Parareal Algorithms Applied to Stochastic Differential Equations with Conserved Quantities

Parareal Algorithms Applied to Stochastic Differential Equations with Conserved Quantities

Year:    2019

Author:    Liying Zhang, Weien Zhou, Lihai Ji

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 48–60

Abstract

In this paper, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of stochastic differential equations. First, projection methods are introduced as the coarse and fine propagators. Second, we apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm. Finally, three numerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration, and preservation in conserved quantities of model systems.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1708-m2017-0089

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 48–60

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Stochastic differential equation Parareal algorithm Conserved quantity Structure-preserving method.

Author Details

Liying Zhang

Weien Zhou

Lihai Ji

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