##############ECHO OF PROBLEM################# ##############temp/add_c_linpostode.ode################# diff ( y , x , 1 ) = 0.3 + (0.1 * x + 0.2) ; ! // 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(0.05 * x * x + 0.5 * x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.0505 y[1] (numeric) = 0.0505 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) = 0.102 y[1] (numeric) = 0.102 absolute error = 5.551115123125783e-17 relative error = 5.442269728554686e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.1545000000000001 y[1] (numeric) = 0.1545 absolute error = 5.551115123125783e-17 relative error = 3.592954772249696e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.2080000000000001 y[1] (numeric) = 0.208 absolute error = 1.110223024625157e-16 relative error = 5.337610695313249e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.2625000000000002 y[1] (numeric) = 0.2625 absolute error = 1.665334536937735e-16 relative error = 6.344131569286604e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.3180000000000002 y[1] (numeric) = 0.318 absolute error = 2.220446049250313e-16 relative error = 6.982534746070162e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.3745000000000003 y[1] (numeric) = 0.3745 absolute error = 2.775557561562891e-16 relative error = 7.41136865570865e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.4320000000000003 y[1] (numeric) = 0.432 absolute error = 3.33066907387547e-16 relative error = 7.70988211545247e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.4905000000000004 y[1] (numeric) = 0.4905 absolute error = 4.440892098500626e-16 relative error = 9.053806520898312e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.5500000000000004 y[1] (numeric) = 0.55 absolute error = 3.33066907387547e-16 relative error = 6.055761952500849e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.613551249999999 y[1] (numeric) = 0.61355125 absolute error = 9.992007221626409e-16 relative error = 1.628552989114834e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.6751012499999977 y[1] (numeric) = 0.67510125 absolute error = 2.331468351712829e-15 relative error = 3.453509161348519e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.7376512499999963 y[1] (numeric) = 0.73765125 absolute error = 3.663735981263017e-15 relative error = 4.966758995206793e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.8012012499999949 y[1] (numeric) = 0.8012012499999999 absolute error = 4.996003610813204e-15 relative error = 6.235641308364454e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.8657512499999934 y[1] (numeric) = 0.8657512499999998 absolute error = 6.328271240363392e-15 relative error = 7.309572166789757e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.931301249999992 y[1] (numeric) = 0.9313012499999996 absolute error = 7.66053886991358e-15 relative error = 8.225629322320406e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.9978512499999904 y[1] (numeric) = 0.9978512499999994 absolute error = 8.992806499463768e-15 relative error = 9.012171402765546e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.065401249999989 y[1] (numeric) = 1.065401249999999 absolute error = 1.043609643147647e-14 relative error = 9.795461035432972e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.133951249999987 y[1] (numeric) = 1.133951249999999 absolute error = 1.199040866595169e-14 relative error = 1.057400718589254e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 1.203501249999986 y[1] (numeric) = 1.203501249999999 absolute error = 1.332267629550188e-14 relative error = 1.10699314151124e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.274051249999984 y[1] (numeric) = 1.274051249999999 absolute error = 1.465494392505207e-14 relative error = 1.150263297889489e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.345601249999982 y[1] (numeric) = 1.345601249999999 absolute error = 1.643130076445232e-14 relative error = 1.221112180480847e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.41815124999998 y[1] (numeric) = 1.418151249999998 absolute error = 1.754152378907747e-14 relative error = 1.236928979830446e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 1.491701249999978 y[1] (numeric) = 1.491701249999998 absolute error = 1.931788062847772e-14 relative error = 1.295023425667707e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 1.566251249999977 y[1] (numeric) = 1.566251249999998 absolute error = 2.109423746787797e-14 relative error = 1.346797805772113e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 1.641801249999975 y[1] (numeric) = 1.641801249999997 absolute error = 2.264854970235319e-14 relative error = 1.379493997970433e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 1.718351249999973 y[1] (numeric) = 1.718351249999997 absolute error = 2.420286193682841e-14 relative error = 1.408493283129907e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 1.795901249999971 y[1] (numeric) = 1.795901249999997 absolute error = 2.597921877622866e-14 relative error = 1.446583924156692e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 1.874451249999969 y[1] (numeric) = 1.874451249999996 absolute error = 2.753353101070388e-14 relative error = 1.468884880879369e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 1.954001249999967 y[1] (numeric) = 1.954001249999996 absolute error = 2.90878432451791e-14 relative error = 1.488629715317715e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 2.034551249999964 y[1] (numeric) = 2.034551249999995 absolute error = 3.108624468950438e-14 relative error = 1.527916521616495e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 2.116101249999962 y[1] (numeric) = 2.116101249999995 absolute error = 3.33066907387547e-14 relative error = 1.573964891271403e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 2.19865124999996 y[1] (numeric) = 2.198651249999995 absolute error = 3.508304757815495e-14 relative error = 1.595662230567744e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 2.282201249999958 y[1] (numeric) = 2.282201249999994 absolute error = 3.641531520770513e-14 relative error = 1.595622437228347e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 2.366751249999955 y[1] (numeric) = 2.366751249999994 absolute error = 3.863576125695545e-14 relative error = 1.632438612082963e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 2.452301249999953 y[1] (numeric) = 2.452301249999993 absolute error = 4.04121180963557e-14 relative error = 1.647926334350499e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 2.538851249999951 y[1] (numeric) = 2.538851249999993 absolute error = 4.218847493575595e-14 relative error = 1.661715113705727e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 2.626401249999948 y[1] (numeric) = 2.626401249999992 absolute error = 4.39648317751562e-14 relative error = 1.673957160017231e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 2.714951249999946 y[1] (numeric) = 2.714951249999991 absolute error = 4.574118861455645e-14 relative error = 1.684788580073302e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 2.804501249999943 y[1] (numeric) = 2.804501249999991 absolute error = 4.796163466380676e-14 relative error = 1.710166278720958e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 2.895051249999941 y[1] (numeric) = 2.895051249999991 absolute error = 4.973799150320701e-14 relative error = 1.71803492263593e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 2.986601249999938 y[1] (numeric) = 2.98660124999999 absolute error = 5.195843755245733e-14 relative error = 1.739717933636384e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 3.079151249999935 y[1] (numeric) = 3.079151249999989 absolute error = 5.373479439185758e-14 relative error = 1.745117080294731e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 3.172701249999933 y[1] (numeric) = 3.172701249999988 absolute error = 5.551115123125783e-14 relative error = 1.749649489729265e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 3.26725124999993 y[1] (numeric) = 3.267251249999988 absolute error = 5.773159728050814e-14 relative error = 1.766977586450059e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 3.362801249999927 y[1] (numeric) = 3.362801249999987 absolute error = 5.995204332975845e-14 relative error = 1.782800673389774e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 3.459351249999924 y[1] (numeric) = 3.459351249999986 absolute error = 6.17284001691587e-14 relative error = 1.784392381928839e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 3.556901249999922 y[1] (numeric) = 3.556901249999985 absolute error = 6.394884621840902e-14 relative error = 1.797880844131122e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 3.655451249999918 y[1] (numeric) = 3.655451249999985 absolute error = 6.661338147750939e-14 relative error = 1.822302553686385e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 3.755001249999915 y[1] (numeric) = 3.755001249999984 absolute error = 6.838973831690964e-14 relative error = 1.821297351549781e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = 0.3 + (0.1 * x + 0.2) ; Iterations = 981 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 17 Seconds Time to Timeout = 9 Minutes 42 Seconds Percent Done = 100.2 %