07-Jan-2022 20:05:56 feynman_kac_2d_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test feynman_kac_2d() FEYNMAN_KAC_2D: MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 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 0.970053 1.000000 0.029947 23 -1.600000 -0.200000 0.716283 0.726149 0.009866 265 -1.600000 0.200000 0.708219 0.726149 0.017930 279 -1.600000 0.600000 0.969075 1.000000 0.030925 24 -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 0.736285 0.755784 0.019498 242 -1.200000 -0.200000 0.533452 0.548812 0.015359 500 -1.200000 0.200000 0.532396 0.548812 0.016416 508 -1.200000 0.600000 0.735610 0.755784 0.020174 245 -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 0.600578 0.618783 0.018206 406 -0.800000 -0.200000 0.434633 0.449329 0.014696 665 -0.800000 0.200000 0.438995 0.449329 0.010334 658 -0.800000 0.600000 0.606285 0.618783 0.012499 398 -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 0.531911 0.548812 0.016901 503 -0.400000 -0.200000 0.387320 0.398519 0.011199 757 -0.400000 0.200000 0.385679 0.398519 0.012840 757 -0.400000 0.600000 0.529823 0.548812 0.018988 507 -0.400000 1.000000 1.000000 1.000000 0.000000 0 0.000000 -1.000000 0.974452 1.000000 0.025548 18 0.000000 -0.600000 0.518795 0.527292 0.008497 526 0.000000 -0.200000 0.372896 0.382893 0.009997 785 0.000000 0.200000 0.369046 0.382893 0.013847 795 0.000000 0.600000 0.513277 0.527292 0.014016 535 0.000000 1.000000 0.975749 1.000000 0.024251 18 0.400000 -1.000000 1.000000 1.000000 0.000000 0 0.400000 -0.600000 0.528050 0.548812 0.020762 513 0.400000 -0.200000 0.388593 0.398519 0.009926 756 0.400000 0.200000 0.385431 0.398519 0.013088 758 0.400000 0.600000 0.535368 0.548812 0.013444 499 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 0.592554 0.618783 0.026229 411 0.800000 -0.200000 0.436328 0.449329 0.013001 664 0.800000 0.200000 0.437308 0.449329 0.012021 653 0.800000 0.600000 0.595823 0.618783 0.022960 410 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 0.734017 0.755784 0.021767 245 1.200000 -0.200000 0.534166 0.548812 0.014645 504 1.200000 0.200000 0.531874 0.548812 0.016937 504 1.200000 0.600000 0.730604 0.755784 0.025179 249 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 0.971755 1.000000 0.028245 22 1.600000 -0.200000 0.708596 0.726149 0.017553 273 1.600000 0.200000 0.712169 0.726149 0.013980 272 1.600000 0.600000 0.970141 1.000000 0.029859 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 = 0.018726 FEYNMAN_KAC_2D: Normal end of execution. Elapsed time is 10.043814 seconds. FEYNMAN_KAC_2D_TEST: Normal end of execution. 07-Jan-2022 20:06:06