] (closed_form) = 0.05550871396502743 y[1] (numeric) = 0.05550871396478144 absolute error = 2.459907277874152e-13 relative error = 4.431569571984653e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 3.2e-05 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] = 0.130016000000004 y[1] (closed_form) = 0.05652993866675293 y[1] (numeric) = 0.05652993866638405 absolute error = 3.688854777195161e-13 relative error = 6.525488730743475e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 3.2e-05 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] = 0.1400000000000053 y[1] (closed_form) = 0.05756001681781853 y[1] (numeric) = 0.05756001681732739 absolute error = 4.911349105185536e-13 relative error = 8.532570657041847e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 3.2e-05 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] = 0.1500160000000066 y[1] (closed_form) = 0.05860561511105222 y[1] (numeric) = 0.05860561511043841 absolute error = 6.138145547396334e-13 relative error = 1.047364750931308e-09 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 11 h = 3.2e-05 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] = 0.160000000000008 y[1] (closed_form) = 0.05966011556928796 y[1] (numeric) = 0.059660115568552 absolute error = 7.359668430240163e-13 relative error = 1.233599425682105e-09 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 11 h = 3.2e-05 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] = 0.1700160000000093 y[1] (closed_form) = 0.06073034104638664 y[1] (numeric) = 0.06073034104552828 absolute error = 8.58355053701132e-13 relative error = 1.41338750764714e-09 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 11 h = 3.2e-05 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] = 0.1800000000000106 y[1] (closed_form) = 0.06180951581041871 y[1] (numeric) = 0.06180951580943883 absolute error = 9.798828415341632e-13 relative error = 1.585326836307287e-09 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 11 h = 3.2e-05 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] = 0.190016000000012 y[1] (closed_form) = 0.06290462048760748 y[1] (numeric) = 0.06290462048650568 absolute error = 1.101799207425813e-12 relative error = 1.751539392313595e-09 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 11 h = 3.2e-05 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 ( 0.2 * x + 0.3 ) , 2.0 ) ; Iterations = 3125 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %