Volume 25, Issue 5
Explicit Integration of Stiff Stochastic Differential Equations via an Efficient Implementation of Stochastic Computational Singular Perturbation

Lijin Wang, Yanzhao Cao & Sau-Hai Lam

Commun. Comput. Phys., 25 (2019), pp. 1523-1546.

Published online: 2019-01

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  • Abstract

Numerical integration of stiff stochastic differential equations based on stochastic computational singular perturbation (SCSP) was recently developed in [62]. In this paper, a modified stochastic computational singular perturbation (MSCSP) method is considered. Similar to what was proposed in [26] for deterministic chemical reaction systems, the current study applies the sensitivity derivatives of the forcing terms with respect to the state variables to measure the reaction scales, which leads to a quasi-steady state equation for the fast species. This yields explicit large-step integrators for stochastic fast-slow stiff differential equations systems, which removes the expensive eigen-calculations of the standard SCSP integrators. The efficiency of the MSCSP integrators is demonstrated with the benchmark stochastic Davis-Skodje model and a nonlinear catalysis model under certain stochastic disturbances.

  • Keywords

Stochastic computational singular perturbation, stochastic fast-slow stiff differential equations systems, numerical integrations of SDEs with stiffness, quasi-steady state approach, stochastic Davis-Skodje model, catalysis model.

  • AMS Subject Headings

34E13, 34E15, 60H10, 60H35, 65C20, 65C30, 65D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-1523, author = {}, title = {Explicit Integration of Stiff Stochastic Differential Equations via an Efficient Implementation of Stochastic Computational Singular Perturbation}, journal = {Communications in Computational Physics}, year = {2019}, volume = {25}, number = {5}, pages = {1523--1546}, abstract = {

Numerical integration of stiff stochastic differential equations based on stochastic computational singular perturbation (SCSP) was recently developed in [62]. In this paper, a modified stochastic computational singular perturbation (MSCSP) method is considered. Similar to what was proposed in [26] for deterministic chemical reaction systems, the current study applies the sensitivity derivatives of the forcing terms with respect to the state variables to measure the reaction scales, which leads to a quasi-steady state equation for the fast species. This yields explicit large-step integrators for stochastic fast-slow stiff differential equations systems, which removes the expensive eigen-calculations of the standard SCSP integrators. The efficiency of the MSCSP integrators is demonstrated with the benchmark stochastic Davis-Skodje model and a nonlinear catalysis model under certain stochastic disturbances.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0138}, url = {http://global-sci.org/intro/article_detail/cicp/12960.html} }
TY - JOUR T1 - Explicit Integration of Stiff Stochastic Differential Equations via an Efficient Implementation of Stochastic Computational Singular Perturbation JO - Communications in Computational Physics VL - 5 SP - 1523 EP - 1546 PY - 2019 DA - 2019/01 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0138 UR - https://global-sci.org/intro/article_detail/cicp/12960.html KW - Stochastic computational singular perturbation, stochastic fast-slow stiff differential equations systems, numerical integrations of SDEs with stiffness, quasi-steady state approach, stochastic Davis-Skodje model, catalysis model. AB -

Numerical integration of stiff stochastic differential equations based on stochastic computational singular perturbation (SCSP) was recently developed in [62]. In this paper, a modified stochastic computational singular perturbation (MSCSP) method is considered. Similar to what was proposed in [26] for deterministic chemical reaction systems, the current study applies the sensitivity derivatives of the forcing terms with respect to the state variables to measure the reaction scales, which leads to a quasi-steady state equation for the fast species. This yields explicit large-step integrators for stochastic fast-slow stiff differential equations systems, which removes the expensive eigen-calculations of the standard SCSP integrators. The efficiency of the MSCSP integrators is demonstrated with the benchmark stochastic Davis-Skodje model and a nonlinear catalysis model under certain stochastic disturbances.

Lijin Wang, Yanzhao Cao & Sau-Hai Lam. (2020). Explicit Integration of Stiff Stochastic Differential Equations via an Efficient Implementation of Stochastic Computational Singular Perturbation. Communications in Computational Physics. 25 (5). 1523-1546. doi:10.4208/cicp.OA-2018-0138
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