Geodesic
A~functional random walk-on-grid algorithm for the biharmonic equation. The error estimation and optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 2, pp. 163-176

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We consider a functional algorithm of random walk-on-grid as applied to the global solution of the Dirichlet problem for the biharmonic equation. In the metric space $C$, a certain upper error bound is constructed, and optimal values (in the sense of the upper error bound) of the algorithm parameters, i.e., the number of grid nodes and the sample size are obtained. We carry out numerical comparison of efficiency of the algorithm in question and the global random walk on spheres algorithm, based on the use of the fundamental solution to the biharmonic equation for the problem of a bending of a thin elastic plate with a simply supported boundary. 
@article{SJVM_2005_8_2_a6,
     author = {E. V. Shkarupa},
     title = {A~functional random walk-on-grid algorithm for the biharmonic equation. {The} error estimation and optimization},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {163--176},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_2_a6/}
}
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E. V. Shkarupa. A~functional random walk-on-grid algorithm for the biharmonic equation. The error estimation and optimization. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 2, pp. 163-176. http://geodesic.mathdoc.fr/item/SJVM_2005_8_2_a6/