##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_lin_sm_hpostode.ode################# diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.4; x_end=-1.3; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.000005; glob_max_h=0.00000001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))); } /* 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 = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 1.05409255338946e-14 est_needed_step_err = 1.05409255338946e-14 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 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 START of Soultion TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (analytic) = 1.095055278569961 y[1] (numeric) = 1.095055278569961 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 1e-08 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 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] = -1.389999990060775 y[1] (analytic) = 1.104023547891391 y[1] (numeric) = 1.10402354799415 absolute error = 1.027589124902306e-10 relative error = 9.307673979100635e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-08 Radius of convergence (given) for eq 1 = 0.11 Order of pole (given) = 0.5 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] = -1.379999990121549 y[1] (analytic) = 1.112895434687031 y[1] (numeric) = 1.112895434891818 absolute error = 2.04786854141048e-10 relative error = 1.840126644051139e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.12 Order of pole (given) = 0.5 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] = -1.369999990182324 y[1] (analytic) = 1.121671273702925 y[1] (numeric) = 1.121671274009004 absolute error = 3.06078717926539e-10 relative error = 2.72877379587421e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.13 Order of pole (given) = 0.5 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] = -1.359999990243099 y[1] (analytic) = 1.130351390013243 y[1] (numeric) = 1.130351390419853 absolute error = 4.066103009847666e-10 relative error = 3.59720264492268e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.14 Order of pole (given) = 0.5 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] = -1.349999990303874 y[1] (analytic) = 1.138936108037783 y[1] (numeric) = 1.13893610854417 absolute error = 5.063869323862491e-10 relative error = 4.446139944221086e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.15 Order of pole (given) = 0.5 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] = -1.339999990364648 y[1] (analytic) = 1.147425751542906 y[1] (numeric) = 1.147425752148352 absolute error = 6.054454715354041e-10 relative error = 5.276554676599171e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.16 Order of pole (given) = 0.5 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] = -1.329999990425423 y[1] (analytic) = 1.155820643642473 y[1] (numeric) = 1.155820644346233 absolute error = 7.037601612580602e-10 relative error = 6.088835366707229e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.17 Order of pole (given) = 0.5 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] = -1.319999990486198 y[1] (analytic) = 1.164121106798779 y[1] (numeric) = 1.16412110760015 absolute error = 8.013703034492892e-10 relative error = 6.883908373184472e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.18 Order of pole (given) = 0.5 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] = -1.309999990546972 y[1] (analytic) = 1.172327462823496 y[1] (numeric) = 1.172327463721695 absolute error = 8.981992927203919e-10 relative error = 7.661675779198426e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-08 Radius of convergence (given) for eq 1 = 0.19 Order of pole (given) = 0.5 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 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 10000001 Total Elapsed Time = 5 Minutes 33.0 Seconds Elapsed Time(since restart) = 5 Minutes 33.0 Seconds Time to Timeout = 4 Minutes 27.0 Seconds Percent Done = 100 %