##############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=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_max_iter=100000000; glob_max_h=0.00001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=10.0; glob_subiter_method=3; /* 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 = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.1 estimated_steps = 100000 step_error = 9.999999999999999e-16 est_needed_step_err = 9.999999999999999e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.321627682506412e-167 estimated_step_error = 9.321627682506412e-167 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.255636641280291e-159 estimated_step_error = 6.255636641280291e-159 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.198084266310498e-151 estimated_step_error = 4.198084266310498e-151 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.817283413329734e-143 estimated_step_error = 2.817283413329734e-143 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.890642535567966e-135 estimated_step_error = 1.890642535567966e-135 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.05350569829701002 y[1] (numeric) = 0.05350569829701002 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 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) = 1.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1100099999999961 y[1] (analytic) = 0.05450220365181602 y[1] (numeric) = 0.05450220365180445 absolute error = 1.156713613781335e-14 relative error = 2.12232448649403e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 1.101 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1200099999999922 y[1] (analytic) = 0.05550972750817018 y[1] (numeric) = 0.05550972750814715 absolute error = 2.303018886706809e-14 relative error = 4.148856407857236e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 1.102 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1300099999999953 y[1] (analytic) = 0.05652932327278937 y[1] (numeric) = 0.05652932327275394 absolute error = 3.54230533794464e-14 relative error = 6.266314777643454e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 1.103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1400000000000053 y[1] (analytic) = 0.05756001681781853 y[1] (numeric) = 0.05756001681777024 absolute error = 4.82877626772904e-14 relative error = 8.389115456676211e-11 % Correct digits = 13 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 1.105 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500000000000153 y[1] (analytic) = 0.05860393503320926 y[1] (numeric) = 0.05860393503314795 absolute error = 6.131900542882818e-14 relative error = 1.046329148274435e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 1.106 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1600000000000253 y[1] (analytic) = 0.05966011556928974 y[1] (numeric) = 0.05966011556921542 absolute error = 7.431555371084642e-14 relative error = 1.245648839290895e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 1.107 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1700000000000353 y[1] (analytic) = 0.06072862152708713 y[1] (numeric) = 0.06072862152699988 absolute error = 8.724965194772949e-14 relative error = 1.436713855077593e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 1.108 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1800000000000453 y[1] (analytic) = 0.06180951581042249 y[1] (numeric) = 0.06180951581032218 absolute error = 1.003086502748829e-13 relative error = 1.62286743326937e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 1.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000000553 y[1] (analytic) = 0.0629028611249034 y[1] (numeric) = 0.06290286112479027 absolute error = 1.131317262093035e-13 relative error = 1.79851479227094e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.69 Order of pole (three term test) = 1.111 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; Iterations = 10000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 100 %