Article ID Journal Published Year Pages File Type
1140391 Mathematics and Computers in Simulation 2010 6 Pages PDF
Abstract

In this paper we consider the Monte Carlo solution of the Cauchy problem for a nonlinear parabolic equation. Using the fundamental solution of the heat equation, we obtain a nonlinear integral equation with solution the same as the original partial differential equation. On the basis of this integral representation, we construct a probabilistic representation of the solution to our original Cauchy problem. This representation is based on a branching stochastic process that allows one to directly sample the solution to the full nonlinear problem. Along a trajectory of these branching stochastic processes we build an unbiased estimator for the solution of original Cauchy problem. We then provide results of numerical experiments to validate the numerical method and the underlying stochastic representation.

Related Topics
Physical Sciences and Engineering Engineering Control and Systems Engineering
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