Convergence and stability of an explicit method for nonlinear stochastic differential equations with piecewise continuous arguments

被引：0

作者：

Shi, Hongling ^{[1
]}

Song, Minghui ^{[1
]}

Liu, Mingzhu ^{[1
]}

机构：

[1] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 438卷

关键词：

Local Lipschitz continuous; Superlinearly growing coefficients; Explicit method; Convergence rate; Mean square exponential stability; EULER-MARUYAMA METHOD; THETA METHOD; TIME; STABILIZATION;

D O I：

10.1016/j.cam.2023.115549

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper constructs a new explicit method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), where the drift coefficients grow superlinearly and the diffusion coefficients have at most linear growth. We show that this method converges strongly with the convergence rate 1/2 to the exact solutions of SDEPCAs over the finite time interval and demonstrate it can inherit the mean square exponential stability of the underlying SDEPCAs. Several numerical experiments are carried out to support our findings.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：16

共 50 条

[21] Convergence and asymptotic stability of the explicit Steklov method for stochastic differential equations
Diaz-Infante, Saul
Jerez, Silvia
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 291 : 36 - 47
[22] Convergence and stability of the compensated split-step theta method for stochastic differential equations with piecewise continuous arguments driven by Poisson random measure
Lu, Yulan
Song, Minghui
Liu, Mingzhu
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 340 : 296 - 317
[23] The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations
Song, Guoting
Hu, Junhao
Gao, Shuaibin
Li, Xiaoyue
NUMERICAL ALGORITHMS, 2022, 89 (02) : 855 - 883
[24] The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations
Guoting Song
Junhao Hu
Shuaibin Gao
Xiaoyue Li
Numerical Algorithms, 2022, 89 : 855 - 883
[25] Stability of θ-methods for advanced differential equations with piecewise continuous arguments
Song, MH
Yang, ZW
Liu, MZ
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (9-10) : 1295 - 1301
[26] Convergence of the Tamed Euler Method for Stochastic Differential Equations with Piecewise Continuous Arguments Under Non-global Lipschitz Continuous Coefficients
Song, M. H.
Lu, Y. L.
Liu, M. Z.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2018, 39 (05) : 517 - 536
[27] Almost Sure Exponential Stability of Numerical Solutions for Stochastic Differential Equations with Piecewise Continuous Arguments
Zhang, Ling
Guo, Shuang
Liu, Guoqing
INTERNATIONAL CONFERENCE ON COMPUTATIONAL AND INFORMATION SCIENCES (ICCIS 2014), 2014, : 439 - 445
[28] Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods
Song, Minghui
Geng, Yidan
Liu, Mingzhu
APPLIED MATHEMATICS AND COMPUTATION, 2021, 400
[29] Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments
Liu, X.
Liu, M. Z.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 280 : 265 - 274
[30] Convergence and stability of spectral collocation method for hyperbolic partial differential equation with piecewise continuous arguments
Yongtang Chen
Qi Wang
Computational and Applied Mathematics, 2022, 41

← 1 2 3 4 5 →