##############ECHO OF PROBLEM################# ##############temp/expt_sin_lin_new_sm_hpostode.ode################# diff ( y , x , 1 ) = ( expt ( sin ( x ) , ( 2.0 * x + 1.0 ) ) ) * ( ( 2.0 * ln ( sin ( x ) ) ) + ( ( ( 2.0 * x + 1.0 ) * cos ( x ) ) / sin ( x ) ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=0.11; 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=0.01; 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(sin(x),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 = 10 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 9999.999999999996 step_error = 1e-14 est_needed_step_err = 1e-14 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.74672146888602e-133 estimated_step_error = 3.74672146888602e-133 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 = 2.96195027342505e-126 estimated_step_error = 2.96195027342505e-126 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 = 1.987712430655581e-118 estimated_step_error = 1.987712430655581e-118 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 = 1.333906066575596e-110 estimated_step_error = 1.333906066575596e-110 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 = 8.95135433829818e-103 estimated_step_error = 8.95135433829818e-103 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.06296962708006738 y[1] (numeric) = 0.06296962708006738 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1134 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1178 Order of pole (six term test) = -0.8546 Finished! diff ( y , x , 1 ) = ( expt ( sin ( x ) , ( 2.0 * x + 1.0 ) ) ) * ( ( 2.0 * ln ( sin ( x ) ) ) + ( ( ( 2.0 * x + 1.0 ) * cos ( x ) ) / sin ( x ) ) ) ; Iterations = 1001 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.2 %