##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.1; x_end = 0.5; glob_h = 0.00001; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_max_iter = 20; /* 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_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 - sin(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 0.9001665833531718 y2[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 x[1] = 0.1 y2[1] (analytic) = 0.9001665833531718 y2[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.2000000000000001 y2[1] (analytic) = 0.8013306692049387 y2[1] (numeric) = 0.801330669204942 absolute error = 3.33066907387547e-15 relative error = 4.156422812545139e-13 % Correct digits = 14 h = 0.005 y1[1] (analytic) = 1.980066577841242 y1[1] (numeric) = 1.980066577841227 absolute error = 1.509903313490213e-14 relative error = 7.625517901202989e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.3000000000000002 y2[1] (analytic) = 0.7044797933386603 y2[1] (numeric) = 0.7044797933386699 absolute error = 9.658940314238862e-15 relative error = 1.371074146564709e-12 % Correct digits = 13 h = 0.005 y1[1] (analytic) = 1.955336489125606 y1[1] (numeric) = 1.955336489125577 absolute error = 2.864375403532904e-14 relative error = 1.464901524347763e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.4000000000000002 y2[1] (analytic) = 0.6105816576913493 y2[1] (numeric) = 0.6105816576913684 absolute error = 1.909583602355269e-14 relative error = 3.12748275075202e-12 % Correct digits = 13 h = 0.005 y1[1] (analytic) = 1.921060994002885 y1[1] (numeric) = 1.921060994002844 absolute error = 4.107825191113079e-14 relative error = 2.138310654339854e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5000000000000003 y2[1] (analytic) = 0.5205744613957967 y2[1] (numeric) = 0.5205744613958275 absolute error = 3.086420008457935e-14 relative error = 5.928873268547277e-12 % Correct digits = 13 h = 0.005 y1[1] (analytic) = 1.877582561890373 y1[1] (numeric) = 1.877582561890321 absolute error = 5.195843755245733e-14 relative error = 2.767305076595138e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; Iterations = 80 Total Elapsed Time Unknown Elapsed Time(since restart) Unknown Time to Timeout = 24 Minutes 17 Seconds Percent Done = 101.3 %