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Monte Carlo methods for the solution of nonlinear partial differential equations

✍ Scribed by Guillermo Marshall

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
752 KB
Volume
56
Category
Article
ISSN
0010-4655

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✦ Synopsis

Stochastic models for the solution of nonlinear partial differential equations are discussed. They consist of a discretized version of these equations and Monte Carlo techniques. The Markov transitions are based on a priori estimates of the solution. To improve the efficiency of stochastic smoothers a Monte Carlo multigrid method is presented. The numerical results presented show the convergence of these methods. Some directions for the pamUelization of the Monte Carlo algorithms presented are outlined. The techniques introduced make possible the extension of Monte Carlo methods to nonlinear problems, offering a new approach with an analytic potential for a wide range of problems in computational physics.

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