Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations

被引：4

作者：

Gao, Jianfang ^{[1
]}

Ma, Shufang ^{[2
]}

Liang, Hui ^{[3
]}

机构：

[1] Harbin Normal Univ, Sch Math Sci, Harbin, Heilongjiang, Peoples R China

[2] Northeast Forest Univ, Dept Math, Harbin, Heilongjiang, Peoples R China

[3] Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2019年 / 12卷 / 02期

关键词：

Stochastic Volterra integro-differential equations; semi-implicit Euler methods; boundedness; convergence; FREDHOLM INTEGRAL-EQUATIONS; BLOCK-PULSE FUNCTIONS; NUMERICAL-SOLUTION; COMPUTATIONAL METHOD; COLLOCATION METHODS; TAYLOR-SERIES; 2ND KIND; SYSTEM; SUPERCONVERGENCE; APPROXIMATIONS;

D O I：

10.4208/nmtma.OA-2017-0030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is mainly concerned with the strong convergence analysis of the semi-implicit Euler method for a kind of stochastic Volterra integro-differential equations (SVIDEs). The solvability and the mean-square boundedness of numerical solutions are presented. In view of the properties of the Ito integral, different from the known stochastic problems, it is proved that the strong convergence order of the semiimplicit Euler method is 1, although the approximation order of the Ito integral is 0.5. The theoretical results are illustrated by extensive numerical examples.

引用

页码：547 / 565

页数：19

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