##############ECHO OF PROBLEM################# ##############temp/sub_full_linpostode.ode################# diff ( y , x , 1 ) = sin(0.3 * x + 0.1) - (0.1 * x + 0.2) ; ! /* 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 - 0.2 * x - cos(0.3 * x + 0.1) / 0.3); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -3.325706312382627 y[1] (numeric) = -3.325706312382627 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) = -3.33275761125209 y[1] (numeric) = -3.33275761125209 absolute error = 4.440892098500626e-16 relative error = 1.332497774067709e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -3.337847450390901 y[1] (numeric) = -3.337847450390901 absolute error = 4.440892098500626e-16 relative error = 1.330465865952186e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -3.340991497768685 y[1] (numeric) = -3.340991497768686 absolute error = 8.881784197001252e-16 relative error = 2.658427656261036e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -3.342208072368816 y[1] (numeric) = -3.342208072368818 absolute error = 2.220446049250313e-15 relative error = 6.643649949886438e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -3.34151812770257 y[1] (numeric) = -3.341518127702572 absolute error = 1.77635683940025e-15 relative error = 5.316017365500777e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -3.338945232952378 y[1] (numeric) = -3.338945232952379 absolute error = 1.332267629550188e-15 relative error = 3.990085301196042e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -3.334515551761154 y[1] (numeric) = -3.334515551761155 absolute error = 8.881784197001252e-16 relative error = 2.663590575341674e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -3.328257818686781 y[1] (numeric) = -3.328257818686782 absolute error = 8.881784197001252e-16 relative error = 2.668598612503435e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -3.32020331334295 y[1] (numeric) = -3.320203313342952 absolute error = 1.332267629550188e-15 relative error = 4.012608577902998e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -3.309849320398182 y[1] (numeric) = -3.309849320398182 absolute error = 4.440892098500626e-16 relative error = 1.341720322774807e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -3.298219808519757 y[1] (numeric) = -3.298219808519758 absolute error = 8.881784197001252e-16 relative error = 2.692902448180797e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -3.284904341394374 y[1] (numeric) = -3.284904341394375 absolute error = 4.440892098500626e-16 relative error = 1.351909108140287e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -3.269944194846619 y[1] (numeric) = -3.269944194846619 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -3.253383024734048 y[1] (numeric) = -3.253383024734048 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -3.235266827659862 y[1] (numeric) = -3.235266827659862 absolute error = 4.440892098500626e-16 relative error = 1.372650954330348e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -3.215643899579068 y[1] (numeric) = -3.215643899579067 absolute error = 8.881784197001252e-16 relative error = 2.762054653552867e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -3.19456479233538 y[1] (numeric) = -3.19456479233538 absolute error = 4.440892098500626e-16 relative error = 1.390139936793744e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -3.172082268167972 y[1] (numeric) = -3.17208226816797 absolute error = 2.220446049250313e-15 relative error = 6.999963624943202e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -3.148251252229022 y[1] (numeric) = -3.14825125222902 absolute error = 2.220446049250313e-15 relative error = 7.052950579081626e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = -3.123128783154784 y[1] (numeric) = -3.123128783154782 absolute error = 2.664535259100376e-15 relative error = 8.531621473543057e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = -3.096773961734668 y[1] (numeric) = -3.096773961734665 absolute error = 3.552713678800501e-15 relative error = 1.147230544657007e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = -3.069247897724514 y[1] (numeric) = -3.069247897724508 absolute error = 5.329070518200751e-15 relative error = 1.736278950342079e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -3.040613654851937 y[1] (numeric) = -3.040613654851931 absolute error = 5.773159728050814e-15 relative error = 1.898682431698788e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -3.010936194063233 y[1] (numeric) = -3.010936194063226 absolute error = 6.661338147750939e-15 relative error = 2.212381039786007e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -2.980282315062909 y[1] (numeric) = -2.980282315062902 absolute error = 7.105427357601002e-15 relative error = 2.38414573065405e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -2.948720596198457 y[1] (numeric) = -2.948720596198449 absolute error = 7.993605777301127e-15 relative error = 2.710872568803781e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -2.916321332744473 y[1] (numeric) = -2.916321332744463 absolute error = 9.769962616701378e-15 relative error = 3.350098120877209e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -2.883156473641652 y[1] (numeric) = -2.883156473641642 absolute error = 9.769962616701378e-15 relative error = 3.388634195202438e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -2.849299556747598 y[1] (numeric) = -2.849299556747588 absolute error = 1.021405182655144e-14 relative error = 3.584758858493109e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -2.814825642657719 y[1] (numeric) = -2.814825642657708 absolute error = 1.06581410364015e-14 relative error = 3.786430276490673e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -2.779811247155753 y[1] (numeric) = -2.779811247155742 absolute error = 1.154631945610163e-14 relative error = 4.1536343404307e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -2.744334272354731 y[1] (numeric) = -2.744334272354719 absolute error = 1.154631945610163e-14 relative error = 4.207329833109032e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -2.708473936590331 y[1] (numeric) = -2.708473936590318 absolute error = 1.243449787580175e-14 relative error = 4.590960875723032e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -2.672310703129724 y[1] (numeric) = -2.672310703129709 absolute error = 1.465494392505207e-14 relative error = 5.48399701722134e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -2.635926207760065 y[1] (numeric) = -2.635926207760049 absolute error = 1.598721155460225e-14 relative error = 6.065121059738516e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -2.599403185321795 y[1] (numeric) = -2.599403185321778 absolute error = 1.731947918415244e-14 relative error = 6.662867569737306e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -2.562825395252868 y[1] (numeric) = -2.56282539525285 absolute error = 1.77635683940025e-14 relative error = 6.9312440975909e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -2.52627754621091 y[1] (numeric) = -2.526277546210892 absolute error = 1.820765760385257e-14 relative error = 7.20730690543551e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -2.489845219841147 y[1] (numeric) = -2.489845219841129 absolute error = 1.820765760385257e-14 relative error = 7.312766857457196e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -2.4536147937587 y[1] (numeric) = -2.453614793758679 absolute error = 2.042810365310288e-14 relative error = 8.325717510778866e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -2.417673363814558 y[1] (numeric) = -2.417673363814537 absolute error = 2.131628207280301e-14 relative error = 8.816857724391102e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -2.382108665715199 y[1] (numeric) = -2.382108665715176 absolute error = 2.309263891220326e-14 relative error = 9.694200455490126e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -2.347008996066368 y[1] (numeric) = -2.347008996066343 absolute error = 2.442490654175344e-14 relative error = 1.040682271891163e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -2.312463132912096 y[1] (numeric) = -2.312463132912071 absolute error = 2.486899575160351e-14 relative error = 1.075433177621555e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -2.278560255840451 y[1] (numeric) = -2.278560255840426 absolute error = 2.531308496145357e-14 relative error = 1.110924536516889e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -2.245389865727932 y[1] (numeric) = -2.245389865727904 absolute error = 2.797762022055394e-14 relative error = 1.246002783195242e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -2.213041704194713 y[1] (numeric) = -2.213041704194684 absolute error = 2.930988785010413e-14 relative error = 1.324416426249386e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -2.181605672843252 y[1] (numeric) = -2.181605672843223 absolute error = 2.930988785010413e-14 relative error = 1.343500716694828e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -2.15117175235291 y[1] (numeric) = -2.151171752352881 absolute error = 2.886579864025407e-14 relative error = 1.341863968262005e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sin(0.3 * x + 0.1) - (0.1 * x + 0.2) ; Iterations = 981 Total Elapsed Time = 20 Seconds Elapsed Time(since restart) = 20 Seconds Time to Timeout = 9 Minutes 40 Seconds Percent Done = 100.2 %