Stability analysis of Runge-Kutta methods for Volterra integro-differential equations

被引：8

作者：

Wen, Jiao ^{[1
]}

Huang, Chengming ^{[1
,2
]}

Li, Min ^{[1
]}

机构：

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

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

来源：

APPLIED NUMERICAL MATHEMATICS | 2019年 / 146卷

基金：

中国国家自然科学基金;

关键词：

Runge-Kutta method; Volterra integro-differential equation; Convolution test equation; Collocation method; Stability; NUMERICAL-METHODS;

D O I：

10.1016/j.apnum.2019.07.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the stability properties of Runge-Kutta methods for Volterra integro-differential equations. Both the basic test equation and a convolution test equation are considered. Some fixed order recurrence relations and the corresponding stability conditions are derived for general methods. The concept of V-0-stability is introduced for the convolution test equation and some V-0-stable one-stage methods are found. The A(0)-stability and V-0-stability of the fully implicit discretized collocation methods with one or two stages are investigated in details. Finally, some numerical experiments are given to illustrate the obtained theoretical results. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：73 / 88

页数：16

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