##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.1); x_end=c(2.0); 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(ln(cosh(c(3.0)*c(x) + c(1.0)))/c(3.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 1.20234563609611 y[1] (numeric) = 1.20234563609611 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 Radius of convergence (six term test) for eq 1 = 1.522 Order of pole (six term test) = -0.08352 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.302317951245919 y[1] (numeric) = 1.302317951245919 absolute error = 2.220446049250313e-16 relative error = 1.704995348582908e-14 % Desired digits = 8 Estimated correct digits = 13 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 Radius of convergence (six term test) for eq 1 = 1.616 Order of pole (six term test) = -0.06497 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 1.402302756500702 y[1] (numeric) = 1.402302756500702 absolute error = 2.220446049250313e-16 relative error = 1.583428427960309e-14 % Desired digits = 8 Estimated correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 1.502294417153335 y[1] (numeric) = 1.502294417153335 absolute error = 2.220446049250313e-16 relative error = 1.478036544566136e-14 % Desired digits = 8 Estimated correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 1.602289840333792 y[1] (numeric) = 1.602289840333792 absolute error = 2.220446049250313e-16 relative error = 1.38579549926357e-14 % Desired digits = 8 Estimated correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (closed_form) = 1.702287328495261 y[1] (numeric) = 1.702287328495261 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 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 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (closed_form) = 1.802285949961004 y[1] (numeric) = 1.802285949961003 absolute error = 2.220446049250313e-16 relative error = 1.232016511751843e-14 % Desired digits = 8 Estimated correct digits = 13 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 Radius of convergence (six term test) for eq 1 = 2.445 Order of pole (six term test) = 5.341 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (closed_form) = 1.902285193402939 y[1] (numeric) = 1.902285193402939 absolute error = 4.440892098500626e-16 relative error = 2.334503845112967e-14 % Desired digits = 8 Estimated correct digits = 13 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 Radius of convergence (six term test) for eq 1 = 2.585 Order of pole (six term test) = 6.022 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (closed_form) = 2.002284778194341 y[1] (numeric) = 2.00228477819434 absolute error = 1.332267629550188e-15 relative error = 6.653736991156802e-14 % Desired digits = 8 Estimated correct digits = 13 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 Finished! diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ; Iterations = 18 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 105.6 %