##############ECHO OF PROBLEM################# ##############temp/expt_lin_cpostode.ode################# diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 2.0); ! /* 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(5.0/3.0 * expt((0.2 * x + 0.3),3.0)) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.05461333333333335 y[1] (numeric) = 0.05461333333333335 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) = 0.06550666666666669 y[1] (numeric) = 0.06550666666666666 absolute error = 2.775557561562891e-17 relative error = 4.237061207352265e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.07776000000000004 y[1] (numeric) = 0.07776 absolute error = 4.163336342344337e-17 relative error = 5.35408480239755e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.09145333333333337 y[1] (numeric) = 0.09145333333333337 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.1066666666666667 y[1] (numeric) = 0.1066666666666667 absolute error = 1.387778780781446e-17 relative error = 1.301042606982604e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.1234800000000001 y[1] (numeric) = 0.1234800000000001 absolute error = 4.163336342344337e-17 relative error = 3.371668563608952e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.1419733333333335 y[1] (numeric) = 0.1419733333333334 absolute error = 5.551115123125783e-17 relative error = 3.90997026891842e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.1622266666666668 y[1] (numeric) = 0.1622266666666667 absolute error = 1.110223024625157e-16 relative error = 6.843653065413549e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.1843200000000002 y[1] (numeric) = 0.1843200000000001 absolute error = 1.110223024625157e-16 relative error = 6.023345402697241e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.2083333333333335 y[1] (numeric) = 0.2083333333333334 absolute error = 5.551115123125783e-17 relative error = 2.664535259100374e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.2357012683333329 y[1] (numeric) = 0.2357012683333334 absolute error = 4.440892098500626e-16 relative error = 1.884118880607905e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.2639007016666656 y[1] (numeric) = 0.2639007016666666 absolute error = 1.054711873393899e-15 relative error = 3.996623982933214e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.2942641349999982 y[1] (numeric) = 0.294264135 absolute error = 1.77635683940025e-15 relative error = 6.036606667680591e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.3268715683333306 y[1] (numeric) = 0.3268715683333333 absolute error = 2.664535259100376e-15 relative error = 8.151627480745553e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.361803001666663 y[1] (numeric) = 0.3618030016666664 absolute error = 3.386180225106727e-15 relative error = 9.359182233171436e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.3991384349999953 y[1] (numeric) = 0.3991384349999995 absolute error = 4.163336342344337e-15 relative error = 1.043080790338917e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.4389578683333275 y[1] (numeric) = 0.4389578683333324 absolute error = 4.940492459581947e-15 relative error = 1.125504932475736e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.4813413016666595 y[1] (numeric) = 0.4813413016666653 absolute error = 5.773159728050814e-15 relative error = 1.199390060246454e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.5263687349999914 y[1] (numeric) = 0.5263687349999981 absolute error = 6.772360450213455e-15 relative error = 1.286619056166694e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.5741201683333235 y[1] (numeric) = 0.5741201683333311 absolute error = 7.66053886991358e-15 relative error = 1.334309312308641e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.624675601666655 y[1] (numeric) = 0.6246756016666638 absolute error = 8.770761894538737e-15 relative error = 1.404050657835532e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.6781150349999866 y[1] (numeric) = 0.6781150349999965 absolute error = 9.880984919163893e-15 relative error = 1.457125179235126e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.7345184683333179 y[1] (numeric) = 0.734518468333329 absolute error = 1.110223024625157e-14 relative error = 1.511497766889841e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.7939659016666492 y[1] (numeric) = 0.7939659016666616 absolute error = 1.243449787580175e-14 relative error = 1.566124924219031e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.8565373349999802 y[1] (numeric) = 0.8565373349999936 absolute error = 1.343369859796439e-14 relative error = 1.568372801632132e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.9223127683333112 y[1] (numeric) = 0.922312768333326 absolute error = 1.476596622751458e-14 relative error = 1.600971680593536e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.991372201666642 y[1] (numeric) = 0.9913722016666583 absolute error = 1.63202784619898e-14 relative error = 1.646231196976577e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 1.063795634999972 y[1] (numeric) = 1.06379563499999 absolute error = 1.798561299892754e-14 relative error = 1.690701898671355e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 1.139663068333303 y[1] (numeric) = 1.139663068333323 absolute error = 1.976196983832779e-14 relative error = 1.734018622471344e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 1.219054501666633 y[1] (numeric) = 1.219054501666655 absolute error = 2.176037128265307e-14 relative error = 1.785020378736417e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 1.302049934999963 y[1] (numeric) = 1.302049934999986 absolute error = 2.309263891220326e-14 relative error = 1.773560160133483e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 1.388729368333293 y[1] (numeric) = 1.388729368333317 absolute error = 2.442490654175344e-14 relative error = 1.75879527708609e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 1.479172801666623 y[1] (numeric) = 1.479172801666649 absolute error = 2.620126338115369e-14 relative error = 1.771345670474203e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 1.573460234999952 y[1] (numeric) = 1.57346023499998 absolute error = 2.819966482547898e-14 relative error = 1.792207022345235e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 1.67167166833328 y[1] (numeric) = 1.671671668333311 absolute error = 3.086420008457935e-14 relative error = 1.846307541680844e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 1.77388710166661 y[1] (numeric) = 1.773887101666643 absolute error = 3.308464613382966e-14 relative error = 1.865093111210169e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 1.880186534999938 y[1] (numeric) = 1.880186534999974 absolute error = 3.552713678800501e-14 relative error = 1.889553835572287e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 1.990649968333267 y[1] (numeric) = 1.990649968333304 absolute error = 3.752553823233029e-14 relative error = 1.885089735979536e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 2.105357401666595 y[1] (numeric) = 2.105357401666635 absolute error = 3.996802888650564e-14 relative error = 1.898396388891836e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 2.224388834999923 y[1] (numeric) = 2.224388834999965 absolute error = 4.218847493575595e-14 relative error = 1.896632201705751e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 2.347824268333251 y[1] (numeric) = 2.347824268333296 absolute error = 4.440892098500626e-14 relative error = 1.891492544138863e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 2.475743701666579 y[1] (numeric) = 2.475743701666626 absolute error = 4.707345624410664e-14 relative error = 1.901386488933347e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 2.608227134999906 y[1] (numeric) = 2.608227134999956 absolute error = 5.018208071305708e-14 relative error = 1.923991972925275e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 2.745354568333233 y[1] (numeric) = 2.745354568333287 absolute error = 5.329070518200751e-14 relative error = 1.941122862478252e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 2.88720600166656 y[1] (numeric) = 2.887206001666616 absolute error = 5.639932965095795e-14 relative error = 1.953422430488264e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 3.033861434999887 y[1] (numeric) = 3.033861434999946 absolute error = 5.950795411990839e-14 relative error = 1.961459196303427e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 3.185400868333213 y[1] (numeric) = 3.185400868333276 absolute error = 6.261657858885883e-14 relative error = 1.965736218990342e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 3.341904301666538 y[1] (numeric) = 3.341904301666605 absolute error = 6.616929226765933e-14 relative error = 1.979987644609155e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 3.503451734999865 y[1] (numeric) = 3.503451734999933 absolute error = 6.838973831690964e-14 relative error = 1.952067374974477e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 3.67012316833319 y[1] (numeric) = 3.670123168333262 absolute error = 7.149836278586008e-14 relative error = 1.948118891561111e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 2.0); Iterations = 981 Total Elapsed Time = 43 Seconds Elapsed Time(since restart) = 42 Seconds Time to Timeout = 9 Minutes 17 Seconds Percent Done = 100.2 %