Numerical Experiments for Some Markov Models for Solving Boundary Value Problems

The main purpose of this work is the analysis of some stochastic algorithms to determine values of harmonic functions at points of a bounded domain of Euclidean space. To solve the Dirichlet problem we use a Random Walk on Spheres algorithm. The Neumann problem is solved by means of integral equations of potential theory.

[1]  V. V. Nekrutkin,et al.  Random processes for classical equations of mathematical physics , 1991, Acta Applicandae Mathematicae.

[2]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[3]  Karl K. Sabelfeld.  Monte Carlo Methods , 1991 .

[4]  Karl K. Sabelfeld.  Monte Carlo Methods in Boundary Value Problems. , 1991 .