##############ECHO OF PROBLEM################# ##############temp/expt_lin_lin_newpostode.ode################# diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_max_h=0.00001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(expt(2.0*x+1.0,3.0*x+2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 900000.0000000001 step_error = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.059527025082972e-152 estimated_step_error = 1.059527025082972e-152 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.473230175068735e-142 estimated_step_error = 1.473230175068735e-142 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.886657497008344e-135 estimated_step_error = 9.886657497008344e-135 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.634792866711539e-127 estimated_step_error = 6.634792866711539e-127 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.452492961488418e-119 estimated_step_error = 4.452492961488418e-119 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.520956754552532 y[1] (numeric) = 1.520956754552532 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 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] = 0.2000000000000653 y[1] (analytic) = 2.39846227969988 y[1] (numeric) = 2.398462280465438 absolute error = 7.655582834331653e-10 relative error = 3.19187126648896e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 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] = 0.3000000000001653 y[1] (analytic) = 3.907940562245493 y[1] (numeric) = 3.907940563009538 absolute error = 7.640448274059963e-10 relative error = 1.955108618558359e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 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] = 0.4000000000002653 y[1] (analytic) = 6.559519331853952 y[1] (numeric) = 6.559519332615331 absolute error = 7.613785157900566e-10 relative error = 1.160723030562156e-08 % Correct digits = 10 h = 1e-05 NO INFO (given) for Equation 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] = 0.5000000000003653 y[1] (analytic) = 11.31370849900782 y[1] (numeric) = 11.31370849976446 absolute error = 7.566445248130549e-10 relative error = 6.68785593052367e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 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] = 0.6000099999999101 y[1] (analytic) = 20.00928005473505 y[1] (numeric) = 20.0092800555313 absolute error = 7.962519532611623e-10 relative error = 3.979413307640397e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 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] = 0.700009999999455 y[1] (analytic) = 36.21532073365865 y[1] (numeric) = 36.21532073452863 absolute error = 8.699814202373091e-10 relative error = 2.402246901623448e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 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] = 0.8000099999989999 y[1] (analytic) = 66.9745616019439 y[1] (numeric) = 66.97456160295363 absolute error = 1.009723860079248e-09 relative error = 1.507622948068601e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.722 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000099999985448 y[1] (analytic) = 126.3777857788888 y[1] (numeric) = 126.377785780169 absolute error = 1.280227479583118e-09 relative error = 1.013016228835509e-09 % Correct digits = 11 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.834 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ; Iterations = 90001 Total Elapsed Time = 3.0 Seconds Elapsed Time(since restart) = 3.0 Seconds Time to Timeout = 2 Minutes 57.0 Seconds Percent Done = 100 %