##############ECHO OF PROBLEM################# ##############temp/exp_sqrtpostode.ode################# diff ( y , x , 1 ) = exp(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 = 0.1; x_end = 0.5 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -17.13332216736344 y[1] (numeric) = -17.13332216736344 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = -16.9743314997657 y[1] (numeric) = -16.97433149976571 absolute error = 7.105427357601002e-15 relative error = 4.185983617498621e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -16.81363673348341 y[1] (numeric) = -16.81363673348341 absolute error = 3.552713678800501e-15 relative error = 2.112995382923595e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -16.65125767648043 y[1] (numeric) = -16.65125767648044 absolute error = 7.105427357601002e-15 relative error = 4.267201610625049e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -16.48721270700128 y[1] (numeric) = -16.48721270700129 absolute error = 1.06581410364015e-14 relative error = 6.464489314118895e-14 % Correct digits = 15 h = 0.005 Finished! diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2)); Iterations = 80 Total Elapsed Time = 3 Seconds Elapsed Time(since restart) = 3 Seconds Time to Timeout = 9 Minutes 57 Seconds Percent Done = 101.3 %