Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations

被引：1
作者：
Brehier, Charles-Edouard [1 ]
Cohen, David [2 ,3 ]
Ulander, Johan [2 ,3 ]
机构：
[1] Univ Pau & Pays Adour, CNRS, LMAP, E2S UPPA, Pau, France
[2] Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden
[3] Univ Gothenburg, S-41296 Gothenburg, Sweden
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS | 2024年 / 58卷 / 04期
基金：
瑞典研究理事会;
关键词：
Stochastic partial differential equations; stochastic heat equation; splitting scheme; positivity-preserving scheme; mean-square convergence; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT DISCRETIZATION; STRONG-CONVERGENCE; STRICT POSITIVITY; EULER SCHEME; NUMERICAL APPROXIMATION; EXPONENTIAL INTEGRATORS; LATTICE APPROXIMATIONS; SCHRODINGER-EQUATION; COMPARISON PRINCIPLE;
D O I：
10.1051/m2an/2024032
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a positivity-preserving Lie-Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of semilinear stochastic heat equations with multiplicative space-time white noise. We prove that this explicit numerical scheme converges in the mean-square sense, with rate 1/4 in time and rate 1/2 in space, under appropriate CFL conditions. Numerical experiments illustrate the superiority of the proposed numerical scheme compared with standard numerical methods which do not preserve positivity.
引用
收藏
页码：1317 / 1346
页数：30
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