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Volume 3, Issue 2
Effectiveness of Implicit Methods for Stiff Stochastic Differential Equations

Tiejun Li, Assyr Abdulle & Weinan E

Commun. Comput. Phys., 3 (2008), pp. 295-307.

Published online: 2008-03

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  • Abstract

In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales. We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale. This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system. 

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@Article{CiCP-3-295, author = {Tiejun Li, Assyr Abdulle and Weinan E}, title = {Effectiveness of Implicit Methods for Stiff Stochastic Differential Equations}, journal = {Communications in Computational Physics}, year = {2008}, volume = {3}, number = {2}, pages = {295--307}, abstract = {

In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales. We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale. This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7854.html} }
TY - JOUR T1 - Effectiveness of Implicit Methods for Stiff Stochastic Differential Equations AU - Tiejun Li, Assyr Abdulle & Weinan E JO - Communications in Computational Physics VL - 2 SP - 295 EP - 307 PY - 2008 DA - 2008/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7854.html KW - AB -

In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales. We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale. This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system. 

Tiejun Li, Assyr Abdulle and Weinan E. (2008). Effectiveness of Implicit Methods for Stiff Stochastic Differential Equations. Communications in Computational Physics. 3 (2). 295-307. doi:
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