Numerical algorithms for semilinear parabolic equations with small parameter based on approximation of stochastic equations
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- by G. N. Milstein and M. V. Tretyakov PDF
- Math. Comp. 69 (2000), 237-267 Request permission
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.References
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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
- Received by editor(s): April 7, 1998
- Published electronically: May 21, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 237-267
- MSC (1991): Primary 35K55, 60H10, 60H30, 65M99
- DOI: https://doi.org/10.1090/S0025-5718-99-01134-5
- MathSciNet review: 1653966