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Random walks for linear boundary value problems

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Abstract

Chapter 2 is devoted to weak numerical methods for SDEs which are suitable for solving the Cauchy problem for linear parabolic equations. The previous chapter deals with mean-square approximations of SDEs in bounded domains, and its results can be applied for solving boundary value problems. However, since solutions of boundary value problems for parabolic and elliptic equations can be represented as expectations of solutions of the corresponding systems of SDEs in bounded domains, one can apply far more simple weak approximations which certainly should be subject to limitations related to nonexit from the bounded domains. Such weak methods are considered in this chapter.

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© 2004 Springer-Verlag Berlin Heidelberg

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Milstein, G.N., Tretyakov, M.V. (2004). Random walks for linear boundary value problems. In: Stochastic Numerics for Mathematical Physics. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10063-9_6

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  • DOI: https://doi.org/10.1007/978-3-662-10063-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05930-8

  • Online ISBN: 978-3-662-10063-9

  • eBook Packages: Springer Book Archive

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