Script H sign -stability of Runge-Kutta methods with general variable stepsize for pantograph equation

Yang Xu; Ming Zhu Liu

doi:10.1016/S0096-3003(02)00947-5

Script H sign -stability of Runge-Kutta methods with general variable stepsize for pantograph equation

Yang Xu^*
, Ming Zhu Liu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

This paper deals with Script H sign-stability of Runge-Kutta methods with variable stepsize for pantograph equations. It is shown that the Runge-Kutta methods with a regular matrix A are Script H sign-stable if and only if the modulus of stability function at infinity is less than 1. Furthermore, the same conclusion can be obtained if the Runge-Kutta methods are stiffly accurate.

Original language	English
Pages (from-to)	881-892
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	148
Issue number	3
DOIs	https://doi.org/10.1016/S0096-3003(02)00947-5
State	Published - 30 Jan 2004

Keywords

Delay differential equations
Infinite lag
Numerical solution
Runge-Kutta method
Stability

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10.1016/S0096-3003(02)00947-5

Cite this

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title = "Script H sign -stability of Runge-Kutta methods with general variable stepsize for pantograph equation",

abstract = "This paper deals with Script H sign-stability of Runge-Kutta methods with variable stepsize for pantograph equations. It is shown that the Runge-Kutta methods with a regular matrix A are Script H sign-stable if and only if the modulus of stability function at infinity is less than 1. Furthermore, the same conclusion can be obtained if the Runge-Kutta methods are stiffly accurate.",

keywords = "Delay differential equations, Infinite lag, Numerical solution, Runge-Kutta method, Stability",

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AU - Xu, Yang

AU - Liu, Ming Zhu

PY - 2004/1/30

Y1 - 2004/1/30

N2 - This paper deals with Script H sign-stability of Runge-Kutta methods with variable stepsize for pantograph equations. It is shown that the Runge-Kutta methods with a regular matrix A are Script H sign-stable if and only if the modulus of stability function at infinity is less than 1. Furthermore, the same conclusion can be obtained if the Runge-Kutta methods are stiffly accurate.

AB - This paper deals with Script H sign-stability of Runge-Kutta methods with variable stepsize for pantograph equations. It is shown that the Runge-Kutta methods with a regular matrix A are Script H sign-stable if and only if the modulus of stability function at infinity is less than 1. Furthermore, the same conclusion can be obtained if the Runge-Kutta methods are stiffly accurate.

KW - Delay differential equations

KW - Infinite lag

KW - Numerical solution

KW - Runge-Kutta method

KW - Stability

UR - https://www.scopus.com/pages/publications/0242438625

U2 - 10.1016/S0096-3003(02)00947-5

DO - 10.1016/S0096-3003(02)00947-5

M3 - 文章

AN - SCOPUS:0242438625

SN - 0096-3003

VL - 148

SP - 881

EP - 892

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 3

ER -

Script H sign -stability of Runge-Kutta methods with general variable stepsize for pantograph equation

Abstract

Keywords

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