THE GPL-STABILITY OF RUNGE-KUTTA METHODS FOR DELAY DIFFERENTIAL SYSTEMS

• 来源期刊: 计算数学（英文版）
• 关键词: Delay differential equation Implicit Runge-Kutta methods GPL stability.
• 年，卷（期）: 2000,（1）
• 页码范围: 75-82
• 页数: 8页
• 语种: 英文

摘要

This paper deals with the GPL-stability of the Implicit Runge-Kutta methods for the numerical solutions of the systems of delay differential equations. We fo cus on the stability behaviour of the Implicit Runge-Kutta(IRK) methods in the solutions of the following test systems with a delay term y＇(t)=Ly(t)+My(t-τ), t≥0, y(t)=φ(t),t≤ 0, where L, M are N×N complex matrices,τ＞ 0,φ(t) is a given vector function. We shall show that the IRK methods is GPL-stable if and only if it is L-stable,when we use the IRK methods to the test systems above.