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Numerical algorithms for semilinear parabolic equations with small parameter based on approximation of stochastic equations


Authors: G. N. Milstein and M. V. Tretyakov
Journal: Math. Comp. 69 (2000), 237-267
MSC (1991): Primary 35K55, 60H10, 60H30, 65M99
Published electronically: May 21, 1999
MathSciNet review: 1653966
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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.


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Additional Information

G. N. Milstein
Affiliation: Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117 Berlin, Germany
Email: milstein@wias-berlin.de

M. V. Tretyakov
Affiliation: Department of Mathematics, Ural State University, Lenin str. 51, 620083 Ekaterinburg, Russia
Email: Michael.Tretyakov@usu.ru

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01134-5
Keywords: Semilinear parabolic equations, reaction-diffusion systems, probabilistic representations for equations of mathematical physics, stochastic differential equations with small noise
Received by editor(s): April 7, 1998
Published electronically: May 21, 1999
Article copyright: © Copyright 1999 American Mathematical Society