Communications on Applied Mathematics and Computation >

2022 , Vol. 4 >Issue 4: 1457 - 1493

DOI: https://doi.org/10.1007/s42967-022-00188-z

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

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  • 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 date: 2021-09-26

  Revised date: 2022-01-23

  Online 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.

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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

Cite this article

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 . DOI: 10.1007/s42967-022-00188-z

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