##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=16; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.0); x_end=c(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; 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(c(2.0) - cos(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.09991670832341408 y[1] (closed_form) = 1.004987522880755 y[1] (numeric) = 1.004987522880754 absolute error = 4.440892098500626e-16 relative error = 4.418852968214964e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09925 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1997501249702424 y[1] (closed_form) = 1.019883810250799 y[1] (numeric) = 1.019883810250799 absolute error = 2.220446049250313e-16 relative error = 2.177155894556542e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2995835416170708 y[1] (closed_form) = 1.044540521856188 y[1] (numeric) = 1.044540521856188 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.282 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4044086290962407 y[1] (closed_form) = 1.08066475233142 y[1] (numeric) = 1.08066475233142 absolute error = 2.220446049250313e-16 relative error = 2.054703870427841e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3617 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5042420457430691 y[1] (closed_form) = 1.124459073091499 y[1] (numeric) = 1.124459073091499 absolute error = 2.220446049250313e-16 relative error = 1.974679294592372e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.423 Order of pole (three term test) = 32.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6040754623898975 y[1] (closed_form) = 1.176972412036779 y[1] (numeric) = 1.17697241203678 absolute error = 2.220446049250313e-16 relative error = 1.886574423106296e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4675 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7039088790367259 y[1] (closed_form) = 1.237681818448275 y[1] (numeric) = 1.237681818448275 absolute error = 2.220446049250313e-16 relative error = 1.79403625079842e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4934 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8037422956835544 y[1] (closed_form) = 1.305982721594626 y[1] (numeric) = 1.305982721594626 absolute error = 2.220446049250313e-16 relative error = 1.700210892942835e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4997 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9035757123303828 y[1] (closed_form) = 1.381194951310972 y[1] (numeric) = 1.381194951310972 absolute error = 2.220446049250313e-16 relative error = 1.607626821356941e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.004991670832341408 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4861 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) ; Iterations = 192 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.8 %