Titlebook: Stochastic Numerics for Mathematical Physics; Grigori N. Milstein,Michael V. Tretyakov Book 20041st edition Springer-Verlag Berlin Heidelb

要素

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Book 20041st editionalgorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics..

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Infinitesimal

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Random walks for linear boundary value problems, 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.

Spirometry

Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approlistic approach takes into account a coefficient dependence on the space variables and a relationship between diffusion and advection in an intrinsic manner. In particular, the layer methods allow us to avoid difficulties stemming from essentially changing coefficients and strong advection.

亲属

Simulation of space and space-time bounded diffusions, in a bounded domain, we have to control space increments at each step in a way such that the constructed approximation belongs to the bounded domain. Of course, this cannot be achieved by “ordinary” mean-square methods, and thus special methods are required.

Parallel

Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equationlution and mostly investigated by means of numerical methods. Their investigation is presented in many publications in which deterministic approaches are applicable (see, e.g., [42, 91,143, 259, 269, 291] and references therein). A few authors only exploit probabilistic approaches (see [70,141,288] and references therein).

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