##############ECHO OF PROBLEM################# ##############temp/tan_sqrtpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.4); x_end=c(2.1); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.0001); 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(tan(sqrt(c(2.0)*c(x) + c(1.0)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = -2.514161640922489 y[1] (numeric) = -2.514161640922489 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 1.633 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.628 Order of pole (three term test) = 0.8935 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = -2.185039863261519 y[1] (numeric) = -2.164735124264809 absolute error = 0.02030473899670948 relative error = 0.9292617191157985 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.05 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 1.765 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.759 Order of pole (three term test) = 0.885 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = -1.927432721977541 y[1] (numeric) = -1.893622868416678 absolute error = 0.03380985356086352 relative error = 1.754139232739325 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.05 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 1.893 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.886 Order of pole (three term test) = 0.8747 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = -1.719231938441568 y[1] (numeric) = -1.676003702992762 absolute error = 0.04322823544880605 relative error = 2.5143922982254 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 h = 0.05 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.017 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.009 Order of pole (three term test) = 0.8625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = -1.546607549764017 y[1] (numeric) = -1.49656180456513 absolute error = 0.05004574519888694 relative error = 3.235839965123859 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.05 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.139 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.129 Order of pole (three term test) = 0.8481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = -1.400460625296089 y[1] (numeric) = -1.345329897481301 absolute error = 0.05513072781478856 relative error = 3.936613912521294 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.05 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.258 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.247 Order of pole (three term test) = 0.8317 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = -1.274556458827018 y[1] (numeric) = -1.215538693837359 absolute error = 0.05901776498965949 relative error = 4.6304551344845 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 3 h = 0.05 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 Radius of convergence (ratio test) for eq 1 = 2.375 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.362 Order of pole (three term test) = 0.8134 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 14 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 107.1 %