##############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=0.001; 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 = 999.9999999999994 step_error = 1.000000000000001e-13 est_needed_step_err = 1.000000000000001e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 3.746559098987943e-107 max_value3 = 3.746559098987943e-107 value3 = 3.746559098987943e-107 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 POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1010099999999996 y[1] (analytic) = 0.06343632922612004 y[1] (numeric) = 0.06343632922614797 absolute error = 2.79359868571305e-14 relative error = 4.403783635959156e-11 % Correct digits = 12 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1020099999999992 y[1] (analytic) = 0.06389676059307803 y[1] (numeric) = 0.06389676059313391 absolute error = 5.588585150206882e-14 relative error = 8.74627304785823e-11 % Correct digits = 12 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1030099999999988 y[1] (analytic) = 0.06435557604347533 y[1] (numeric) = 0.06435557604355906 absolute error = 8.372469384454462e-14 relative error = 1.300970312005047e-10 % Correct digits = 11 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1040099999999985 y[1] (analytic) = 0.06481280091834679 y[1] (numeric) = 0.06481280091845838 absolute error = 1.11591291762636e-13 relative error = 1.721747713128804e-10 % Correct digits = 11 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1050099999999981 y[1] (analytic) = 0.06526846015568059 y[1] (numeric) = 0.06526846015581995 absolute error = 1.393607451660728e-13 relative error = 2.135192784289145e-10 % Correct digits = 11 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1060099999999977 y[1] (analytic) = 0.06572257829957534 y[1] (numeric) = 0.06572257829974243 absolute error = 1.670885652060861e-13 relative error = 2.542331258589191e-10 % Correct digits = 11 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1070099999999973 y[1] (analytic) = 0.06617517950912487 y[1] (numeric) = 0.06617517950931953 absolute error = 1.946637295802134e-13 relative error = 2.941642637378434e-10 % Correct digits = 11 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1080099999999969 y[1] (analytic) = 0.06662628756704009 y[1] (numeric) = 0.0666262875672624 absolute error = 2.223082828933798e-13 relative error = 3.336645204337564e-10 % Correct digits = 11 h = 1e-05 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.1090099999999965 y[1] (analytic) = 0.06707592588801875 y[1] (numeric) = 0.06707592588826858 absolute error = 2.498279361162759e-13 relative error = 3.724554418128437e-10 % Correct digits = 11 h = 1e-05 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 = 1001 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Time to Timeout = 2 Minutes 59 Seconds Percent Done = 100.2 %