##############ECHO OF PROBLEM################# ##############temp/mult_lin_linpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 0.2) * (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(0.06 * x + 2.0/300.0 * x * x * x + 0.035 * x * x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.006356666666666667 y[1] (numeric) = 0.006356666666666667 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) = 0.01345333333333334 y[1] (numeric) = 0.01345333333333334 absolute error = 1.734723475976807e-18 relative error = 1.289437667970867e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.02133000000000001 y[1] (numeric) = 0.02133000000000001 absolute error = 6.938893903907228e-18 relative error = 3.253114816646613e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.03002666666666669 y[1] (numeric) = 0.03002666666666668 absolute error = 6.938893903907228e-18 relative error = 2.310910491976207e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.03958333333333337 y[1] (numeric) = 0.03958333333333335 absolute error = 1.387778780781446e-17 relative error = 3.505967446184702e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.05004000000000004 y[1] (numeric) = 0.05004000000000002 absolute error = 2.081668171172169e-17 relative error = 4.160008335675793e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.06143666666666673 y[1] (numeric) = 0.06143666666666669 absolute error = 4.163336342344337e-17 relative error = 6.776631233808799e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.07381333333333341 y[1] (numeric) = 0.07381333333333334 absolute error = 6.938893903907228e-17 relative error = 9.40059687126159e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.08721000000000009 y[1] (numeric) = 0.08721000000000001 absolute error = 8.326672684688674e-17 relative error = 9.547841629043303e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.1016666666666668 y[1] (numeric) = 0.1016666666666667 absolute error = 6.938893903907228e-17 relative error = 6.825141544826775e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.1180307591666664 y[1] (numeric) = 0.1180307591666667 absolute error = 2.636779683484747e-16 relative error = 2.233976721069343e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.1347854758333327 y[1] (numeric) = 0.1347854758333333 absolute error = 5.828670879282072e-16 relative error = 4.324405759037007e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.1527221924999989 y[1] (numeric) = 0.1527221924999999 absolute error = 9.436895709313831e-16 relative error = 6.17912534834379e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.1718809091666651 y[1] (numeric) = 0.1718809091666665 absolute error = 1.360023205165817e-15 relative error = 7.912590244953058e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.1923016258333312 y[1] (numeric) = 0.192301625833333 absolute error = 1.804112415015879e-15 relative error = 9.381680509448801e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.2140243424999973 y[1] (numeric) = 0.2140243424999995 absolute error = 2.248201624865942e-15 relative error = 1.050442019167035e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.2370890591666633 y[1] (numeric) = 0.2370890591666659 absolute error = 2.692290834716005e-15 relative error = 1.135560976191416e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.2615357758333292 y[1] (numeric) = 0.2615357758333324 absolute error = 3.219646771412954e-15 relative error = 1.231054054136273e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.2874044924999951 y[1] (numeric) = 0.2874044924999988 absolute error = 3.774758283725532e-15 relative error = 1.313395713090879e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.3147352091666609 y[1] (numeric) = 0.3147352091666653 absolute error = 4.385380947269368e-15 relative error = 1.393355690607589e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.3435679258333266 y[1] (numeric) = 0.3435679258333317 absolute error = 5.10702591327572e-15 relative error = 1.48646760342619e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.3739426424999923 y[1] (numeric) = 0.3739426424999979 absolute error = 5.662137425588298e-15 relative error = 1.514172705133091e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.4058993591666579 y[1] (numeric) = 0.4058993591666641 absolute error = 6.217248937900877e-15 relative error = 1.531721791989364e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.4394780758333234 y[1] (numeric) = 0.4394780758333304 absolute error = 6.994405055138486e-15 relative error = 1.591525366055163e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.4747187924999888 y[1] (numeric) = 0.4747187924999964 absolute error = 7.66053886991358e-15 relative error = 1.613700361338394e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.5116615091666541 y[1] (numeric) = 0.5116615091666628 absolute error = 8.659739592076221e-15 relative error = 1.692474309076011e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.5503462258333194 y[1] (numeric) = 0.5503462258333289 absolute error = 9.547918011776346e-15 relative error = 1.734892975293716e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.5908129424999845 y[1] (numeric) = 0.5908129424999948 absolute error = 1.032507412901396e-14 relative error = 1.74760459466648e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.6331016591666495 y[1] (numeric) = 0.6331016591666606 absolute error = 1.110223024625157e-14 relative error = 1.75362520149851e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 0.6772523758333145 y[1] (numeric) = 0.6772523758333264 absolute error = 1.187938636348917e-14 relative error = 1.754056063498097e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 0.7233050924999793 y[1] (numeric) = 0.7233050924999922 absolute error = 1.287858708565182e-14 relative error = 1.780519343661635e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 0.7712998091666441 y[1] (numeric) = 0.7712998091666579 absolute error = 1.376676550535194e-14 relative error = 1.784878634966387e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 0.8212765258333088 y[1] (numeric) = 0.8212765258333236 absolute error = 1.476596622751458e-14 relative error = 1.797928683342347e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 0.8732752424999733 y[1] (numeric) = 0.8732752424999897 absolute error = 1.63202784619898e-14 relative error = 1.868858484441725e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 0.9273359591666378 y[1] (numeric) = 0.9273359591666553 absolute error = 1.754152378907747e-14 relative error = 1.891603966791214e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.9834986758333021 y[1] (numeric) = 0.9834986758333208 absolute error = 1.876276911616515e-14 relative error = 1.90775743549098e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 1.041803392499966 y[1] (numeric) = 1.041803392499987 absolute error = 2.042810365310288e-14 relative error = 1.960840577038488e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 1.10229010916663 y[1] (numeric) = 1.102290109166652 absolute error = 2.131628207280301e-14 relative error = 1.933817775877428e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 1.164998825833294 y[1] (numeric) = 1.164998825833317 absolute error = 2.220446049250313e-14 relative error = 1.905964194995719e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 1.229969542499958 y[1] (numeric) = 1.229969542499981 absolute error = 2.309263891220326e-14 relative error = 1.877496809007695e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 1.297242259166622 y[1] (numeric) = 1.297242259166647 absolute error = 2.486899575160351e-14 relative error = 1.917066421161759e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 1.366856975833286 y[1] (numeric) = 1.366856975833312 absolute error = 2.642330798607873e-14 relative error = 1.933143588045861e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 1.438853692499949 y[1] (numeric) = 1.438853692499977 absolute error = 2.775557561562891e-14 relative error = 1.929006108147434e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 1.513272409166613 y[1] (numeric) = 1.513272409166642 absolute error = 2.90878432451791e-14 relative error = 1.922181562881882e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 1.590153125833276 y[1] (numeric) = 1.590153125833307 absolute error = 3.086420008457935e-14 relative error = 1.940957734394656e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 1.669535842499939 y[1] (numeric) = 1.669535842499971 absolute error = 3.197442310920451e-14 relative error = 1.915168413594911e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 1.751460559166602 y[1] (numeric) = 1.751460559166635 absolute error = 3.375077994860476e-14 relative error = 1.927007706337641e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.835967275833265 y[1] (numeric) = 1.8359672758333 absolute error = 3.574918139293004e-14 relative error = 1.94715787495205e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.923095992499927 y[1] (numeric) = 1.923095992499965 absolute error = 3.730349362740526e-14 relative error = 1.939762433746878e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.01288670916659 y[1] (numeric) = 2.012886709166628 absolute error = 3.863576125695545e-14 relative error = 1.91942055561349e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3); Iterations = 981 Total Elapsed Time = 43 Seconds Elapsed Time(since restart) = 42 Seconds Time to Timeout = 9 Minutes 17 Seconds Percent Done = 100.2 %