Iterative and Noniterative Splitting Methods of the Stochastic Burgers’ Equation: Theory and Application

Jürgen Geiser
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Jürgen Geiser: The Institute of Theoretical Electrical Engineering, Ruhr University of Bochum, Universitätsstrasse 150, D-44801 Bochum, Germany

Mathematics, 2020, vol. 8, issue 8, 1-28

Abstract: In this paper, we discuss iterative and noniterative splitting methods, in theory and application, to solve stochastic Burgers’ equations in an inviscid form. We present the noniterative splitting methods, which are given as Lie–Trotter and Strang-splitting methods, and we then extend them to deterministic–stochastic splitting approaches. We also discuss the iterative splitting methods, which are based on Picard’s iterative schemes in deterministic–stochastic versions. The numerical approaches are discussed with respect to decomping deterministic and stochastic behaviours, and we describe the underlying numerical analysis. We present numerical experiments based on the nonlinearity of Burgers’ equation, and we show the benefits of the iterative splitting approaches as efficient and accurate solver methods.

Keywords: Burgers’ equation; stochastic differential equation; noniterative splitting; iterative splitting; splitting analysis; deterministic–stochastic splitting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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