WIAS Preprint No. 396, (1998)

Numerical methods for nonlinear parabolic equations with small parameter based on probability approach



Authors

  • Milstein, Grigori N.
  • Tretyakov, Michael V.

2010 Mathematics Subject Classification

  • 35K55 60H10 60H30 65M99

Keywords

  • Semilinear parabolic equations, reaction-diffusion systems, probabilistic representations for equations of mathematical physics, stochastic differential equations with small noise

Abstract

The probabilistic approach is used for constructing special layer methods to solve the Cauchy problem for semilinear parabolic equations with small parameter. In spite of the 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.

Appeared in

  • Mathematics of Computation, vol. 60 (2000), no. 229, pp. 237-267, under new title: Numerical algorithms for semilinear parabolic equations with small parameter based on weak approximation of stochastic differential equations.

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