Numerical Algorithms for Semilinear Parabolic Equations with Small Parameter Based on Approximation of Stochastic Equations

Abstract

The probabilistic approach is used for constructing special layer methods to solve the Cauchy problem for semilinear parabolic equations with small parameter. Despite their probabilistic nature these methods are nevertheless deterministic. The algorithms are tested by simulating the Burgers equation with small viscosity and the generalized KPP-equation with a small parameter.