Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) + a0u([t]) + a1u([t - 1])

Zhanwen Yang; Mingzhu Liu; Minghui Song

doi:10.1016/j.amc.2003.12.081

Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) + a₀u([t]) + a₁u([t - 1])

Zhanwen Yang
, Mingzhu Liu^*
, Minghui Song

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

28 Scopus citations

Abstract

This paper is concerned with the stability analysis of the Runge-Kutta methods for the equation u′(t) = au(t) + a₀u([t]) + a ₁u([t - 1]). The stability regions for the Runge-Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given.

Original language	English
Pages (from-to)	37-50
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	162
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2003.12.081
State	Published - 4 Mar 2005

Keywords

Asymptotic stability
Delay differential equation
Piecewise continuous arguments

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10.1016/j.amc.2003.12.081

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title = "Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) + a0u([t]) + a1u([t - 1])",

abstract = "This paper is concerned with the stability analysis of the Runge-Kutta methods for the equation u′(t) = au(t) + a0u([t]) + a 1u([t - 1]). The stability regions for the Runge-Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given.",

keywords = "Asymptotic stability, Delay differential equation, Piecewise continuous arguments",

author = "Zhanwen Yang and Mingzhu Liu and Minghui Song",

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T1 - Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) + a0u([t]) + a1u([t - 1])

AU - Yang, Zhanwen

AU - Liu, Mingzhu

AU - Song, Minghui

PY - 2005/3/4

Y1 - 2005/3/4

N2 - This paper is concerned with the stability analysis of the Runge-Kutta methods for the equation u′(t) = au(t) + a0u([t]) + a 1u([t - 1]). The stability regions for the Runge-Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given.

AB - This paper is concerned with the stability analysis of the Runge-Kutta methods for the equation u′(t) = au(t) + a0u([t]) + a 1u([t - 1]). The stability regions for the Runge-Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given.

KW - Asymptotic stability

KW - Delay differential equation

KW - Piecewise continuous arguments

UR - https://www.scopus.com/pages/publications/10444220192

U2 - 10.1016/j.amc.2003.12.081

DO - 10.1016/j.amc.2003.12.081

M3 - 文章

AN - SCOPUS:10444220192

SN - 0096-3003

VL - 162

SP - 37

EP - 50

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) + a₀u([t]) + a₁u([t - 1])

Abstract

Keywords

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