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Modified optimal prediction and its application to a particle-method problem. (English) Zbl 1203.65209

Summary: The paper is concerned with system reduction by statistical methods and, in particular, by the optimal prediction method introduced by A. Chorin, O. H. Hald and R. Kupferman [Physica D 166, No. 3-4, 239–257 (2002; Zbl 1017.60046)]. The optimal prediction method deals with problems that possess large and small scales and uses the conditional expectation to model the influence of the small scales on the large ones. In the current paper, we develop a different variant of the optimal prediction method as well as introduce and compare several approximations of this method. We apply the original and modified optimal prediction methods to a system of ODEs obtained from a particle method discretization of a hyperbolic PDE and demonstrate their performance in a number of numerical experiments.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
90C59 Approximation methods and heuristics in mathematical programming

Citations:

Zbl 1017.60046
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References:

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