##############ECHO OF PROBLEM################# ##############temp/div_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(10.0* ln(0.2* x + 0.3)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -11.39434283188365 y[1] (numeric) = -11.39434283188365 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) = -10.7880966137193 y[1] (numeric) = -10.78809661371927 absolute error = 2.486899575160351e-14 relative error = 2.305225531626908e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = -10.21651247531981 y[1] (numeric) = -10.21651247531977 absolute error = 4.263256414560601e-14 relative error = 4.172907755811404e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -9.675840262617054 y[1] (numeric) = -9.675840262616999 absolute error = 5.506706202140776e-14 relative error = 5.691191723592345e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -9.162907318741549 y[1] (numeric) = -9.162907318741484 absolute error = 6.572520305780927e-14 relative error = 7.172963860867261e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -8.675005677047228 y[1] (numeric) = -8.675005677047157 absolute error = 7.105427357601002e-14 relative error = 8.19068900023997e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -8.2098055206983 y[1] (numeric) = -8.20980552069822 absolute error = 7.993605777301127e-14 relative error = 9.736656681023567e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -7.76528789498996 y[1] (numeric) = -7.765287894989879 absolute error = 8.08242361927114e-14 relative error = 1.040840175994736e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -7.339691750802001 y[1] (numeric) = -7.339691750801917 absolute error = 8.43769498715119e-14 relative error = 1.149598004061848e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -6.93147180559945 y[1] (numeric) = -6.931471805599362 absolute error = 8.881784197001252e-14 relative error = 1.281370601525968e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -6.520052372287707 y[1] (numeric) = -6.520052372287607 absolute error = 1.003641614261142e-13 relative error = 1.539315264593482e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -6.143360001356569 y[1] (numeric) = -6.143360001356458 absolute error = 1.110223024625157e-13 relative error = 1.807191869563233e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -5.780343734594428 y[1] (numeric) = -5.780343734594309 absolute error = 1.190159082398168e-13 relative error = 2.058976311867505e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -5.430045221302286 y[1] (numeric) = -5.430045221302159 absolute error = 1.270095140171179e-13 relative error = 2.339013927892432e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -5.091603444469328 y[1] (numeric) = -5.09160344446919 absolute error = 1.376676550535194e-13 relative error = 2.703817305392443e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -4.764241970486623 y[1] (numeric) = -4.764241970486479 absolute error = 1.438849039914203e-13 relative error = 3.020100676723684e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -4.447258220614715 y[1] (numeric) = -4.447258220614565 absolute error = 1.501021529293212e-13 relative error = 3.375161627304239e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -4.140014391304558 y[1] (numeric) = -4.140014391304401 absolute error = 1.56319401867222e-13 relative error = 3.775817837627476e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -3.841929728326301 y[1] (numeric) = -3.841929728326138 absolute error = 1.63424829224823e-13 relative error = 4.253717292638183e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -3.552473919475527 y[1] (numeric) = -3.552473919475359 absolute error = 1.683098105331737e-13 relative error = 4.73781973768923e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = -3.271161416971942 y[1] (numeric) = -3.271161416971767 absolute error = 1.749711486809247e-13 relative error = 5.348899866974234e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = -2.997546536860567 y[1] (numeric) = -2.997546536860387 absolute error = 1.803002191991254e-13 relative error = 6.01492644007322e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = -2.731219211204582 y[1] (numeric) = -2.731219211204395 absolute error = 1.869615573468764e-13 relative error = 6.845351577049668e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -2.471801291424584 y[1] (numeric) = -2.471801291424391 absolute error = 1.931788062847772e-13 relative error = 7.815304852981998e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -2.218943319137856 y[1] (numeric) = -2.218943319137657 absolute error = 1.98507876802978e-13 relative error = 8.946054416572745e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -1.972321695297169 y[1] (numeric) = -1.972321695296965 absolute error = 2.040589919261038e-13 relative error = 1.034613128338368e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -1.731636190091974 y[1] (numeric) = -1.731636190091764 absolute error = 2.098321516541546e-13 relative error = 1.211756562116027e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -1.496607745544149 y[1] (numeric) = -1.496607745543934 absolute error = 2.151612221723553e-13 relative error = 1.437659418862123e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -1.266976530459665 y[1] (numeric) = -1.266976530459445 absolute error = 2.20046203480706e-13 relative error = 1.736782001801346e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -1.042500213738084 y[1] (numeric) = -1.042500213737859 absolute error = 2.247091401841317e-13 relative error = 2.155482917153505e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -0.8229524272683969 y[1] (numeric) = -0.8229524272681675 absolute error = 2.293720768875573e-13 relative error = 2.787185131088387e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -0.6081213939676715 y[1] (numeric) = -0.6081213939674377 absolute error = 2.33812968986058e-13 relative error = 3.844840377355442e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -0.3978087001185454 y[1] (numeric) = -0.397808700118307 absolute error = 2.383648833870211e-13 relative error = 5.991947469122454e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -0.1918281941678417 y[1] (numeric) = -0.191828194167599 absolute error = 2.426947531830592e-13 relative error = 1.265167272391207e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 0.009995003330729975 y[1] (numeric) = 0.009995003330978126 absolute error = 2.481504585150063e-13 relative error = 2.48274513078009e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 0.2078253918251776 y[1] (numeric) = 0.2078253918254299 absolute error = 2.523536934972981e-13 relative error = 1.214258235151447e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 0.4018178963282088 y[1] (numeric) = 0.4018178963284654 absolute error = 2.566280521421049e-13 relative error = 6.386675518615741e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 0.5921185963183494 y[1] (numeric) = 0.5921185963186101 absolute error = 2.606803661819868e-13 relative error = 4.402502603411452e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 0.778865386570599 y[1] (numeric) = 0.7788653865708636 absolute error = 2.645661467681748e-13 relative error = 3.39681479405676e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 0.9621885774053139 y[1] (numeric) = 0.9621885774055825 absolute error = 2.685629496568254e-13 relative error = 2.791167510853701e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 1.142211440900112 y[1] (numeric) = 1.142211440900384 absolute error = 2.722266856380884e-13 relative error = 2.383330055104001e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 1.319050708799267 y[1] (numeric) = 1.319050708799543 absolute error = 2.760014439218139e-13 relative error = 2.092424817943945e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 1.492817027157424 y[1] (numeric) = 1.492817027157703 absolute error = 2.791100683907644e-13 relative error = 1.869687063539442e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 1.663615372152131 y[1] (numeric) = 1.663615372152413 absolute error = 2.826627820695649e-13 relative error = 1.699087341949113e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 1.831545430978342 y[1] (numeric) = 1.831545430978628 absolute error = 2.864375403532904e-13 relative error = 1.563911740918632e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 1.996701951285552 y[1] (numeric) = 1.996701951285841 absolute error = 2.899902540320909e-13 relative error = 1.452346224459711e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 2.159175062224575 y[1] (numeric) = 2.159175062224869 absolute error = 2.935429677108914e-13 relative error = 1.359514440707078e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 2.319050569827698 y[1] (numeric) = 2.319050569827994 absolute error = 2.966515921798418e-13 relative error = 1.279194149707062e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 2.476410229145843 y[1] (numeric) = 2.476410229146144 absolute error = 3.006483950684924e-13 relative error = 1.21404923760225e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.631331995303552 y[1] (numeric) = 2.631331995303857 absolute error = 3.04645197957143e-13 relative error = 1.15776039853914e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = 2.0 / (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 %