A two-parameter Milstein method for stochastic Volterra integral equations

被引：3

作者：

Li, Min ^{[1
,2
]}

Huang, Chengming ^{[3
,4
]}

Wen, Jiao ^{[3
]}

机构：

[1] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China

[2] China Univ Geosci, Ctr Math Sci, Wuhan 430074, Peoples R China

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[4] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 404卷

基金：

中国国家自然科学基金;

关键词：

Two-parameter Milstein scheme; Stochastic Volterra integral equations; Strong convergence; Convolution test equation; Mean-square stability; SEMIIMPLICIT EULER METHOD; STABILITY ANALYSIS; MEAN-SQUARE; INTEGRODIFFERENTIAL EQUATIONS; EXPONENTIAL STABILITY; NUMERICAL-ANALYSIS; MARUYAMA METHOD; CONVERGENCE; APPROXIMATIONS; SCHEMES;

D O I：

10.1016/j.cam.2021.113870

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a two-parameter Milstein method for stochastic Volterra integral equations is introduced. First, the method is proved to be strongly convergent with order one in L-p norm (p >= 1). Then, we investigate the mean square stability of the exact and numerical solutions of a stochastic convolution test equation. Stability conditions are derived. Based on these conditions, analytical and numerical stability regions are plotted and compared with each other. The results show that additional implicitness offers benefits for numerical stability. Finally, some numerical experiments are carried out to confirm the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：20

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