##############ECHO OF PROBLEM################# ##############temp/expt_sin_sin_newpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 2.0 * x + 3.0 ), sin ( x + 1.0 ) ) * ( ( cos ( x + 1.0 ) * ln ( sin ( 2.0 * x + 3.0 ) )) + ( ( 2.0 * sin ( x + 1.0 ) * cos ( 2.0 * x + 3.0 ) ) / sin( 2.0 * x + 3.0 ) ) ); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.8; x_end=1.81; 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(2.0*x+3.0),sin(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 = 0.01000000000000001 estimated_steps = 10.00000000000001 step_error = 9.999999999999991e-12 est_needed_step_err = 9.999999999999991e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.143101718135028e-59 max_value3 = 1.143101718135028e-59 value3 = 1.143101718135028e-59 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0.6766027626496453 y[1] (numeric) = 0.6766027626496453 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.801 y[1] (analytic) = 0.6787237979586986 y[1] (numeric) = 0.6787201504758374 absolute error = 3.647482861190987e-06 relative error = 0.0005374031192306803 % Correct digits = 5 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.802 y[1] (analytic) = 0.6808347093191602 y[1] (numeric) = 0.6808274700688374 absolute error = 7.239250322865765e-06 relative error = 0.001063290432138084 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.803 y[1] (analytic) = 0.6829355457266133 y[1] (numeric) = 0.6829247695960937 absolute error = 1.077613051958526e-05 relative error = 0.001577913257995662 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.804 y[1] (analytic) = 0.6850263555271954 y[1] (numeric) = 0.6850120965906888 absolute error = 1.425893650652821e-05 relative error = 0.002081516483486909 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.804999999999999 y[1] (analytic) = 0.687107186433478 y[1] (numeric) = 0.6870894979668289 absolute error = 1.768846664906842e-05 relative error = 0.002574338763779023 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.805999999999999 y[1] (analytic) = 0.6891780855398592 y[1] (numeric) = 0.68915702003489 absolute error = 2.106550496916437e-05 relative error = 0.003056612711743869 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.806999999999999 y[1] (analytic) = 0.6912390993375453 y[1] (numeric) = 0.6912147085160344 absolute error = 2.439082151095562e-05 relative error = 0.003528565084690777 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.807999999999999 y[1] (analytic) = 0.6932902737290785 y[1] (numeric) = 0.6932626085564124 absolute error = 2.766517266605817e-05 relative error = 0.003990416960164808 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.808999999999999 y[1] (analytic) = 0.6953316540424799 y[1] (numeric) = 0.695300764740963 absolute error = 3.088930151684544e-05 relative error = 0.004442383909500303 % Correct digits = 4 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.809999999999999 y[1] (analytic) = 0.6973632850449677 y[1] (numeric) = 0.6973292211068264 absolute error = 3.406393814131548e-05 relative error = 0.004884676161165977 % Correct digits = 4 h = 0.001 NO POLE for equation 1 Finished! diff ( y , x , 1 ) = expt ( sin ( 2.0 * x + 3.0 ), sin ( x + 1.0 ) ) * ( ( cos ( x + 1.0 ) * ln ( sin ( 2.0 * x + 3.0 ) )) + ( ( 2.0 * sin ( x + 1.0 ) * cos ( 2.0 * x + 3.0 ) ) / sin( 2.0 * x + 3.0 ) ) ); Iterations = 11 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 120 %