##############ECHO OF PROBLEM################# ##############temp/div_c_linpostode.ode################# diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(2.5); x_end=c(3.1); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* 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(10.0) * ln(c(0.2) * c(x) + c(0.3))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = -2.231435513142097 y[1] (numeric) = -2.231435513142097 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 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] = 2.6 y[1] (closed_form) = -1.984509387238385 y[1] (numeric) = -1.984509387226252 absolute error = 1.213207312389386e-11 relative error = 6.113386614299005e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 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] = 2.699999999999999 y[1] (closed_form) = -1.743533871447779 y[1] (numeric) = -1.743533871425176 absolute error = 2.260280851373864e-11 relative error = 1.296379088693581e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 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] = 2.799999999999999 y[1] (closed_form) = -1.508228897345838 y[1] (numeric) = -1.508228897314164 absolute error = 3.167421880334587e-11 relative error = 2.100093617028938e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 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] = 2.899999999999999 y[1] (closed_form) = -1.278333715098853 y[1] (numeric) = -1.278333715059291 absolute error = 3.956168725949283e-11 relative error = 3.094785562816322e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 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] = 2.999999999999998 y[1] (closed_form) = -1.053605156578266 y[1] (numeric) = -1.053605156531829 absolute error = 4.64370764063915e-11 relative error = 4.407445817482761e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 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] = 3.099999999999998 y[1] (closed_form) = -0.8338160893905138 y[1] (numeric) = -0.8338160893380627 absolute error = 5.245104350848351e-11 relative error = 6.290481099593931e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 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 ) = 2.0 / ( 0.2 * x + 0.3 ) ; Iterations = 13 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 116.7 %