Year: 2022
Author: Michelle Muniz, Matthias Ehrhardt, Michael Günther, Renate Winkler
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 528–538
Abstract
In this paper we present how nonlinear stochastic Itô differential equations arising in the modelling of perturbed rigid bodies can be solved numerically in such a way that the solution evolves on the correct manifold. To this end, we formulate an approach based on Runge-Kutta–Munthe-Kaas (RKMK) schemes for ordinary differential equations on manifolds.
Moreover, we provide a proof of the mean-square convergence of this stochastic
version of the RKMK schemes applied to the rigid body problem and illustrate the
effectiveness of our proposed schemes by demonstrating the structure preservation of
the stochastic RKMK schemes in contrast to the stochastic Runge-Kutta methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0176
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 528–538
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Stochastic Runge-Kutta method Runge-Kutta–Munthe-Kaas scheme nonlinear Itô SDEs rigid body problem.