##############ECHO OF PROBLEM################# ##############temp/expt_sin_lin_newpostode.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; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.001; 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 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.009999999999999995 estimated_steps = 9.999999999999995 step_error = 1.000000000000001e-11 est_needed_step_err = 1.000000000000001e-11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 3.728784451731742e-55 max_value3 = 3.728784451731742e-55 value3 = 3.728784451731742e-55 best_h = 0.001 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 = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = 0.06343171666528524 y[1] (numeric) = 0.06343171666528524 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 0.06389216432076887 y[1] (numeric) = 0.06389216459537395 absolute error = 2.746050747903794e-10 relative error = 4.29794604251833e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.103 y[1] (analytic) = 0.06435099580421433 y[1] (numeric) = 0.06435099635293964 absolute error = 5.487253151859051e-10 relative error = 8.527067970406904e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = 0.06480823646073421 y[1] (numeric) = 0.06480823728310636 absolute error = 8.223721564837305e-10 relative error = 1.268931545424765e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.105 y[1] (analytic) = 0.06526391123230128 y[1] (numeric) = 0.06526391232785818 absolute error = 1.095556895203131e-09 relative error = 1.678656510952264e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 0.06571804466690874 y[1] (numeric) = 0.06571804603519936 absolute error = 1.368290619696566e-09 relative error = 2.082062280811509e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = 0.06617066092745721 y[1] (numeric) = 0.06617066256804159 absolute error = 1.64058437668313e-09 relative error = 2.479322941147134e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 0.06662178380037974 y[1] (numeric) = 0.06662178571282872 absolute error = 1.912448976959524e-09 relative error = 2.87060608087264e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = 0.06707143670401347 y[1] (numeric) = 0.06707143888790863 absolute error = 2.183895161933513e-09 relative error = 3.256073329055186e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 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 = 10 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 110 %