##############ECHO OF PROBLEM################# ##############temp/ln_sqrtpostode.ode################# diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(10.0); x_end=c(11.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); 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(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 10 y[1] (closed_form) = -4.906070659236272 y[1] (numeric) = -4.906070659236272 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 = 12 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 12.71 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.01 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.1 y[1] (closed_form) = -4.896746824367669 y[1] (numeric) = -4.896746752441335 absolute error = 7.192633333374943e-08 relative error = 1.468859549279179e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 12.81 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.11 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.2 y[1] (closed_form) = -4.887009761654492 y[1] (numeric) = -4.887009618982454 absolute error = 1.426720386277225e-07 relative error = 2.91941382534544e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 12.92 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.21 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.3 y[1] (closed_form) = -4.876862858286394 y[1] (numeric) = -4.876862646020448 absolute error = 2.122659461534226e-07 relative error = 4.352510052497304e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 13.02 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.31 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.40000000000001 y[1] (closed_form) = -4.866309446374936 y[1] (numeric) = -4.866309165638978 absolute error = 2.807359580359048e-07 relative error = 5.768970533615235e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 13.13 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.41 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.50000000000001 y[1] (closed_form) = -4.855352804286189 y[1] (numeric) = -4.855352456177105 absolute error = 3.48109083780912e-07 relative error = 7.169594009185278e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 13.24 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.51 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.60000000000001 y[1] (closed_form) = -4.843996157930663 y[1] (numeric) = -4.843995743519195 absolute error = 4.144114678084065e-07 relative error = 8.55515682294516e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 13.34 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.61 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.70000000000001 y[1] (closed_form) = -4.832242682012325 y[1] (numeric) = -4.832242202343887 absolute error = 4.796684374142046e-07 relative error = 9.926414482445922e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.05 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 13.45 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.71 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.80000000000001 y[1] (closed_form) = -4.820095501238233 y[1] (numeric) = -4.820094957333711 absolute error = 5.439045223099015e-07 relative error = 1.128410261104117e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 13.55 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.81 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.90000000000001 y[1] (closed_form) = -4.807557691490402 y[1] (numeric) = -4.807557084346908 absolute error = 6.07143493702722e-07 relative error = 1.262893828143537e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.05 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 13.66 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 12.91 Order of pole (three term test) = 0.911 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 20 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 105 %