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Stochastic methods for Dirichlet problems

  • Research Article
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Journal of Mathematical Modelling and Algorithms

Abstract

Using an equivalent expression for solutions of second order Dirichlet problems in terms of Ito type stochastic differential equations, we develop a numerical solution method for Dirichlet boundary value problems. It is possible with this idea to solve for solution values of a partial differential equation at isolated points without having to construct any kind of mesh and without knowing approximations for the solution at any other points. Our method is similar to a recently published approach, but differs primarily in the handling of the boundary. Some numerical examples are presented, applying these techniques to model Laplace and Poisson equations on the unit disk.

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Authors and Affiliations

  1. Departamento de Mátematica Aplicada, Universidad de Salamanca, Salamanca, Spain, 37008

    J. Vigo-Aguiar

  2. Departamento de Estadística, Universidad de Salamanca, Salamanca, Spain, 37008

    R. Ardanuy-Albajar

  3. Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, WI, 53201-0413, USA

    Bruce A. Wade

Authors
  1. J. Vigo-Aguiar
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  2. R. Ardanuy-Albajar
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  3. Bruce A. Wade
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Corresponding author

Correspondence to J. Vigo-Aguiar.

Additional information

Visiting Professor, Universidad de Salamanca.

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Vigo-Aguiar, J., Ardanuy-Albajar, R. & Wade, B.A. Stochastic methods for Dirichlet problems. J Math Model Algor 4, 317–330 (2005). https://doi.org/10.1007/s10852-005-9007-0

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  • DOI: https://doi.org/10.1007/s10852-005-9007-0

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