##############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=1.4; x_end=2.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(tan(sqrt(2.0*x + 1.0))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.7000000000000002 estimated_steps = 700000.0000000002 step_error = 2.988071523335984e-21 est_needed_step_err = 2.988071523335984e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 min_size = 2.514161640922489 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 2.514161640922489 desired_abs_gbl_error = 2.514161640922489e-16 range = 0.7000000000000002 estimated_steps = 700000.0000000002 step_error = 7.512494804304158e-21 est_needed_step_err = 7.512494804304158e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.784103097827485e-224 estimated_step_error = 2.784103097827485e-224 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 min_size = 2.514161640922489 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 2.514161640922489 desired_abs_gbl_error = 2.514161640922489e-16 range = 0.7000000000000002 estimated_steps = 350000.0000000001 step_error = 1.062427203950435e-20 est_needed_step_err = 1.062427203950435e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.91322049460318e-213 estimated_step_error = 1.91322049460318e-213 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 min_size = 2.514161640922489 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 2.514161640922489 desired_abs_gbl_error = 2.514161640922489e-16 range = 0.7000000000000002 estimated_steps = 175000.0000000001 step_error = 1.502498960860832e-20 est_needed_step_err = 1.502498960860832e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.314754307285578e-202 estimated_step_error = 1.314754307285578e-202 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 min_size = 2.514161640922489 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 2.514161640922489 desired_abs_gbl_error = 2.514161640922489e-16 range = 0.7000000000000002 estimated_steps = 87500.00000000003 step_error = 2.12485440790087e-20 est_needed_step_err = 2.12485440790087e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.03491173383377e-192 estimated_step_error = 9.03491173383377e-192 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 min_size = 2.514161640922489 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 2.514161640922489 desired_abs_gbl_error = 2.514161640922489e-16 range = 0.7000000000000002 estimated_steps = 43750.00000000001 step_error = 3.004997921721663e-20 est_needed_step_err = 3.004997921721663e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.208728853338198e-181 estimated_step_error = 6.208728853338198e-181 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 min_size = 2.514161640922489 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 2.514161640922489 desired_abs_gbl_error = 2.514161640922489e-16 range = 0.7000000000000002 estimated_steps = 21875.00000000001 step_error = 4.24970881580174e-20 est_needed_step_err = 4.24970881580174e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.266585070558453e-170 estimated_step_error = 4.266585070558453e-170 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 min_size = 2.514161640922489 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 2.514161640922489 desired_abs_gbl_error = 2.514161640922489e-16 range = 0.7000000000000002 estimated_steps = 10937.5 step_error = 6.009995843443327e-20 est_needed_step_err = 6.009995843443327e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.931946197728727e-159 estimated_step_error = 2.931946197728727e-159 Double H and LOOP opt_iter = 8 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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 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 = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.0001 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 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] = 1.469999999999992 y[1] (closed_form) = -2.274947836382328 y[1] (numeric) = -2.274918702816858 absolute error = 2.913356546940804e-05 relative error = 0.001280625647915377 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 0.5 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] = 1.539999999999984 y[1] (closed_form) = -2.074898511298209 y[1] (numeric) = -2.074847639745541 absolute error = 5.087155266814136e-05 relative error = 0.002451761008605302 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 0.5 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] = 1.609999999999977 y[1] (closed_form) = -1.904666892960579 y[1] (numeric) = -1.904599386910069 absolute error = 6.750605050953595e-05 relative error = 0.003544244442901289 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 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] = 1.679999999999969 y[1] (closed_form) = -1.757667378246064 y[1] (numeric) = -1.757586870970808 absolute error = 8.050727525610313e-05 relative error = 0.004580347581829703 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 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] = 1.749999999999961 y[1] (closed_form) = -1.629125005006734 y[1] (numeric) = -1.629034152119513 absolute error = 9.085288722121554e-05 relative error = 0.005576790420747363 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 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] = 1.819999999999954 y[1] (closed_form) = -1.515492378335865 y[1] (numeric) = -1.51539316513815 absolute error = 9.921319771555304e-05 relative error = 0.006546598262968321 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 0.5 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] = 1.889999999999946 y[1] (closed_form) = -1.414078344665924 y[1] (numeric) = -1.413972284636747 absolute error = 0.000106060029176902 relative error = 0.007500293712648484 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 0.5 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] = 1.959999999999938 y[1] (closed_form) = -1.322803810219309 y[1] (numeric) = -1.322692077058504 absolute error = 0.0001117331608042615 relative error = 0.008446691787630791 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 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] = 2.029999999999997 y[1] (closed_form) = -1.240036647921339 y[1] (numeric) = -1.23992016569007 absolute error = 0.0001164822312689218 relative error = 0.009393450706814167 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 5 h = 0.0001 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 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 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 7000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %