##############ECHO OF PROBLEM################# ##############temp/add_lin_linpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ; ! // 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(0.4 * x * x / 2.0 + 0.3 * x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.032 y[1] (numeric) = 0.032 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) = 0.06800000000000003 y[1] (numeric) = 0.06799999999999999 absolute error = 4.163336342344337e-17 relative error = 6.122553444624022e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.1080000000000001 y[1] (numeric) = 0.108 absolute error = 6.938893903907228e-17 relative error = 6.424901762877059e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.1520000000000001 y[1] (numeric) = 0.152 absolute error = 1.110223024625157e-16 relative error = 7.304098846218129e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.2000000000000002 y[1] (numeric) = 0.2 absolute error = 1.665334536937735e-16 relative error = 8.326672684688666e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.2520000000000002 y[1] (numeric) = 0.252 absolute error = 2.220446049250313e-16 relative error = 8.811293846231393e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.3080000000000003 y[1] (numeric) = 0.3080000000000001 absolute error = 2.220446049250313e-16 relative error = 7.209240419643867e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.3680000000000004 y[1] (numeric) = 0.368 absolute error = 3.33066907387547e-16 relative error = 9.050731179009419e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.4320000000000004 y[1] (numeric) = 0.4320000000000001 absolute error = 3.33066907387547e-16 relative error = 7.709882115452469e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.5000000000000004 y[1] (numeric) = 0.5000000000000001 absolute error = 3.33066907387547e-16 relative error = 6.661338147750933e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.5757049999999988 y[1] (numeric) = 0.575705 absolute error = 1.221245327087672e-15 relative error = 2.121304013492457e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.6519049999999971 y[1] (numeric) = 0.651905 absolute error = 2.886579864025407e-15 relative error = 4.427914901750132e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.7321049999999952 y[1] (numeric) = 0.7321049999999998 absolute error = 4.551914400963142e-15 relative error = 6.217570431786659e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.8163049999999932 y[1] (numeric) = 0.8163049999999995 absolute error = 6.328271240363392e-15 relative error = 7.752336737326667e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.9045049999999909 y[1] (numeric) = 0.9045049999999991 absolute error = 8.215650382226158e-15 relative error = 9.083034789444216e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.9967049999999885 y[1] (numeric) = 0.9967049999999986 absolute error = 1.010302952408892e-14 relative error = 1.013642905783461e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 1.092904999999986 y[1] (numeric) = 1.092904999999998 absolute error = 1.221245327087672e-14 relative error = 1.117430451034342e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.193104999999983 y[1] (numeric) = 1.193104999999997 absolute error = 1.4210854715202e-14 relative error = 1.191081649578386e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.29730499999998 y[1] (numeric) = 1.297304999999997 absolute error = 1.643130076445232e-14 relative error = 1.266571913655815e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 1.405504999999977 y[1] (numeric) = 1.405504999999996 absolute error = 1.84297022087776e-14 relative error = 1.311251273298771e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.517704999999974 y[1] (numeric) = 1.517704999999995 absolute error = 2.087219286295294e-14 relative error = 1.375247025143443e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.633904999999971 y[1] (numeric) = 1.633904999999994 absolute error = 2.353672812205332e-14 relative error = 1.440519988741924e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.754104999999967 y[1] (numeric) = 1.754104999999993 absolute error = 2.597921877622866e-14 relative error = 1.481052660828693e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 1.878304999999963 y[1] (numeric) = 1.878304999999992 absolute error = 2.864375403532904e-14 relative error = 1.524978852493583e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.006504999999959 y[1] (numeric) = 2.00650499999999 absolute error = 3.108624468950438e-14 relative error = 1.549273223316414e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.138704999999955 y[1] (numeric) = 2.138704999999989 absolute error = 3.375077994860476e-14 relative error = 1.578094218164986e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 2.274904999999951 y[1] (numeric) = 2.274904999999988 absolute error = 3.68594044175552e-14 relative error = 1.6202612600331e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 2.415104999999947 y[1] (numeric) = 2.415104999999987 absolute error = 3.996802888650564e-14 relative error = 1.654918891166492e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 2.559304999999942 y[1] (numeric) = 2.559304999999985 absolute error = 4.307665335545607e-14 relative error = 1.683138717560316e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 2.707504999999937 y[1] (numeric) = 2.707504999999983 absolute error = 4.618527782440651e-14 relative error = 1.705824285621174e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 2.859704999999932 y[1] (numeric) = 2.859704999999982 absolute error = 4.929390229335695e-14 relative error = 1.723740815691063e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 3.015904999999927 y[1] (numeric) = 3.01590499999998 absolute error = 5.240252676230739e-14 relative error = 1.737539039270423e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 3.176104999999922 y[1] (numeric) = 3.176104999999978 absolute error = 5.551115123125783e-14 relative error = 1.747774435393641e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 3.340304999999916 y[1] (numeric) = 3.340304999999976 absolute error = 5.950795411990839e-14 relative error = 1.781512590015279e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 3.508504999999911 y[1] (numeric) = 3.508504999999974 absolute error = 6.306066779870889e-14 relative error = 1.797365766863963e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 3.680704999999905 y[1] (numeric) = 3.680704999999972 absolute error = 6.661338147750939e-14 relative error = 1.809799521491429e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 3.856904999999899 y[1] (numeric) = 3.85690499999997 absolute error = 7.061018436615996e-14 relative error = 1.830747305576928e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 4.037104999999893 y[1] (numeric) = 4.037104999999968 absolute error = 7.549516567451064e-14 relative error = 1.870032255155926e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 4.221304999999886 y[1] (numeric) = 4.221304999999965 absolute error = 7.904787935331115e-14 relative error = 1.872593412542171e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 4.40950499999988 y[1] (numeric) = 4.409504999999963 absolute error = 8.260059303211165e-14 relative error = 1.873239582041837e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 4.601704999999873 y[1] (numeric) = 4.601704999999961 absolute error = 8.79296635503124e-14 relative error = 1.9108061805421e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 4.797904999999867 y[1] (numeric) = 4.797904999999958 absolute error = 9.14823772291129e-14 relative error = 1.906715060617404e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 4.998104999999859 y[1] (numeric) = 4.998104999999955 absolute error = 9.592326932761353e-14 relative error = 1.919192760608595e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 5.202304999999853 y[1] (numeric) = 5.202304999999953 absolute error = 1.003641614261142e-13 relative error = 1.929224861405031e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 5.410504999999845 y[1] (numeric) = 5.41050499999995 absolute error = 1.048050535246148e-13 relative error = 1.937066013701452e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 5.622704999999837 y[1] (numeric) = 5.622704999999947 absolute error = 1.092459456231154e-13 relative error = 1.942942865099957e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 5.83890499999983 y[1] (numeric) = 5.838904999999945 absolute error = 1.145750161413162e-13 relative error = 1.962268886740228e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 6.059104999999822 y[1] (numeric) = 6.05910499999994 absolute error = 1.181277298201167e-13 relative error = 1.949590406835995e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 6.283304999999814 y[1] (numeric) = 6.283304999999937 absolute error = 1.234568003383174e-13 relative error = 1.96483857362202e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 6.511504999999806 y[1] (numeric) = 6.511504999999934 absolute error = 1.27897692436818e-13 relative error = 1.964180207752614e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ; Iterations = 981 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 17 Seconds Time to Timeout = 9 Minutes 42 Seconds Percent Done = 100.2 %