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Volume 37, Issue 1
Parareal Algorithms Applied to Stochastic Differential Equations with Conserved Quantities

Liying Zhang, Weien Zhou & Lihai Ji

DOI: 10.4208/jcm.1708-m2017-0089

J. Comp. Math., 37 (2019), pp. 48-60.

Published online: 2018-08

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  • 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.

  • Keywords

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

  • AMS Subject Headings

60H10, 60H35, 65Y05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lyzhang@lsec.cc.ac.cn (Liying Zhang)

weienzhou@nudt.edu.cn (Weien Zhou)

jilihai@lsec.cc.ac.cn (Lihai Ji)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-48, author = {Zhang , LiyingZhou , Weien and Ji , Lihai}, title = {Parareal Algorithms Applied to Stochastic Differential Equations with Conserved Quantities}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {1}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1708-m2017-0089}, url = {http://global-sci.org/intro/article_detail/jcm/12648.html} }
TY - JOUR T1 - Parareal Algorithms Applied to Stochastic Differential Equations with Conserved Quantities AU - Zhang , Liying AU - Zhou , Weien AU - Ji , Lihai JO - Journal of Computational Mathematics VL - 1 SP - 48 EP - 60 PY - 2018 DA - 2018/08 SN - 37 DO - http://doi.org/10.4208/jcm.1708-m2017-0089 UR - https://global-sci.org/intro/article_detail/jcm/12648.html KW - Stochastic differential equation, Parareal algorithm, Conserved quantity, Structure-preserving method. AB -

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.

Zhang , LiyingZhou , Weien and Ji , Lihai. (2018). Parareal Algorithms Applied to Stochastic Differential Equations with Conserved Quantities. Journal of Computational Mathematics. 37 (1). 48-60. doi:10.4208/jcm.1708-m2017-0089
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