##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostode.ode################# diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.9; x_end=-1.8; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.000005; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; 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=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 1.05409255338946e-14 est_needed_step_err = 1.05409255338946e-14 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-09 range = 0.09999999999999987 estimated_steps = 99999.99999999987 step_error = 2.097617814287357e-13 est_needed_step_err = 2.097617814287357e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.689350542413945e-138 estimated_step_error = 4.689350542413945e-138 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-09 range = 0.09999999999999987 estimated_steps = 49999.99999999993 step_error = 2.966479561640588e-13 est_needed_step_err = 2.966479561640588e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.146955635139175e-130 estimated_step_error = 3.146955635139175e-130 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 min_size = 19.89974986107638 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 19.89974986107638 desired_abs_gbl_error = 1.989974986107638e-09 range = 0.09999999999999987 estimated_steps = 24999.99999999997 step_error = 4.195235628574713e-13 est_needed_step_err = 4.195235628574713e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.111867061153189e-122 estimated_step_error = 2.111867061153189e-122 Double H and LOOP opt_iter = 4 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0623 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = -19.89974986107638 y[1] (numeric) = -19.89974986107638 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 5e-06 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09968 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.889999999999934 y[1] (analytic) = -19.88969731508798 y[1] (numeric) = -19.88969731634023 absolute error = 1.252246306648885e-09 relative error = 6.295954567890549e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 5e-06 Radius of convergence (given) for eq 1 = 0.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1096 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.879999999999869 y[1] (analytic) = -19.87963975992785 y[1] (numeric) = -19.87963976243245 absolute error = 2.504595641994456e-09 relative error = 1.259879792712876e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1196 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.869999999999803 y[1] (analytic) = -19.86957719476172 y[1] (numeric) = -19.86957719851897 absolute error = 3.757243405289046e-09 relative error = 1.89095287154856e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1296 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.859999999999738 y[1] (analytic) = -19.85950961875521 y[1] (numeric) = -19.85950962376536 absolute error = 5.010150516682188e-09 relative error = 2.522796691792747e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1395 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.849999999999672 y[1] (analytic) = -19.84943703107385 y[1] (numeric) = -19.84943703733709 absolute error = 6.263245921900307e-09 relative error = 3.155377108224952e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.839999999999607 y[1] (analytic) = -19.8393594308831 y[1] (numeric) = -19.83935943839968 absolute error = 7.516579358934905e-09 relative error = 3.788720792685554e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1595 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.829999999999541 y[1] (analytic) = -19.82927681734835 y[1] (numeric) = -19.82927682611842 absolute error = 8.770072668085049e-09 relative error = 4.422789973062577e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1695 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.819999999999476 y[1] (analytic) = -19.81918918963488 y[1] (numeric) = -19.81918919965867 absolute error = 1.002379335091064e-08 relative error = 5.057620296673349e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1794 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.80999999999941 y[1] (analytic) = -19.80909654690789 y[1] (numeric) = -19.80909655818562 absolute error = 1.127773430198431e-08 relative error = 5.69320982169917e-08 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 10 h = 5e-06 Radius of convergence (given) for eq 1 = 0.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1894 Order of pole (three term test) = 1.637 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 20000 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 9 Minutes 59.0 Seconds Percent Done = 100 %