Numerical solution of the Dirichlet problem for nonlinear parabolic equations by a probabilistic approach

摘要

A number of new layer methods for solving the Dirichlet problem for semilinear parabolic equations are constructed by using probabilistic representations of their solutions. The methods exploit the ideas of weak sense numerical integration of stochastic differential equations in a bounded domain. Despite their probabilistic nature these methods are nevertheless deterministic. Some theorems are proved. Numerical tests are presented.