##############ECHO OF PROBLEM################# ##############temp/sub_sin_cospostode.ode################# diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cos(c(x)) - sin(c(x))) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.8951707486311977 y[1] (numeric) = 0.8951707486311977 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.49 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.1967995120753825 y[1] (closed_form) = 0.7851657686770491 y[1] (numeric) = 0.7851657686770491 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.04779618318332043 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4618 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.3291643613931532 y[1] (closed_form) = 0.6230604302122458 y[1] (numeric) = 0.6230604302122457 absolute error = 1.110223024625157e-16 relative error = 1.781886588828886e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.04197658684543444 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3955 Order of pole (three term test) = 32.81 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.4057250938577733 y[1] (closed_form) = 0.5241313627583153 y[1] (numeric) = 0.5241313627583152 absolute error = 1.110223024625157e-16 relative error = 2.118215209985625e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.03700994166690441 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3442 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.5013218203094326 y[1] (closed_form) = 0.3963629551095028 y[1] (numeric) = 0.3963629551095028 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.02932816827335712 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.269 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.6141753882114268 y[1] (closed_form) = 0.2409641307618553 y[1] (numeric) = 0.2409641307618554 absolute error = 1.387778780781446e-16 relative error = 5.759275359339629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.01852235191762681 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1679 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.7027758388245808 y[1] (closed_form) = 0.1167127172413652 y[1] (numeric) = 0.1167127172413653 absolute error = 2.775557561562891e-17 relative error = 2.378110652520376e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009123151322957606 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08225 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.7999889786608239 y[1] (closed_form) = -0.02063379668536569 y[1] (numeric) = -0.02063379668537185 absolute error = 6.158268339717665e-15 relative error = 2.984554143680864e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001677370941755501 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01504 Order of pole (three term test) = 33.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9001280238835985 y[1] (closed_form) = -0.1618968055063672 y[1] (numeric) = -0.1618968055064141 absolute error = 4.687916721479723e-14 relative error = 2.895620272936981e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001677370941755501 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 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 17.18 %