##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 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); array_y_init[1 + 1] = exact_soln_yp(x_start); array_y_init[2 + 1] = exact_soln_ypp(x_start); glob_h = 0.00001; glob_look_poles = true; glob_max_iter = 20; /* 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(1.0 - sin(x)); } double exact_soln_yp (double x) { return(-cos(x)); } double exact_soln_ypp (double x) { return(sin(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.9001665833531718 y[1] (numeric) = 0.9001665833531718 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) = 0.8013306692049387 y[1] (numeric) = 0.8011861089629688 absolute error = 0.0001445602419698488 relative error = 0.01804002361637776 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.7044797933386603 y[1] (numeric) = 0.7033615091136379 absolute error = 0.001118284225022359 relative error = 0.1587390065118267 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.6105816576913493 y[1] (numeric) = 0.6069398786774196 absolute error = 0.003641779013929702 relative error = 0.5964442213510829 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.5205744613957967 y[1] (numeric) = 0.5122636870720679 absolute error = 0.008310774323728731 relative error = 1.596462166323981 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.4353575266049643 y[1] (numeric) = 0.4197673564196338 absolute error = 0.01559017018533049 relative error = 3.581003941038265 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.3557823127623085 y[1] (numeric) = 0.3299729209442216 absolute error = 0.02580939181808689 relative error = 7.254265007639561 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.2826439091004768 y[1] (numeric) = 0.2434848109785839 absolute error = 0.03915909812189294 relative error = 13.85456995925297 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.2166730903725162 y[1] (numeric) = 0.1609838136960348 absolute error = 0.05568927667648144 relative error = 25.70198107237839 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.1585290151921031 y[1] (numeric) = 0.08322027091005249 absolute error = 0.07530874428205064 relative error = 47.50470706626961 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.1065358088501371 y[1] (numeric) = 0.007556913371019216 absolute error = 0.09897889547911791 relative error = 92.90669170058169 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.06616078327380481 y[1] (numeric) = -0.05789618082584124 absolute error = 0.1240569640996461 relative error = 187.5083062215864 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.035116370464796 y[1] (numeric) = -0.1159748499073947 absolute error = 0.1510912203721907 relative error = 430.2586468144793 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.01371275593397977 y[1] (numeric) = -0.1657297320544759 absolute error = 0.1794424879884556 relative error = 1308.580775829335 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.002163797522653718 y[1] (numeric) = -0.206185241423361 absolute error = 0.2083490389460147 relative error = 9628.860222119669 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.0005848886056857181 y[1] (numeric) = -0.2363493158770332 absolute error = 0.2369342044827189 relative error = 40509.28709834233 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.008991805119056217 y[1] (numeric) = -0.2552233293421231 absolute error = 0.2642151344611793 relative error = 2938.399253129181 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.02730054793192075 y[1] (numeric) = -0.2618120697505317 absolute error = 0.2891126176824525 relative error = 1058.999322663455 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.05532818213815891 y[1] (numeric) = -0.2551336828694424 absolute error = 0.3104618650076014 relative error = 561.1278972302997 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.09279466488148617 y[1] (numeric) = -0.2342294826642562 absolute error = 0.3270241475457424 relative error = 352.4169713457182 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.1393256434511037 y[1] (numeric) = -0.1981735301725509 absolute error = 0.3374991736236546 relative error = 242.2376565173373 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.1944561956902404 y[1] (numeric) = -0.1460818851801185 absolute error = 0.3405380808703589 relative error = 175.1232865898601 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.2576354753446606 y[1] (numeric) = -0.07712143825939409 absolute error = 0.3347569136040547 relative error = 129.934324128392 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.3282322159363506 y[1] (numeric) = 0.009481765076533749 absolute error = 0.3187504508598168 relative error = 97.11126311916549 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.405541038169498 y[1] (numeric) = 0.1144347912765248 absolute error = 0.2911062468929733 relative error = 71.7821920580338 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.4887894978472484 y[1] (numeric) = 0.2383707539771553 absolute error = 0.2504187438700931 relative error = 51.23243133762082 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.5771458038787838 y[1] (numeric) = 0.3818424881405408 absolute error = 0.1953033157382429 relative error = 33.83951064456875 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.6697271292609487 y[1] (numeric) = 0.5453170263101376 absolute error = 0.1244101029508111 relative error = 18.57623762204453 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.7656084319938419 y[1] (numeric) = 0.7291709321759494 absolute error = 0.03643749981789246 relative error = 4.759286639908055 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.8638316977947014 y[1] (numeric) = 0.9336865380746119 absolute error = 0.06985484027991051 relative error = 8.086626186356066 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.9634155122599398 y[1] (numeric) = 1.159049124018011 absolute error = 0.1956336117580714 relative error = 20.30625511718845 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 1.063364866833453 y[1] (numeric) = 1.405345066436651 absolute error = 0.3419801996031975 relative error = 32.16019357697655 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 1.162681100603207 y[1] (numeric) = 1.672560975134912 absolute error = 0.5098798745317048 relative error = 43.8538025832858 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 1.260371878590955 y[1] (numeric) = 1.960583827081458 absolute error = 0.7002119484905025 relative error = 55.55597997579183 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 1.355461106835324 y[1] (numeric) = 2.269202095698009 absolute error = 0.9137409888626857 relative error = 67.41181906694848 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 1.446998685200013 y[1] (numeric) = 2.598107864362986 absolute error = 1.151109179162972 relative error = 79.55150138950256 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 1.534070000460305 y[1] (numeric) = 2.946899903012608 absolute error = 1.412829902552303 relative error = 92.09683405114346 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 1.615805064816068 y[1] (numeric) = 3.315087677099068 absolute error = 1.699282612282999 relative error = 105.1663130215793 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 1.691387208522281 y[1] (numeric) = 3.702096248849579 absolute error = 2.010709040327298 relative error = 118.8792861975112 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 1.760061239783164 y[1] (numeric) = 4.107272021854552 absolute error = 2.347210782071388 relative error = 133.3596086895567 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 1.821140990378977 y[1] (numeric) = 4.529889271586875 absolute error = 2.708748281207898 relative error = 148.7390759704009 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 1.874016171632046 y[1] (numeric) = 4.969157396601484 absolute error = 3.095141224969438 relative error = 165.1608599660021 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 1.918158472209504 y[1] (numeric) = 5.424228817963678 absolute error = 3.506070345754174 relative error = 182.7831431318379 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 1.953126836835484 y[1] (numeric) = 5.894207447977651 absolute error = 3.941080611142167 relative error = 201.7831375215563 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 1.978571873169648 y[1] (numeric) = 6.378157643598548 absolute error = 4.399585770428899 relative error = 222.3616857233908 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 1.994239342819955 y[1] (numeric) = 6.875113555068482 absolute error = 4.880874212248527 relative error = 244.7486671959206 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 1.999972701608638 y[1] (numeric) = 7.384088776368052 absolute error = 5.384116074759413 relative error = 269.2094782308182 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.995714663709875 y[1] (numeric) = 7.904086201059226 absolute error = 5.90837153734935 relative error = 296.0529200284652 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.981507774030832 y[1] (numeric) = 8.434107985043262 absolute error = 6.45260021101243 relative error = 325.6409233200429 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 1.957493983117007 y[1] (numeric) = 8.973165516689116 absolute error = 7.015671533572109 relative error = 358.4006691249562 % Correct digits = 0 h = 0.005 Finished! diff ( y , x , 3 ) = sin(x); Iterations = 981 Total Elapsed Time = 2 Minutes 16 Seconds Elapsed Time(since restart) = 2 Minutes 15 Seconds Time to Timeout = 7 Minutes 44 Seconds Percent Done = 100.2 %