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A probabilistic approach to the solution of the Neumann problem for nonlinear parabolic equations |
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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 2 Institute of Mathematics and Mechanics, Russian Academy of Sciences, S. Kovalevskaya Str. 16, 620219 Ekaterinburg, Russia |
| Abstract: | A number of new layer methods for solving the Neumann 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. In spite of theprobabilistic nature these methods are nevertheless deterministic.Some convergence theorems are proved. Numerical tests on theBurgers equation are presented. |
| Keywords: | Numerical methods for parabolic equations probabilistic representations weak approximation of stochastic differential equations |
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