##############ECHO OF PROBLEM################# ##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode################# diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02); ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.1; x_end = 5.0 ; 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((sin(0.1) + cos(0.05) - tan(0.02)) * x) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.1078581009948392 y[1] (numeric) = 0.1078581009948392 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) = 0.2157162019896785 y[1] (numeric) = 0.2157162019896785 absolute error = 2.775557561562891e-17 relative error = 1.286670883300502e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.3235743029845178 y[1] (numeric) = 0.3235743029845174 absolute error = 3.885780586188048e-16 relative error = 1.200892824413802e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.4314324039793571 y[1] (numeric) = 0.4314324039793561 absolute error = 9.992007221626409e-16 relative error = 2.316007589940903e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.5392905049741964 y[1] (numeric) = 0.5392905049741953 absolute error = 1.110223024625157e-15 relative error = 2.058673413280803e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.6471486059690357 y[1] (numeric) = 0.6471486059690351 absolute error = 5.551115123125783e-16 relative error = 8.57780588867001e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.7550067069638751 y[1] (numeric) = 0.755006706963875 absolute error = 1.110223024625157e-16 relative error = 1.470481009486287e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.8628648079587143 y[1] (numeric) = 0.8628648079587148 absolute error = 4.440892098500626e-16 relative error = 5.146683533202006e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.9707229089535536 y[1] (numeric) = 0.9707229089535546 absolute error = 9.992007221626409e-16 relative error = 1.029336706640401e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 1.078581009948393 y[1] (numeric) = 1.078581009948393 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 1.191832015992972 y[1] (numeric) = 1.191832015992972 absolute error = 6.661338147750939e-16 relative error = 5.589158588092688e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.299690116987809 y[1] (numeric) = 1.29969011698781 absolute error = 1.332267629550188e-15 relative error = 1.025065599973847e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.407548217982646 y[1] (numeric) = 1.407548217982648 absolute error = 1.998401444325282e-15 relative error = 1.419774767779871e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.515406318977482 y[1] (numeric) = 1.515406318977485 absolute error = 2.886579864025407e-15 relative error = 1.904822375277623e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.623264419972319 y[1] (numeric) = 1.623264419972323 absolute error = 3.552713678800501e-15 relative error = 2.188622897840072e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 1.731122520967156 y[1] (numeric) = 1.73112252096716 absolute error = 4.218847493575595e-15 relative error = 2.437058869304397e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 1.838980621961993 y[1] (numeric) = 1.838980621961998 absolute error = 4.884981308350689e-15 relative error = 2.656352791330092e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.94683872295683 y[1] (numeric) = 1.946838722956836 absolute error = 5.551115123125783e-15 relative error = 2.851348217840475e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 2.054696823951667 y[1] (numeric) = 2.054696823951673 absolute error = 6.661338147750939e-15 relative error = 3.242005375245392e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 2.162554924946504 y[1] (numeric) = 2.162554924946511 absolute error = 7.105427357601002e-15 relative error = 3.28566330299184e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 2.270413025941341 y[1] (numeric) = 2.270413025941349 absolute error = 7.549516567451064e-15 relative error = 3.325173209099671e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 2.378271126936178 y[1] (numeric) = 2.378271126936186 absolute error = 8.43769498715119e-15 relative error = 3.547827197490768e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 2.486129227931015 y[1] (numeric) = 2.486129227931024 absolute error = 8.881784197001252e-15 relative error = 3.572535207428768e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 2.593987328925852 y[1] (numeric) = 2.593987328925861 absolute error = 9.769962616701378e-15 relative error = 3.766387949453492e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.701845429920688 y[1] (numeric) = 2.701845429920699 absolute error = 1.06581410364015e-14 relative error = 3.944763426645901e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.809703530915526 y[1] (numeric) = 2.809703530915537 absolute error = 1.110223024625157e-14 relative error = 3.951388509176257e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 2.917561631910362 y[1] (numeric) = 2.917561631910374 absolute error = 1.199040866595169e-14 relative error = 4.109736203961733e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 3.025419732905199 y[1] (numeric) = 3.025419732905212 absolute error = 1.243449787580175e-14 relative error = 4.110007527405581e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 3.133277833900036 y[1] (numeric) = 3.13327783390005 absolute error = 1.332267629550188e-14 relative error = 4.251993280442338e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 3.241135934894873 y[1] (numeric) = 3.241135934894887 absolute error = 1.376676550535194e-14 relative error = 4.247512533225012e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 3.34899403588971 y[1] (numeric) = 3.348994035889725 absolute error = 1.465494392505207e-14 relative error = 4.375924163495491e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 3.456852136884547 y[1] (numeric) = 3.456852136884562 absolute error = 1.554312234475219e-14 relative error = 4.496322587508841e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 3.564710237879384 y[1] (numeric) = 3.5647102378794 absolute error = 1.598721155460225e-14 relative error = 4.484855847389411e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 3.672568338874221 y[1] (numeric) = 3.672568338874238 absolute error = 1.687538997430238e-14 relative error = 4.594983242565151e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 3.780426439869058 y[1] (numeric) = 3.780426439869075 absolute error = 1.731947918415244e-14 relative error = 4.581355955375323e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 3.888284540863895 y[1] (numeric) = 3.888284540863913 absolute error = 1.820765760385257e-14 relative error = 4.682696806907863e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 3.996142641858731 y[1] (numeric) = 3.99614264185875 absolute error = 1.909583602355269e-14 relative error = 4.778567167129605e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 4.104000742853568 y[1] (numeric) = 4.104000742853597 absolute error = 2.842170943040401e-14 relative error = 6.925366541391511e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 4.211858843848406 y[1] (numeric) = 4.211858843848443 absolute error = 3.730349362740526e-14 relative error = 8.85677678440923e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 4.319716944843242 y[1] (numeric) = 4.319716944843289 absolute error = 4.707345624410664e-14 relative error = 1.089734740613077e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 4.427575045838079 y[1] (numeric) = 4.427575045838136 absolute error = 5.684341886080801e-14 relative error = 1.28384992399487e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 4.535433146832916 y[1] (numeric) = 4.535433146832982 absolute error = 6.661338147750939e-14 relative error = 1.468732518392987e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 4.643291247827753 y[1] (numeric) = 4.643291247827829 absolute error = 7.549516567451064e-14 relative error = 1.625897701545841e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 4.75114934882259 y[1] (numeric) = 4.751149348822675 absolute error = 8.526512829121202e-14 relative error = 1.794621091259572e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 4.859007449817427 y[1] (numeric) = 4.859007449817522 absolute error = 9.50350909079134e-14 relative error = 1.955853986424414e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 4.966865550812264 y[1] (numeric) = 4.966865550812368 absolute error = 1.048050535246148e-13 relative error = 2.110084367141272e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 5.0747236518071 y[1] (numeric) = 5.074723651807215 absolute error = 1.145750161413162e-13 relative error = 2.257758727423831e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 5.182581752801938 y[1] (numeric) = 5.182581752802061 absolute error = 1.234568003383174e-13 relative error = 2.38214863222507e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 5.290439853796775 y[1] (numeric) = 5.290439853796908 absolute error = 1.332267629550188e-13 relative error = 2.518254939793074e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 5.398297954791611 y[1] (numeric) = 5.398297954791754 absolute error = 1.429967255717202e-13 relative error = 2.648922433871848e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02); Iterations = 981 Total Elapsed Time = 19 Seconds Elapsed Time(since restart) = 19 Seconds Time to Timeout = 9 Minutes 41 Seconds Percent Done = 100.2 %