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arXiv · 1903.10786

A splitting/polynomial chaos expansion approach for stochastic evolution equations

Andreas Kofler·Tijana Levajković·Hermann Mena·Alexander Ostermann
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Abstract

In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve explicitly by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.

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Andreas Kofler, Tijana Levajković, Hermann Mena, Alexander Ostermann. 2019-03-26. A splitting/polynomial chaos expansion approach for stochastic evolution equations. https://doi.org/10.1007/s00028-020-00627-5

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