Convergence and stability of exponential integrators for semi-linear stochastic variable delay integro-differential equations

被引：4

作者：

Yuan, Haiyan ^{[1
]}

机构：

[1] Heilongjiang Inst Technol, Dept Math, Harbin 150050, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2021年 / 98卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Semi-linear stochastic variable delay integro-differential equation; exponential integrators; mean-square exponential stability; convergence; strong convergence order; EULER-MARUYAMA METHOD; DIFFERENTIAL-EQUATIONS; NUMERICAL-SIMULATION; SCHEME; DISCRETIZATION; RATES;

D O I：

10.1080/00207160.2020.1792452

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the numerical method for semi-linear stochastic variable delay integro-differential equations is studied. The stability of analytic solutions of semi-linear stochastic variable delay integro-differential equations are studied first, some suitable conditions for the mean-square stability of the analytic solutions are also obtained. Then the numerical approximation of exponential integrators for semi-linear stochastic variable delay integro-differential equations are constructed, the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with the strong order 1/2 and the exponential Euler method can keep the mean-square exponential stability of the analytical solution under some restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results.

引用

页码：903 / 932

页数：30

共 45 条

[1] Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition
Andersson, Adam
Kruse, Raphael
[J]. BIT NUMERICAL MATHEMATICS, 2017, 57 (01) : 21 - 53
[2] Arnulf J., 2011, TAYLOR APPROXIMATION
[3] Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
Baker, CTH
Buckwar, E
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 184 (02) : 404 - 427
[4] Ergodicity for functional stochastic differential equations and applications
Bao, Jianhai
Yin, George
Yuan, Chenggui
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 98 : 66 - 82
[5] MS-stability of the Euler-Maruyama method for stochastic differential delay equations
Cao, WR
Liu, MZ
Fan, ZC
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 159 (01) : 127 - 135
[6] Dekker K., 1984, Stability of Runge-Kutta methods for stiff nonlinear differential equations
[7] Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations
Ding, Xiaohua
Wu, Kaining
Liu, Mingzhu
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2006, 83 (10) : 753 - 763
[8] Continuous numerical methods for ODEs with defect control
Enright, WH
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 125 (1-2) : 159 - 170
[9] Erdoan U., 2018, IMA J NUMER ANAL, V39, P820
[10] Friedman A., 1975, STOCHASTIC DIFFERENT, V1

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