Geodesic
The Monte Carlo solution of a boundary value problem for the metaharmonic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 4, pp. 961-969

Voir la notice de l'article provenant de la source Math-Net.Ru

An algorithm of the Monte Carlo method is constructed for solving the metaharmonic equation (1). A system of integral equations of the second kind is derived for the functions $\delta^ku(x)$, $k = 0, 1,..., n-1$. It is shown that if the singularities of the kernels are included in the transition density of the simulated Markov chain, the Neumann series for this system converges, which enables the Monte Carlo method to be used. The case $n=2$, $x\in R^m$, important in the theory of plasticity is discussed in detail. 
@article{ZVMMF_1979_19_4_a15,
     author = {K. K. Sabelfeld},
     title = {The {Monte~Carlo} solution of~a~boundary value problem for the~metaharmonic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {961--969},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_4_a15/}
}
TY  - JOUR
AU  - K. K. Sabelfeld
TI  - The Monte Carlo solution of a boundary value problem for the metaharmonic equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1979
SP  - 961
EP  - 969
VL  - 19
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_4_a15/
LA  - ru
ID  - ZVMMF_1979_19_4_a15
ER  - 
%0 Journal Article
%A K. K. Sabelfeld
%T The Monte Carlo solution of a boundary value problem for the metaharmonic equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1979
%P 961-969
%V 19
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_4_a15/
%G ru
%F ZVMMF_1979_19_4_a15
K. K. Sabelfeld. The Monte Carlo solution of a boundary value problem for the metaharmonic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 4, pp. 961-969. http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_4_a15/