14-May-2025 16:50:24 feynman_kac_2d_test(): MATLAB/Octave version 6.4.0 Test feynman_kac_2d() feynman_kac_2d(): Program parameters: The calculation takes place inside a 2D ellipse. A rectangular grid of points will be defined. The solution will be estimated for those grid points that lie inside the ellipse. Each solution will be estimated by computing 10000 trajectories from the point to the boundary. (X/A)^2 + (Y/B)^2 = 1 The ellipse parameters A, B are set to: A = 2.000000 B = 1.000000 Stepsize H = 0.001000 X coordinate marked by 11 points Y coordinate marked by 6 points X Y W W Error Average approx exact Steps -2.000000 -1.000000 1.000000 1.000000 0.000000 0 -2.000000 -0.600000 1.000000 1.000000 0.000000 0 -2.000000 -0.200000 1.000000 1.000000 0.000000 0 -2.000000 0.200000 1.000000 1.000000 0.000000 0 -2.000000 0.600000 1.000000 1.000000 0.000000 0 -2.000000 1.000000 1.000000 1.000000 0.000000 0 -1.600000 -1.000000 1.000000 1.000000 0.000000 0 -1.600000 -0.600000 0.970409 1.000000 0.029591 23 -1.600000 -0.200000 0.714988 0.726149 0.011161 268 -1.600000 0.200000 0.708648 0.726149 0.017501 279 -1.600000 0.600000 0.970135 1.000000 0.029865 25 -1.600000 1.000000 1.000000 1.000000 0.000000 0 -1.200000 -1.000000 1.000000 1.000000 0.000000 0 -1.200000 -0.600000 0.735418 0.755784 0.020366 244 -1.200000 -0.200000 0.538454 0.548812 0.010358 496 -1.200000 0.200000 0.533125 0.548812 0.015687 503 -1.200000 0.600000 0.732710 0.755784 0.023074 250 -1.200000 1.000000 1.000000 1.000000 0.000000 0 -0.800000 -1.000000 1.000000 1.000000 0.000000 0 -0.800000 -0.600000 0.602812 0.618783 0.015972 399 -0.800000 -0.200000 0.435382 0.449329 0.013947 664 -0.800000 0.200000 0.437867 0.449329 0.011462 662 -0.800000 0.600000 0.598541 0.618783 0.020242 407 -0.800000 1.000000 1.000000 1.000000 0.000000 0 -0.400000 -1.000000 1.000000 1.000000 0.000000 0 -0.400000 -0.600000 0.535747 0.548812 0.013065 496 -0.400000 -0.200000 0.386636 0.398519 0.011883 759 -0.400000 0.200000 0.382181 0.398519 0.016338 766 -0.400000 0.600000 0.536065 0.548812 0.012747 494 -0.400000 1.000000 1.000000 1.000000 0.000000 0 0.000000 -1.000000 0.975650 1.000000 0.024350 18 0.000000 -0.600000 0.512516 0.527292 0.014776 536 0.000000 -0.200000 0.370107 0.382893 0.012785 795 0.000000 0.200000 0.373780 0.382893 0.009113 781 0.000000 0.600000 0.516670 0.527292 0.010622 527 0.000000 1.000000 0.975570 1.000000 0.024430 19 0.400000 -1.000000 1.000000 1.000000 0.000000 0 0.400000 -0.600000 0.533355 0.548812 0.015457 507 0.400000 -0.200000 0.387732 0.398519 0.010787 759 0.400000 0.200000 0.386934 0.398519 0.011585 756 0.400000 0.600000 0.530516 0.548812 0.018296 503 0.400000 1.000000 1.000000 1.000000 0.000000 0 0.800000 -1.000000 1.000000 1.000000 0.000000 0 0.800000 -0.600000 0.599904 0.618783 0.018880 403 0.800000 -0.200000 0.432301 0.449329 0.017028 670 0.800000 0.200000 0.435752 0.449329 0.013577 663 0.800000 0.600000 0.604285 0.618783 0.014499 397 0.800000 1.000000 1.000000 1.000000 0.000000 0 1.200000 -1.000000 1.000000 1.000000 0.000000 0 1.200000 -0.600000 0.735521 0.755784 0.020262 245 1.200000 -0.200000 0.540082 0.548812 0.008730 491 1.200000 0.200000 0.536481 0.548812 0.012331 494 1.200000 0.600000 0.731875 0.755784 0.023909 251 1.200000 1.000000 1.000000 1.000000 0.000000 0 1.600000 -1.000000 1.000000 1.000000 0.000000 0 1.600000 -0.600000 0.967992 1.000000 0.032008 25 1.600000 -0.200000 0.711778 0.726149 0.014371 272 1.600000 0.200000 0.710014 0.726149 0.016135 278 1.600000 0.600000 0.969660 1.000000 0.030340 24 1.600000 1.000000 1.000000 1.000000 0.000000 0 2.000000 -1.000000 1.000000 1.000000 0.000000 0 2.000000 -0.600000 1.000000 1.000000 0.000000 0 2.000000 -0.200000 1.000000 1.000000 0.000000 0 2.000000 0.200000 1.000000 1.000000 0.000000 0 2.000000 0.600000 1.000000 1.000000 0.000000 0 2.000000 1.000000 1.000000 1.000000 0.000000 0 RMS absolute error in solution = 0.018127 Elapsed time is 2991.4 seconds. feynman_kac_2d_test(): Normal end of execution. 14-May-2025 17:40:15