##############ECHO OF PROBLEM################# ##############temp/sub_lin_cpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 0.2) - 0.3 ; ! /* 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 - 0.1 * x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -0.009500000000000001 y[1] (numeric) = -0.009500000000000001 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) = -0.01800000000000001 y[1] (numeric) = -0.018 absolute error = 1.040834085586084e-17 relative error = 5.782411586589354e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -0.02550000000000001 y[1] (numeric) = -0.02549999999999999 absolute error = 1.734723475976807e-17 relative error = 6.802837160693357e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -0.03200000000000001 y[1] (numeric) = -0.03199999999999999 absolute error = 2.775557561562891e-17 relative error = 8.673617379884032e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -0.03750000000000002 y[1] (numeric) = -0.03749999999999998 absolute error = 4.163336342344337e-17 relative error = 1.110223024625156e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -0.04200000000000002 y[1] (numeric) = -0.04199999999999997 absolute error = 4.85722573273506e-17 relative error = 1.156482317317871e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -0.04550000000000002 y[1] (numeric) = -0.04549999999999996 absolute error = 6.245004513516506e-17 relative error = 1.372528464509122e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -0.04800000000000001 y[1] (numeric) = -0.04799999999999995 absolute error = 6.245004513516506e-17 relative error = 1.301042606982605e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -0.04950000000000001 y[1] (numeric) = -0.04949999999999994 absolute error = 6.938893903907228e-17 relative error = 1.401796748264086e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -0.05 y[1] (numeric) = -0.04999999999999993 absolute error = 6.938893903907228e-17 relative error = 1.387778780781446e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.04944875000000002 y[1] (numeric) = -0.04944874999999993 absolute error = 9.020562075079397e-17 relative error = 1.824224490018331e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.04789875000000008 y[1] (numeric) = -0.04789874999999996 absolute error = 1.249000902703301e-16 relative error = 2.60758558981873e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -0.04534875000000018 y[1] (numeric) = -0.04534875 absolute error = 1.804112415015879e-16 relative error = 3.978306822163504e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -0.04179875000000032 y[1] (numeric) = -0.04179875000000007 absolute error = 2.567390744445674e-16 relative error = 6.142266800910685e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -0.03724875000000051 y[1] (numeric) = -0.03724875000000016 absolute error = 3.538835890992686e-16 relative error = 9.500549390228229e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -0.03169875000000074 y[1] (numeric) = -0.03169875000000026 absolute error = 4.787836793695988e-16 relative error = 1.510418169074767e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -0.02514875000000101 y[1] (numeric) = -0.02514875000000039 absolute error = 6.210310043996969e-16 relative error = 2.469430903721545e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -0.01759875000000133 y[1] (numeric) = -0.01759875000000054 absolute error = 7.840950111415168e-16 relative error = 4.455401725358094e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -0.009048750000001686 y[1] (numeric) = -0.009048750000000714 absolute error = 9.71445146547012e-16 relative error = 1.073568334352072e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.0005012499999979363 y[1] (numeric) = 0.0005012499999990936 absolute error = 1.157277398911027e-15 relative error = 2.30878284072976e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.0110512499999975 y[1] (numeric) = 0.01105124999999888 absolute error = 1.386044057305469e-15 relative error = 1.254196635951393e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.02260124999999701 y[1] (numeric) = 0.02260124999999865 absolute error = 1.634109514370152e-15 relative error = 7.230173173476548e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.03515124999999649 y[1] (numeric) = 0.03515124999999839 absolute error = 1.901256929670581e-15 relative error = 5.408788961049096e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.04870124999999592 y[1] (numeric) = 0.04870124999999811 absolute error = 2.192690473634684e-15 relative error = 4.50232894152587e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.0632512499999953 y[1] (numeric) = 0.06325124999999782 absolute error = 2.511879593214417e-15 relative error = 3.971272651867913e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.07880124999999466 y[1] (numeric) = 0.07880124999999751 absolute error = 2.844946500601964e-15 relative error = 3.610280929048913e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.09535124999999396 y[1] (numeric) = 0.09535124999999715 absolute error = 3.191891195797325e-15 relative error = 3.347508497054341e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.1129012499999932 y[1] (numeric) = 0.1129012499999968 absolute error = 3.58046925441613e-15 relative error = 3.171328266441997e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.1314512499999924 y[1] (numeric) = 0.1314512499999964 absolute error = 3.996802888650564e-15 relative error = 3.040521021025508e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.1510012499999916 y[1] (numeric) = 0.151001249999996 absolute error = 4.413136522884997e-15 relative error = 2.922582775232154e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.1715512499999907 y[1] (numeric) = 0.1715512499999956 absolute error = 4.85722573273506e-15 relative error = 2.831355488657367e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 0.1931012499999898 y[1] (numeric) = 0.1931012499999951 absolute error = 5.301314942585122e-15 relative error = 2.745355062479089e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 0.2156512499999889 y[1] (numeric) = 0.2156512499999947 absolute error = 5.800915303666443e-15 relative error = 2.689952088692619e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 0.2392012499999879 y[1] (numeric) = 0.2392012499999942 absolute error = 6.300515664747763e-15 relative error = 2.633981078588879e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 0.2637512499999868 y[1] (numeric) = 0.2637512499999937 absolute error = 6.883382752675971e-15 relative error = 2.609800997218521e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.2893012499999858 y[1] (numeric) = 0.2893012499999932 absolute error = 7.382983113757291e-15 relative error = 2.552005258794303e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 0.3158512499999847 y[1] (numeric) = 0.3158512499999926 absolute error = 7.938094626069869e-15 relative error = 2.51323831267733e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 0.3434012499999835 y[1] (numeric) = 0.343401249999992 absolute error = 8.493206138382448e-15 relative error = 2.473260111424421e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 0.3719512499999823 y[1] (numeric) = 0.3719512499999914 absolute error = 9.103828801926284e-15 relative error = 2.447586559240416e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 0.401501249999981 y[1] (numeric) = 0.4015012499999908 absolute error = 9.769962616701378e-15 relative error = 2.433357957590877e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 0.4320512499999797 y[1] (numeric) = 0.4320512499999902 absolute error = 1.043609643147647e-14 relative error = 2.415476504576011e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 0.4636012499999784 y[1] (numeric) = 0.4636012499999895 absolute error = 1.104671909502031e-14 relative error = 2.382806149685926e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 0.4961512499999771 y[1] (numeric) = 0.4961512499999888 absolute error = 1.17128529097954e-14 relative error = 2.360742396556684e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 0.5297012499999756 y[1] (numeric) = 0.5297012499999881 absolute error = 1.254552017826427e-14 relative error = 2.368414304905802e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 0.5642512499999741 y[1] (numeric) = 0.5642512499999873 absolute error = 1.321165399303936e-14 relative error = 2.341448777125433e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 0.5998012499999726 y[1] (numeric) = 0.5998012499999865 absolute error = 1.387778780781446e-14 relative error = 2.313731058048827e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 0.6363512499999711 y[1] (numeric) = 0.6363512499999858 absolute error = 1.476596622751458e-14 relative error = 2.32041128661494e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 0.6739012499999695 y[1] (numeric) = 0.673901249999985 absolute error = 1.554312234475219e-14 relative error = 2.306439162229317e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 0.7124512499999679 y[1] (numeric) = 0.7124512499999842 absolute error = 1.63202784619898e-14 relative error = 2.290722131793654e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 0.7520012499999662 y[1] (numeric) = 0.7520012499999834 absolute error = 1.720845688168993e-14 relative error = 2.288354824103112e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = (0.1 * x + 0.2) - 0.3 ; Iterations = 981 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 17 Seconds Time to Timeout = 9 Minutes 43 Seconds Percent Done = 100.2 %