##############ECHO OF PROBLEM################# ##############temp/mult_c_linpostode.ode################# diff ( y , x , 1 ) = 2.0 * (0.2 * x + 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(0.2 * x * x + 0.6 * x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.062 y[1] (numeric) = 0.062 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) = 0.1280000000000001 y[1] (numeric) = 0.128 absolute error = 5.551115123125783e-17 relative error = 4.336808689942016e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.1980000000000001 y[1] (numeric) = 0.198 absolute error = 8.326672684688674e-17 relative error = 4.205390244792257e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.2720000000000002 y[1] (numeric) = 0.2720000000000001 absolute error = 1.110223024625157e-16 relative error = 4.081702296416014e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.3500000000000003 y[1] (numeric) = 0.3500000000000001 absolute error = 1.110223024625157e-16 relative error = 3.172065784643302e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.4320000000000003 y[1] (numeric) = 0.4320000000000001 absolute error = 2.220446049250313e-16 relative error = 5.139921410301647e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.5180000000000005 y[1] (numeric) = 0.5180000000000001 absolute error = 3.33066907387547e-16 relative error = 6.429863076979666e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.6080000000000005 y[1] (numeric) = 0.6080000000000001 absolute error = 4.440892098500626e-16 relative error = 7.304098846218128e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.7020000000000006 y[1] (numeric) = 0.7020000000000002 absolute error = 4.440892098500626e-16 relative error = 6.326057120371257e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.8000000000000007 y[1] (numeric) = 0.8000000000000002 absolute error = 5.551115123125783e-16 relative error = 6.938893903907222e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.9072049999999984 y[1] (numeric) = 0.9072050000000002 absolute error = 1.77635683940025e-15 relative error = 1.958054507415913e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 1.013404999999996 y[1] (numeric) = 1.013405 absolute error = 4.218847493575595e-15 relative error = 4.163041916682483e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 1.123604999999994 y[1] (numeric) = 1.123605 absolute error = 6.439293542825908e-15 relative error = 5.730922826817204e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 1.237804999999991 y[1] (numeric) = 1.237805 absolute error = 9.103828801926284e-15 relative error = 7.354816632608813e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 1.356004999999988 y[1] (numeric) = 1.356004999999999 absolute error = 1.154631945610163e-14 relative error = 8.514953452311555e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 1.478204999999985 y[1] (numeric) = 1.478204999999999 absolute error = 1.398881011027697e-14 relative error = 9.463376263966848e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 1.604404999999982 y[1] (numeric) = 1.604404999999998 absolute error = 1.665334536937735e-14 relative error = 1.037976406791149e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.734604999999978 y[1] (numeric) = 1.734604999999998 absolute error = 1.953992523340276e-14 relative error = 1.126476934714416e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.868804999999975 y[1] (numeric) = 1.868804999999997 absolute error = 2.242650509742816e-14 relative error = 1.20004522127394e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 2.007004999999971 y[1] (numeric) = 2.007004999999996 absolute error = 2.531308496145357e-14 relative error = 1.261236766298735e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 2.149204999999967 y[1] (numeric) = 2.149204999999995 absolute error = 2.797762022055394e-14 relative error = 1.301766012109332e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 2.295404999999963 y[1] (numeric) = 2.295404999999994 absolute error = 3.108624468950438e-14 relative error = 1.354281474925117e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 2.445604999999959 y[1] (numeric) = 2.445604999999993 absolute error = 3.419486915845482e-14 relative error = 1.39821717564592e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 2.599804999999955 y[1] (numeric) = 2.599804999999992 absolute error = 3.774758283725532e-14 relative error = 1.451939004550571e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 2.75800499999995 y[1] (numeric) = 2.758004999999991 absolute error = 4.085620730620576e-14 relative error = 1.481368137701219e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 2.920204999999945 y[1] (numeric) = 2.92020499999999 absolute error = 4.440892098500626e-14 relative error = 1.520746693639902e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 3.086404999999941 y[1] (numeric) = 3.086404999999988 absolute error = 4.75175454539567e-14 relative error = 1.539575831880703e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 3.256604999999935 y[1] (numeric) = 3.256604999999987 absolute error = 5.151434834260726e-14 relative error = 1.581842082248485e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 3.43080499999993 y[1] (numeric) = 3.430804999999985 absolute error = 5.506706202140776e-14 relative error = 1.605077001502822e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 3.609004999999925 y[1] (numeric) = 3.609004999999984 absolute error = 5.906386491005833e-14 relative error = 1.636569218110243e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 3.791204999999919 y[1] (numeric) = 3.791204999999982 absolute error = 6.350475700855895e-14 relative error = 1.675054686005118e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 3.977404999999913 y[1] (numeric) = 3.977404999999981 absolute error = 6.750155989720952e-14 relative error = 1.697125635865872e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 4.167604999999908 y[1] (numeric) = 4.167604999999978 absolute error = 7.016609515630989e-14 relative error = 1.683607135424577e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 4.361804999999901 y[1] (numeric) = 4.361804999999976 absolute error = 7.549516567451064e-14 relative error = 1.730823951884882e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 4.560004999999895 y[1] (numeric) = 4.560004999999975 absolute error = 7.993605777301127e-14 relative error = 1.752981800963225e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 4.762204999999889 y[1] (numeric) = 4.762204999999972 absolute error = 8.348877145181177e-14 relative error = 1.753153664149563e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 4.968404999999882 y[1] (numeric) = 4.96840499999997 absolute error = 8.881784197001252e-14 relative error = 1.787653018826256e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 5.178604999999875 y[1] (numeric) = 5.178604999999968 absolute error = 9.325873406851315e-14 relative error = 1.800846638593123e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 5.392804999999868 y[1] (numeric) = 5.392804999999965 absolute error = 9.769962616701378e-14 relative error = 1.811666213909388e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 5.611004999999861 y[1] (numeric) = 5.611004999999964 absolute error = 1.030286966852145e-13 relative error = 1.83618971441332e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 5.833204999999854 y[1] (numeric) = 5.83320499999996 absolute error = 1.06581410364015e-13 relative error = 1.827150089256553e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 6.059404999999846 y[1] (numeric) = 6.059404999999958 absolute error = 1.119104808822158e-13 relative error = 1.846888941772643e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 6.289604999999838 y[1] (numeric) = 6.289604999999955 absolute error = 1.172395514004165e-13 relative error = 1.864020894800541e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 6.523804999999831 y[1] (numeric) = 6.523804999999952 absolute error = 1.216804434989172e-13 relative error = 1.865175974740513e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 6.762004999999823 y[1] (numeric) = 6.76200499999995 absolute error = 1.270095140171179e-13 relative error = 1.878281870793074e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 7.004204999999815 y[1] (numeric) = 7.004204999999947 absolute error = 1.323385845353187e-13 relative error = 1.88941620833945e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 7.250404999999806 y[1] (numeric) = 7.250404999999944 absolute error = 1.376676550535194e-13 relative error = 1.898758139076687e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 7.500604999999798 y[1] (numeric) = 7.500604999999941 absolute error = 1.429967255717202e-13 relative error = 1.906469219105979e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 7.754804999999789 y[1] (numeric) = 7.754804999999938 absolute error = 1.49213974509621e-13 relative error = 1.924148634422466e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 8.013004999999781 y[1] (numeric) = 8.013004999999934 absolute error = 1.527666881884215e-13 relative error = 1.906484373695333e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3); Iterations = 981 Total Elapsed Time = 40 Seconds Elapsed Time(since restart) = 39 Seconds Time to Timeout = 9 Minutes 20 Seconds Percent Done = 100.2 %