31 May 2012 01:33:18 PM
FEYNMAN-KAC_2D:
C++ version.
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 ellipsoid parameters A, B are set to:
A = 2
B = 1
Stepsize H = 0.0001
X coordinate marked by %d points
21
Y coordinate marked by %d points
11
X Y W Approx W Exact Error Ave Steps
-2 -1 1 1 0 0
-2 -0.9 1 1 0 0
-2 -0.8 1 1 0 0
-2 -0.7 1 1 0 0
-2 -0.6 1 1 0 0
-2 -0.5 1 1 0 0
-2 -0.4 1 1 0 0
-2 -0.3 1 1 0 0
-2 -0.2 1 1 0 0
-2 -0.1 1 1 0 0
-2 0 0.996029 1 0.0039714 34
-2 0.1 1 1 0 0
-2 0.2 1 1 0 0
-2 0.3 1 1 0 0
-2 0.4 1 1 0 0
-2 0.5 1 1 0 0
-2 0.6 1 1 0 0
-2 0.7 1 1 0 0
-2 0.8 1 1 0 0
-2 0.9 1 1 0 0
-2 1 1 1 0 0
-1.6 -1 1 1 0 0
-1.6 -0.9 1 1 0 0
-1.6 -0.8 1 1 0 0
-1.6 -0.7 1 1 0 0
-1.6 -0.6 0.991435 1 0.00856457 67
-1.6 -0.5 0.889418 0.895834 0.00641612 935
-1.6 -0.4 0.812774 0.818731 0.00595701 1643
-1.6 -0.3 0.754936 0.763379 0.00844366 2284
-1.6 -0.2 0.72409 0.726149 0.00205884 2586
-1.6 -0.1 0.704143 0.704688 0.000544958 2812
-1.6 0 0.69361 0.697676 0.00406601 2907
-1.6 0.1 0.698569 0.704688 0.00611917 2884
-1.6 0.2 0.72244 0.726149 0.00370923 2604
-1.6 0.3 0.757637 0.763379 0.00574299 2226
-1.6 0.4 0.810955 0.818731 0.0077754 1679
-1.6 0.5 0.889728 0.895834 0.00610596 933
-1.6 0.6 0.991988 1 0.00801202 58
-1.6 0.7 1 1 0 0
-1.6 0.8 1 1 0 0
-1.6 0.9 1 1 0 0
-1.6 1 1 1 0 0
-1.2 -1 1 1 0 0
-1.2 -0.9 1 1 0 0
-1.2 -0.8 0.989955 1 0.0100451 82
-1.2 -0.7 0.851214 0.860708 0.00949388 1298
-1.2 -0.6 0.74911 0.755784 0.00667408 2285
-1.2 -0.5 0.675165 0.677057 0.00189192 3125
-1.2 -0.4 0.618513 0.618783 0.000269965 3823
-1.2 -0.3 0.571009 0.57695 0.00594049 4499
-1.2 -0.2 0.54556 0.548812 0.00325213 4856
-1.2 -0.1 0.529337 0.532592 0.00325483 5054
-1.2 0 0.525814 0.527292 0.00147836 5070
-1.2 0.1 0.526124 0.532592 0.00646798 5142
-1.2 0.2 0.543962 0.548812 0.0048501 4863
-1.2 0.3 0.573676 0.57695 0.00327407 4404
-1.2 0.4 0.610494 0.618783 0.00828894 3973
-1.2 0.5 0.672208 0.677057 0.00484844 3178
-1.2 0.6 0.751161 0.755784 0.00462264 2278
-1.2 0.7 0.852566 0.860708 0.00814247 1264
-1.2 0.8 0.989358 1 0.0106425 90
-1.2 0.9 1 1 0 0
-1.2 1 1 1 0 0
-0.8 -1 1 1 0 0
-0.8 -0.9 0.960324 0.970446 0.0101211 313
-0.8 -0.8 0.81255 0.818731 0.00618114 1637
-0.8 -0.7 0.698866 0.704688 0.00582257 2865
-0.8 -0.6 0.613127 0.618783 0.00565657 3907
-0.8 -0.5 0.550366 0.554327 0.003961 4746
-0.8 -0.4 0.499052 0.506617 0.00756479 5573
-0.8 -0.3 0.47031 0.472367 0.00205637 6004
-0.8 -0.2 0.451078 0.449329 0.00174883 6376
-0.8 -0.1 0.43427 0.436049 0.00177921 6677
-0.8 0 0.425333 0.431711 0.00637744 6789
-0.8 0.1 0.433274 0.436049 0.00277485 6698
-0.8 0.2 0.445965 0.449329 0.00336408 6482
-0.8 0.3 0.464204 0.472367 0.00816277 6142
-0.8 0.4 0.497972 0.506617 0.00864472 5619
-0.8 0.5 0.555076 0.554327 0.000748456 4679
-0.8 0.6 0.613292 0.618783 0.00549184 3883
-0.8 0.7 0.697396 0.704688 0.00729193 2875
-0.8 0.8 0.810508 0.818731 0.0082232 1683
-0.8 0.9 0.957916 0.970446 0.0125299 342
-0.8 1 1 1 0 0
-0.4 -1 1 1 0 0
-0.4 -0.9 0.849753 0.860708 0.0109548 1298
-0.4 -0.8 0.718378 0.726149 0.00777085 2627
-0.4 -0.7 0.615675 0.625002 0.00932746 3889
-0.4 -0.6 0.54693 0.548812 0.00188178 4790
-0.4 -0.5 0.486001 0.491644 0.00564314 5770
-0.4 -0.4 0.44641 0.449329 0.00291854 6465
-0.4 -0.3 0.415023 0.418952 0.00392823 6997
-0.4 -0.2 0.395638 0.398519 0.00288137 7439
-0.4 -0.1 0.382118 0.386741 0.00462261 7691
-0.4 0 0.378675 0.382893 0.0042183 7753
-0.4 0.1 0.383302 0.386741 0.00343948 7622
-0.4 0.2 0.39388 0.398519 0.00463923 7526
-0.4 0.3 0.415447 0.418952 0.00350412 7000
-0.4 0.4 0.446283 0.449329 0.00304635 6469
-0.4 0.5 0.488071 0.491644 0.00357359 5758
-0.4 0.6 0.540407 0.548812 0.00840459 4924
-0.4 0.7 0.621933 0.625002 0.00306904 3758
-0.4 0.8 0.717652 0.726149 0.00849697 2662
-0.4 0.9 0.849167 0.860708 0.0115412 1305
-0.4 1 1 1 0 0
0 -1 0.992862 1 0.00713784 53
0 -0.9 0.81407 0.826959 0.012889 1604
0 -0.8 0.683945 0.697676 0.013731 3004
0 -0.7 0.593283 0.600496 0.00721244 4129
0 -0.6 0.51715 0.527292 0.0101426 5274
0 -0.5 0.469941 0.472367 0.00242575 6037
0 -0.4 0.423134 0.431711 0.00857647 6892
0 -0.3 0.399051 0.402524 0.00347293 7292
0 -0.2 0.378374 0.382893 0.00451907 7782
0 -0.1 0.365327 0.371577 0.0062493 7989
0 0 0.364465 0.367879 0.00341474 8101
0 0.1 0.367184 0.371577 0.00439237 7970
0 0.2 0.382486 0.382893 0.000406743 7644
0 0.3 0.395795 0.402524 0.00672939 7350
0 0.4 0.425066 0.431711 0.0066445 6821
0 0.5 0.466269 0.472367 0.00609747 6123
0 0.6 0.517553 0.527292 0.0097399 5299
0 0.7 0.591987 0.600496 0.00850808 4095
0 0.8 0.68728 0.697676 0.0103959 2964
0 0.9 0.812742 0.826959 0.0142175 1683
0 1 0.992868 1 0.00713158 51
0.4 -1 1 1 0 0
0.4 -0.9 0.851527 0.860708 0.0091809 1270
0.4 -0.8 0.720592 0.726149 0.00555686 2602
0.4 -0.7 0.62048 0.625002 0.00452227 3819
0.4 -0.6 0.539831 0.548812 0.00898067 4927
0.4 -0.5 0.486223 0.491644 0.00542128 5738
0.4 -0.4 0.448411 0.449329 0.000917924 6394
0.4 -0.3 0.415248 0.418952 0.00370393 7024
0.4 -0.2 0.394773 0.398519 0.00374611 7385
0.4 -0.1 0.381538 0.386741 0.00520262 7687
0.4 0 0.380041 0.382893 0.00285193 7731
0.4 0.1 0.380601 0.386741 0.00613959 7734
0.4 0.2 0.394348 0.398519 0.00417148 7399
0.4 0.3 0.417196 0.418952 0.00175547 6978
0.4 0.4 0.443375 0.449329 0.00595415 6523
0.4 0.5 0.484059 0.491644 0.00758554 5810
0.4 0.6 0.540187 0.548812 0.00862448 4940
0.4 0.7 0.617597 0.625002 0.00740559 3875
0.4 0.8 0.718704 0.726149 0.00744543 2633
0.4 0.9 0.848387 0.860708 0.0123205 1313
0.4 1 1 1 0 0
0.8 -1 1 1 0 0
0.8 -0.9 0.959545 0.970446 0.0109008 325
0.8 -0.8 0.808388 0.818731 0.0103427 1682
0.8 -0.7 0.69743 0.704688 0.00725839 2847
0.8 -0.6 0.61508 0.618783 0.0037035 3867
0.8 -0.5 0.547997 0.554327 0.00633035 4848
0.8 -0.4 0.500734 0.506617 0.00588273 5550
0.8 -0.3 0.464682 0.472367 0.00768477 6133
0.8 -0.2 0.444687 0.449329 0.00464245 6499
0.8 -0.1 0.43411 0.436049 0.00193967 6646
0.8 0 0.432037 0.431711 0.000326821 6712
0.8 0.1 0.433746 0.436049 0.00230318 6684
0.8 0.2 0.443473 0.449329 0.00585613 6533
0.8 0.3 0.469876 0.472367 0.00249085 6047
0.8 0.4 0.501957 0.506617 0.00465985 5497
0.8 0.5 0.551934 0.554327 0.00239365 4748
0.8 0.6 0.612345 0.618783 0.00643861 3896
0.8 0.7 0.695709 0.704688 0.00897913 2922
0.8 0.8 0.807133 0.818731 0.0115982 1724
0.8 0.9 0.963166 0.970446 0.00727987 301
0.8 1 1 1 0 0
1.2 -1 1 1 0 0
1.2 -0.9 1 1 0 0
1.2 -0.8 0.989069 1 0.0109308 91
1.2 -0.7 0.850681 0.860708 0.0100269 1293
1.2 -0.6 0.745163 0.755784 0.0106206 2357
1.2 -0.5 0.668339 0.677057 0.008718 3196
1.2 -0.4 0.616306 0.618783 0.00247696 3861
1.2 -0.3 0.567613 0.57695 0.00933648 4563
1.2 -0.2 0.54528 0.548812 0.00353198 4853
1.2 -0.1 0.528247 0.532592 0.0043451 5095
1.2 0 0.523779 0.527292 0.00351369 5129
1.2 0.1 0.527828 0.532592 0.00476405 5127
1.2 0.2 0.547309 0.548812 0.00150264 4819
1.2 0.3 0.573876 0.57695 0.00307343 4441
1.2 0.4 0.611253 0.618783 0.00753011 3966
1.2 0.5 0.672302 0.677057 0.00475517 3187
1.2 0.6 0.749237 0.755784 0.00654695 2323
1.2 0.7 0.852286 0.860708 0.00842161 1268
1.2 0.8 0.989236 1 0.0107638 86
1.2 0.9 1 1 0 0
1.2 1 1 1 0 0
1.6 -1 1 1 0 0
1.6 -0.9 1 1 0 0
1.6 -0.8 1 1 0 0
1.6 -0.7 1 1 0 0
1.6 -0.6 0.991527 1 0.0084726 69
1.6 -0.5 0.888088 0.895834 0.00774564 951
1.6 -0.4 0.814629 0.818731 0.00410214 1643
1.6 -0.3 0.761054 0.763379 0.0023256 2167
1.6 -0.2 0.721418 0.726149 0.00473056 2589
1.6 -0.1 0.701224 0.704688 0.00346399 2822
1.6 0 0.692306 0.697676 0.00537037 2921
1.6 0.1 0.700056 0.704688 0.00463182 2857
1.6 0.2 0.720337 0.726149 0.00581189 2606
1.6 0.3 0.759352 0.763379 0.00402736 2221
1.6 0.4 0.810802 0.818731 0.00792838 1714
1.6 0.5 0.887967 0.895834 0.0078672 956
1.6 0.6 0.992113 1 0.00788699 64
1.6 0.7 1 1 0 0
1.6 0.8 1 1 0 0
1.6 0.9 1 1 0 0
1.6 1 1 1 0 0
2 -1 1 1 0 0
2 -0.9 1 1 0 0
2 -0.8 1 1 0 0
2 -0.7 1 1 0 0
2 -0.6 1 1 0 0
2 -0.5 1 1 0 0
2 -0.4 1 1 0 0
2 -0.3 1 1 0 0
2 -0.2 1 1 0 0
2 -0.1 1 1 0 0
2 0 0.996294 1 0.00370631 26
2 0.1 1 1 0 0
2 0.2 1 1 0 0
2 0.3 1 1 0 0
2 0.4 1 1 0 0
2 0.5 1 1 0 0
2 0.6 1 1 0 0
2 0.7 1 1 0 0
2 0.8 1 1 0 0
2 0.9 1 1 0 0
2 1 1 1 0 0
RMS absolute error in solution = 0.00668498
FEYNMAN_KAC_2D:
Normal end of execution.
31 May 2012 01:47:18 PM