Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation

A. Rasulov, G. Raimova and M. Mascagni

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 80, issue 6, 1118-1123

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.

Keywords: Monte Carlo method; Cauchy problem; Branching random process; Martingale; Unbiased estimator (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2010:i:6:p:1118-1123

DOI: 10.1016/j.matcom.2009.12.009

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