##############ECHO OF PROBLEM################# ##############temp/sub_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(- 0.2 * x * x / 2.0 + 0.1 * x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.009000000000000001 y[1] (numeric) = 0.009000000000000001 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) = 0.01600000000000001 y[1] (numeric) = 0.016 absolute error = 3.469446951953614e-18 relative error = 2.168404344971008e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.02100000000000001 y[1] (numeric) = 0.021 absolute error = 3.469446951953614e-18 relative error = 1.652117596168387e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.02400000000000001 y[1] (numeric) = 0.024 absolute error = 6.938893903907228e-18 relative error = 2.891205793294677e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.025 y[1] (numeric) = 0.02499999999999999 absolute error = 6.938893903907228e-18 relative error = 2.775557561562891e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.02399999999999999 y[1] (numeric) = 0.02399999999999999 absolute error = 3.469446951953614e-18 relative error = 1.44560289664734e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.02099999999999998 y[1] (numeric) = 0.02099999999999998 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.01599999999999997 y[1] (numeric) = 0.01599999999999997 absolute error = 6.938893903907228e-18 relative error = 4.336808689942027e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.008999999999999946 y[1] (numeric) = 0.008999999999999963 absolute error = 1.734723475976807e-17 relative error = 1.927470528863131e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -6.661067097207818e-17 y[1] (numeric) = -4.846383711010205e-17 absolute error = 1.814683386197613e-17 relative error = 27.24313326551373 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.01160249999999981 y[1] (numeric) = -0.01160250000000004 absolute error = 2.324529457808922e-16 relative error = 2.003472922050385e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.02470249999999948 y[1] (numeric) = -0.02470249999999999 absolute error = 5.100087019371813e-16 relative error = 2.064603590475426e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -0.03980249999999906 y[1] (numeric) = -0.03980249999999989 absolute error = 8.326672684688674e-16 relative error = 2.091997408376075e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -0.05690249999999856 y[1] (numeric) = -0.05690249999999976 absolute error = 1.200428645375951e-15 relative error = 2.109623734240114e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -0.07600249999999797 y[1] (numeric) = -0.07600249999999956 absolute error = 1.582067810090848e-15 relative error = 2.081599697497964e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -0.0971024999999973 y[1] (numeric) = -0.09710249999999933 absolute error = 2.026157019940911e-15 relative error = 2.086616739981944e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -0.1202024999999965 y[1] (numeric) = -0.1202024999999991 absolute error = 2.511879593214417e-15 relative error = 2.089706614433551e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -0.1453024999999957 y[1] (numeric) = -0.1453024999999988 absolute error = 3.05311331771918e-15 relative error = 2.101211828921918e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -0.1724024999999948 y[1] (numeric) = -0.1724024999999984 absolute error = 3.608224830031759e-15 relative error = 2.092907486858873e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -0.2015024999999938 y[1] (numeric) = -0.201502499999998 absolute error = 4.163336342344337e-15 relative error = 2.066146247487979e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = -0.2326024999999927 y[1] (numeric) = -0.2326024999999975 absolute error = 4.801714581503802e-15 relative error = 2.064343496524737e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = -0.2657024999999916 y[1] (numeric) = -0.2657024999999971 absolute error = 5.495603971894525e-15 relative error = 2.068329794373293e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = -0.3008024999999903 y[1] (numeric) = -0.3008024999999965 absolute error = 6.217248937900877e-15 relative error = 2.066887388868469e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -0.3379024999999889 y[1] (numeric) = -0.337902499999996 absolute error = 7.049916206369744e-15 relative error = 2.086375864745e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -0.3770024999999875 y[1] (numeric) = -0.3770024999999954 absolute error = 7.827072323607354e-15 relative error = 2.076132737477235e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -0.418102499999986 y[1] (numeric) = -0.4181024999999947 absolute error = 8.715250743307479e-15 relative error = 2.084477070409235e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -0.4612024999999844 y[1] (numeric) = -0.461202499999994 absolute error = 9.603429163007604e-15 relative error = 2.082258696127607e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -0.5063024999999827 y[1] (numeric) = -0.5063024999999933 absolute error = 1.06581410364015e-14 relative error = 2.105093503666655e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -0.5534024999999809 y[1] (numeric) = -0.5534024999999925 absolute error = 1.154631945610163e-14 relative error = 2.086423436125067e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -0.6025024999999791 y[1] (numeric) = -0.6025024999999917 absolute error = 1.265654248072678e-14 relative error = 2.100662234717238e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -0.6536024999999771 y[1] (numeric) = -0.6536024999999909 absolute error = 1.376676550535194e-14 relative error = 2.106290215437123e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -0.7067024999999751 y[1] (numeric) = -0.7067024999999899 absolute error = 1.476596622751458e-14 relative error = 2.089417573521404e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -0.761802499999973 y[1] (numeric) = -0.7618024999999889 absolute error = 1.598721155460225e-14 relative error = 2.098603188438319e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -0.8189024999999708 y[1] (numeric) = -0.818902499999988 absolute error = 1.720845688168993e-14 relative error = 2.101404853653584e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -0.8780024999999685 y[1] (numeric) = -0.8780024999999869 absolute error = 1.84297022087776e-14 relative error = 2.099048944482306e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -0.9391024999999661 y[1] (numeric) = -0.9391024999999859 absolute error = 1.976196983832779e-14 relative error = 2.104346419941221e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -1.002202499999964 y[1] (numeric) = -1.002202499999985 absolute error = 2.109423746787797e-14 relative error = 2.10478795132508e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -1.067302499999961 y[1] (numeric) = -1.067302499999984 absolute error = 2.242650509742816e-14 relative error = 2.101232321429864e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -1.134402499999958 y[1] (numeric) = -1.134402499999982 absolute error = 2.398081733190338e-14 relative error = 2.113960197716795e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -1.203502499999956 y[1] (numeric) = -1.203502499999981 absolute error = 2.55351295663786e-14 relative error = 2.121734650852785e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -1.274602499999953 y[1] (numeric) = -1.27460249999998 absolute error = 2.708944180085382e-14 relative error = 2.125324703258845e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -1.34770249999995 y[1] (numeric) = -1.347702499999979 absolute error = 2.864375403532904e-14 relative error = 2.125376634333623e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -1.422802499999947 y[1] (numeric) = -1.422802499999977 absolute error = 3.019806626980426e-14 relative error = 2.122435564303927e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -1.499902499999944 y[1] (numeric) = -1.499902499999976 absolute error = 3.175237850427948e-14 relative error = 2.116962836203064e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -1.579002499999941 y[1] (numeric) = -1.579002499999975 absolute error = 3.352873534367973e-14 relative error = 2.123412429282473e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -1.660102499999938 y[1] (numeric) = -1.660102499999973 absolute error = 3.530509218307998e-14 relative error = 2.126681465938477e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -1.743202499999934 y[1] (numeric) = -1.743202499999971 absolute error = 3.68594044175552e-14 relative error = 2.11446486667823e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -1.828302499999931 y[1] (numeric) = -1.82830249999997 absolute error = 3.863576125695545e-14 relative error = 2.113203983310032e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -1.915402499999928 y[1] (numeric) = -1.915402499999968 absolute error = 4.063416270128073e-14 relative error = 2.121442501055641e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -2.004502499999924 y[1] (numeric) = -2.004502499999967 absolute error = 4.263256414560601e-14 relative error = 2.126840158373842e-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 = 40 Seconds Elapsed Time(since restart) = 39 Seconds Time to Timeout = 9 Minutes 20 Seconds Percent Done = 100.2 %