##############ECHO OF PROBLEM################# ##############temp/mult_lin_sinpostode.ode################# diff ( y , x , 1 ) = (0.2 * x + 0.3) * 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 = 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(0.2 * sin(x) - 0.2 * cos(x) * x - 0.3 * cos(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -0.2984346495596026 y[1] (numeric) = -0.2984346495596026 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) = -0.2934887703070099 y[1] (numeric) = -0.2934887703070028 absolute error = 7.105427357601002e-15 relative error = 2.421021884472181e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -0.2848170947529503 y[1] (numeric) = -0.2848170947529342 absolute error = 1.609823385706477e-14 relative error = 5.652130491334568e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -0.2721195092593662 y[1] (numeric) = -0.2721195092593396 absolute error = 2.653433028854124e-14 relative error = 9.750984176312948e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -0.2551479170353084 y[1] (numeric) = -0.2551479170352698 absolute error = 3.858025010572419e-14 relative error = 1.512073880673119e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -0.2337124635830577 y[1] (numeric) = -0.233712463583006 absolute error = 5.173639294753229e-14 relative error = 2.213677103666574e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -0.2076870249576366 y[1] (numeric) = -0.2076870249575704 absolute error = 6.61415366920437e-14 relative error = 3.184673510804783e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -0.1770138681197914 y[1] (numeric) = -0.1770138681197099 absolute error = 8.146261443187086e-14 relative error = 4.602047020222298e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -0.141707402844422 y[1] (numeric) = -0.1417074028443245 absolute error = 9.747758156208874e-14 relative error = 6.878792469939459e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -0.1018569559724903 y[1] (numeric) = -0.1018569559723761 absolute error = 1.141864380826974e-13 relative error = 1.12104703102984e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.05530620149450838 y[1] (numeric) = -0.0553062014943753 absolute error = 1.330810461830367e-13 relative error = 2.406259019546858e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.006744096164736128 y[1] (numeric) = -0.006744096164584849 absolute error = 1.512791628077714e-13 relative error = 2.243134722763705e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.04561452832879519 y[1] (numeric) = 0.04561452832896459 absolute error = 1.694061557699911e-13 relative error = 3.713864024831967e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.1013704927095471 y[1] (numeric) = 0.1013704927097344 absolute error = 1.873223798298795e-13 relative error = 1.847898484291747e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.1600521736505866 y[1] (numeric) = 0.1600521736507913 absolute error = 2.046973701652632e-13 relative error = 1.278941519483156e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.2211193620726124 y[1] (numeric) = 0.2211193620728338 absolute error = 2.214062266858718e-13 relative error = 1.001297329236891e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.2839681999299103 y[1] (numeric) = 0.2839681999301474 absolute error = 2.370326157574709e-13 relative error = 8.347153512822063e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.3479371507617143 y[1] (numeric) = 0.347937150761966 absolute error = 2.516320485312917e-13 relative error = 7.232112120835944e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.4123139449826562 y[1] (numeric) = 0.412313944982921 absolute error = 2.647326802218686e-13 relative error = 6.420657934162387e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.4763434271656858 y[1] (numeric) = 0.476343427165962 absolute error = 2.761124662242764e-13 relative error = 5.796499972030403e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.5392362196108827 y[1] (numeric) = 0.5392362196111687 absolute error = 2.859934511434403e-13 relative error = 5.303676584444115e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.6001781044629069 y[1] (numeric) = 0.6001781044632007 absolute error = 2.938760346182789e-13 relative error = 4.896480435274551e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.6583400156973593 y[1] (numeric) = 0.6583400156976591 absolute error = 2.997602166487923e-13 relative error = 4.553273528896242e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.7128885225889898 y[1] (numeric) = 0.7128885225892934 absolute error = 3.035349749325178e-13 relative error = 4.257818232648395e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.7629966779355801 y[1] (numeric) = 0.7629966779358852 absolute error = 3.05089287166993e-13 relative error = 3.998566389469283e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.807855097458042 y[1] (numeric) = 0.8078550974583463 absolute error = 3.043121310497554e-13 relative error = 3.766914784684647e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.8466831315303208 y[1] (numeric) = 0.846683131530622 absolute error = 3.01203506580805e-13 relative error = 3.557452550594703e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.8787399867942708 y[1] (numeric) = 0.8787399867945668 absolute error = 2.959854583650667e-13 relative error = 3.368293952854593e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.9033356533474587 y[1] (numeric) = 0.9033356533477468 absolute error = 2.881028748902281e-13 relative error = 3.18932252726454e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.9198414930981563 y[1] (numeric) = 0.9198414930984343 absolute error = 2.779998453661392e-13 relative error = 3.022258154824006e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.9277003465829156 y[1] (numeric) = 0.9277003465831815 absolute error = 2.65898414397725e-13 relative error = 2.866210144009682e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 0.926436019037877 y[1] (numeric) = 0.9264360190381286 absolute error = 2.515765373800605e-13 relative error = 2.715530616364937e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 0.9156620117835905 y[1] (numeric) = 0.9156620117838258 absolute error = 2.352562589180707e-13 relative error = 2.569247778007325e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 0.8950893719812986 y[1] (numeric) = 0.8950893719815158 absolute error = 2.172706459191431e-13 relative error = 2.42736259328172e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 0.864533542481839 y[1] (numeric) = 0.8645335424820366 absolute error = 1.976196983832779e-13 relative error = 2.285853453597252e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.8239201037314782 y[1] (numeric) = 0.8239201037316547 absolute error = 1.765254609153999e-13 relative error = 2.14250702362921e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 0.7732893114172029 y[1] (numeric) = 0.7732893114173574 absolute error = 1.544320227253593e-13 relative error = 1.997079494637428e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 0.7127993466037278 y[1] (numeric) = 0.712799346603859 absolute error = 1.312283615106935e-13 relative error = 1.841028083652949e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 0.6427282093947658 y[1] (numeric) = 0.6427282093948733 absolute error = 1.074695887837152e-13 relative error = 1.672084517418575e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 0.563474202485123 y[1] (numeric) = 0.5634742024852065 absolute error = 8.348877145181177e-14 relative error = 1.481678683488905e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 0.4755549671869218 y[1] (numeric) = 0.4755549671869809 absolute error = 5.911937606128959e-14 relative error = 1.243165987961432e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 0.3796050514294296 y[1] (numeric) = 0.3796050514294647 absolute error = 3.502753642692369e-14 relative error = 9.227363096203548e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 0.2763720066540575 y[1] (numeric) = 0.2763720066540692 absolute error = 1.165734175856414e-14 relative error = 4.21798933245651e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 0.1667110282524814 y[1] (numeric) = 0.1667110282524703 absolute error = 1.110223024625157e-14 relative error = 6.65956557441263e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 0.05157817201918315 y[1] (numeric) = 0.05157817201915031 absolute error = 3.284178484719291e-14 relative error = 6.367380533567237e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -0.06797780320077421 y[1] (numeric) = -0.0679778032008275 absolute error = 5.329070518200751e-14 relative error = 7.839427382584287e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -0.19082489910396 y[1] (numeric) = -0.1908248991040322 absolute error = 7.222000775186643e-14 relative error = 3.78462182298975e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -0.3157585633478301 y[1] (numeric) = -0.3157585633479194 absolute error = 8.926193117986259e-14 relative error = 2.826904525833376e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -0.4415134962779729 y[1] (numeric) = -0.441513496278077 absolute error = 1.040834085586084e-13 relative error = 2.357423033181266e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -0.566776463280141 y[1] (numeric) = -0.5667764632802578 absolute error = 1.167954621905665e-13 relative error = 2.060697113543296e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = (0.2 * x + 0.3) * sin(x); Iterations = 981 Total Elapsed Time = 21 Seconds Elapsed Time(since restart) = 21 Seconds Time to Timeout = 9 Minutes 39 Seconds Percent Done = 100.2 %