Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations

doi:10.1007/s42967-022-00188-z

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4): 1457-1493.doi: 10.1007/s42967-022-00188-z

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Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations

Xiaoying Han¹, Habib N. Najm²

1. Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL, 36849, USA;
2. Sandia National Laboratories, P. O. Box 969, Livermore, CA, 94551, USA

收稿日期:2021-09-26 修回日期:2022-01-23 出版日期:2022-12-20 发布日期:2022-09-26
通讯作者: Xiaoying Han,E-mail:xzh0003@auburn.edu;Habib N. Najm,E-mail:hnnajm@sandia.gov E-mail:xzh0003@auburn.edu;hnnajm@sandia.gov
基金资助:
The authors acknowledge technical discussions with Prof. Mauro Valorani from Sapienza University of Rome, that helped with the development of ideas. This work was partially supported by the Simons Foundation (Collaboration Grants for Mathematicians No. 419717), and by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES) Division of Chemical Sciences, Geosciences, and Biosciences. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations

Xiaoying Han¹, Habib N. Najm²

1. Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL, 36849, USA;
2. Sandia National Laboratories, P. O. Box 969, Livermore, CA, 94551, USA

Received:2021-09-26 Revised:2022-01-23 Online:2022-12-20 Published:2022-09-26
Supported by:
The authors acknowledge technical discussions with Prof. Mauro Valorani from Sapienza University of Rome, that helped with the development of ideas. This work was partially supported by the Simons Foundation (Collaboration Grants for Mathematicians No. 419717), and by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES) Division of Chemical Sciences, Geosciences, and Biosciences. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

摘要/Abstract

摘要： Numerical algorithms for stiff stochastic differential equations are developed using linear approximations of the fast diffusion processes, under the assumption of decoupling between fast and slow processes. Three numerical schemes are proposed, all of which are based on the linearized formulation albeit with different degrees of approximation. The schemes are of comparable complexity to the classical explicit Euler-Maruyama scheme but can achieve better accuracy at larger time steps in stiff systems. Convergence analysis is conducted for one of the schemes, that shows it to have a strong convergence order of 1/2 and a weak convergence order of 1. Approximations arriving at the other two schemes are discussed. Numerical experiments are carried out to examine the convergence of the schemes proposed on model problems.

关键词: Stiff stochastic differential equation, Fast diffusion, Linear diffusion approximation, Mean-square convergence, Weak convergence

Abstract: Numerical algorithms for stiff stochastic differential equations are developed using linear approximations of the fast diffusion processes, under the assumption of decoupling between fast and slow processes. Three numerical schemes are proposed, all of which are based on the linearized formulation albeit with different degrees of approximation. The schemes are of comparable complexity to the classical explicit Euler-Maruyama scheme but can achieve better accuracy at larger time steps in stiff systems. Convergence analysis is conducted for one of the schemes, that shows it to have a strong convergence order of 1/2 and a weak convergence order of 1. Approximations arriving at the other two schemes are discussed. Numerical experiments are carried out to examine the convergence of the schemes proposed on model problems.

Key words: Stiff stochastic differential equation, Fast diffusion, Linear diffusion approximation, Mean-square convergence, Weak convergence

中图分类号:

Xiaoying Han, Habib N. Najm. Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations[J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1457-1493.

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Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations

Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations

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