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Numerical solution of the Dirichlet problem for nonlinear parabolic equations by a probabilistic approach |
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| Authors: | Milstein G N; Tretyakov M V |
| Institution: | 1 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany. Email: milstein@wias-berlin.de 2 Institute of Mathematics and Mechanics, Russian Academy of Sciences, S. Kovalevskaya Str. 16, 620219 Ekaterinburg, Russia. Email: Michael.Tretyakov@usu.ru |
| Abstract: | A number of new layer methods for solving the Dirichlet problemfor semilinear parabolic equations are constructed by usingprobabilistic representations of their solutions. The methodsexploit the ideas of weak sense numerical integration of stochasticdifferential equations in a bounded domain. Despite their probabilisticnature these methods are nevertheless deterministic. Some convergencetheorems are proved. Numerical tests are presented. |
| Keywords: | weak approximation of stochastic differential equations probabilistic representations for parabolic equations |
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