##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.0; x_end = 5.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); array_y2_init[4 + 1] = exact_soln_y2pppp(x_start); glob_h = 0.00001; glob_look_poles = true; glob_max_iter = 20; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; glob_max_minutes = 1; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(x)); } double exact_soln_y2pppp (double x) { return( sin(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1e-05 y2[1] (analytic) = 1.00001 y2[1] (numeric) = 1.00001 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 1.99999999995 y1[1] (numeric) = 1.99999999995 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 2e-05 y2[1] (analytic) = 1.000019999999999 y2[1] (numeric) = 1.000019999999999 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 1.9999999998 y1[1] (numeric) = 1.9999999998 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3e-05 y2[1] (analytic) = 1.000029999999996 y2[1] (numeric) = 1.000029999999995 absolute error = 2.220446049250313e-16 relative error = 2.220379437867187e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999999955 y1[1] (numeric) = 1.99999999955 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 4e-05 y2[1] (analytic) = 1.000039999999989 y2[1] (numeric) = 1.000039999999989 absolute error = 2.220446049250313e-16 relative error = 2.220357234960938e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999992 y1[1] (numeric) = 1.9999999992 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 5e-05 y2[1] (analytic) = 1.000049999999979 y2[1] (numeric) = 1.000049999999979 absolute error = 2.220446049250313e-16 relative error = 2.220335032498734e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999999875 y1[1] (numeric) = 1.99999999875 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 6e-05 y2[1] (analytic) = 1.000059999999964 y2[1] (numeric) = 1.000059999999964 absolute error = 2.220446049250313e-16 relative error = 2.220312830480564e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999982 y1[1] (numeric) = 1.9999999982 absolute error = 2.220446049250313e-16 relative error = 1.110223025624357e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 7.000000000000001e-05 y2[1] (analytic) = 1.000069999999943 y2[1] (numeric) = 1.000069999999943 absolute error = 2.220446049250313e-16 relative error = 2.220290628906417e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999999755 y1[1] (numeric) = 1.99999999755 absolute error = 2.220446049250313e-16 relative error = 1.11022302598518e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 8.000000000000001e-05 y2[1] (analytic) = 1.000079999999915 y2[1] (numeric) = 1.000079999999914 absolute error = 2.220446049250313e-16 relative error = 2.220268427776281e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999968 y1[1] (numeric) = 1.9999999968 absolute error = 2.220446049250313e-16 relative error = 1.110223026401513e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 9.000000000000001e-05 y2[1] (analytic) = 1.000089999999878 y2[1] (numeric) = 1.000089999999878 absolute error = 2.220446049250313e-16 relative error = 2.220246227090145e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999999595 y1[1] (numeric) = 1.99999999595 absolute error = 4.440892098500626e-16 relative error = 2.220446053746716e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0001 y2[1] (analytic) = 1.000099999999833 y2[1] (numeric) = 1.000099999999833 absolute error = 2.220446049250313e-16 relative error = 2.220224026847999e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.999999995 y1[1] (numeric) = 1.999999995 absolute error = 4.440892098500626e-16 relative error = 2.220446054801428e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00011 y2[1] (analytic) = 1.000109999999778 y2[1] (numeric) = 1.000109999999778 absolute error = 4.440892098500626e-16 relative error = 4.44040365409966e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999999395 y1[1] (numeric) = 1.999999993949999 absolute error = 4.440892098500626e-16 relative error = 2.220446055967162e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00012 y2[1] (analytic) = 1.000119999999712 y2[1] (numeric) = 1.000119999999712 absolute error = 2.220446049250313e-16 relative error = 2.220179627695629e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999928 y1[1] (numeric) = 1.999999992799999 absolute error = 6.661338147750939e-16 relative error = 3.330669085865878e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00013 y2[1] (analytic) = 1.000129999999634 y2[1] (numeric) = 1.000129999999634 absolute error = 2.220446049250313e-16 relative error = 2.220157428785384e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999999155 y1[1] (numeric) = 1.999999991549999 absolute error = 6.661338147750939e-16 relative error = 3.330669087947547e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00014 y2[1] (analytic) = 1.000139999999543 y2[1] (numeric) = 1.000139999999542 absolute error = 2.220446049250313e-16 relative error = 2.220135230319084e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999902 y1[1] (numeric) = 1.999999990199999 absolute error = 6.661338147750939e-16 relative error = 3.330669090195748e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00015 y2[1] (analytic) = 1.000149999999437 y2[1] (numeric) = 1.000149999999437 absolute error = 2.220446049250313e-16 relative error = 2.220113032296718e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999998875 y1[1] (numeric) = 1.99999998875 absolute error = 4.440892098500626e-16 relative error = 2.220446061740322e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00016 y2[1] (analytic) = 1.000159999999317 y2[1] (numeric) = 1.000159999999317 absolute error = 2.220446049250313e-16 relative error = 2.220090834718274e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999872 y1[1] (numeric) = 1.9999999872 absolute error = 4.440892098500626e-16 relative error = 2.220446063461168e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00017 y2[1] (analytic) = 1.000169999999181 y2[1] (numeric) = 1.000169999999181 absolute error = 2.220446049250313e-16 relative error = 2.220068637583742e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999998555 y1[1] (numeric) = 1.99999998555 absolute error = 4.440892098500626e-16 relative error = 2.220446065293036e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00018 y2[1] (analytic) = 1.000179999999028 y2[1] (numeric) = 1.000179999999028 absolute error = 2.220446049250313e-16 relative error = 2.22004644089311e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999838 y1[1] (numeric) = 1.9999999838 absolute error = 2.220446049250313e-16 relative error = 1.110223033617963e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00019 y2[1] (analytic) = 1.000189999998857 y2[1] (numeric) = 1.000189999998857 absolute error = 2.220446049250313e-16 relative error = 2.220024244646368e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999998195 y1[1] (numeric) = 1.99999998195 absolute error = 2.220446049250313e-16 relative error = 1.110223034644919e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0002 y2[1] (analytic) = 1.000199999998667 y2[1] (numeric) = 1.000199999998666 absolute error = 2.220446049250313e-16 relative error = 2.220002048843505e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999998 y1[1] (numeric) = 1.99999998 absolute error = 2.220446049250313e-16 relative error = 1.110223035727387e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00021 y2[1] (analytic) = 1.000209999998456 y2[1] (numeric) = 1.000209999998456 absolute error = 2.220446049250313e-16 relative error = 2.219979853484508e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999997795 y1[1] (numeric) = 1.99999997795 absolute error = 2.220446049250313e-16 relative error = 1.110223036865365e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00022 y2[1] (analytic) = 1.000219999998225 y2[1] (numeric) = 1.000219999998225 absolute error = 2.220446049250313e-16 relative error = 2.219957658569368e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999758 y1[1] (numeric) = 1.9999999758 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00023 y2[1] (analytic) = 1.000229999997972 y2[1] (numeric) = 1.000229999997972 absolute error = 2.220446049250313e-16 relative error = 2.219935464098072e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.99999997355 y1[1] (numeric) = 1.99999997355 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00024 y2[1] (analytic) = 1.000239999997696 y2[1] (numeric) = 1.000239999997696 absolute error = 2.220446049250313e-16 relative error = 2.219913270070611e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 1.9999999712 y1[1] (numeric) = 1.9999999712 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 24 Total Elapsed Time = 1 Minutes 3 Seconds Elapsed Time(since restart) = 1 Minutes 2 Seconds Expected Time Remaining = 14 Days 13 Hours 58 Minutes 57 Seconds Optimized Time Remaining = 14 Days 8 Hours 25 Minutes 38 Seconds Time to Timeout Unknown Percent Done = 0.005 %