Stability of Runge-Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments

被引：8

作者：

Lv, W. J. ^{[1
]}

Yang, Z. W. ^{[1
]}

Liu, M. Z. ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2007年 / 54卷 / 03期

基金：

中国国家自然科学基金;

关键词：

alternately advanced and retarded differential equations; piecewise continuous arguments; asymptotical stability;

D O I：

10.1016/j.camwa.2006.07.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the numerical properties of Runge-Kutta methods for the solution of u'(t) = au(t) + a(0)u([t + 1/2]). It is shown that the Runge-Kutta method can preserve the convergence order. The necessary and sufficient conditions under which the analytical stability region is contained in the numerical stability region are obtained. It is interesting that the theta-methods with 0 <= theta < 1/2 are asymptotically stable. Some numerical experiments are given. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：326 / 335

页数：10

共 50 条

[41] Stability analysis of Runge-Kutta methods for systems of delay differential equations
intHout, KJ
IMA JOURNAL OF NUMERICAL ANALYSIS, 1997, 17 (01) : 17 - 27
[42] Stability of Runge-Kutta methods for delay integro-differential equations
Koto, T
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 145 (02) : 483 - 492
[43] STABILITY OF RUNGE-KUTTA METHODS FOR STIFF ORDINARY DIFFERENTIAL-EQUATIONS
ALEXANDER, RK
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (04) : 1147 - 1168
[44] Stability and convergence analysis of stochastic Runge-Kutta and balanced stochastic Runge-Kutta methods for solving stochastic differential equations
Rahimi, Vaz'he
Ahmadian, Davood
Rathinasamy, Anandaraman
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2024, : 1397 - 1417
[45] Analytical Approximation Solution for Differential Equations with Piecewise Constant Arguments of Alternately Advanced and Retarded Type
Wang, Qi
Guo, Cui
Zeng, Ruixiang
INFORMATION COMPUTING AND APPLICATIONS, ICICA 2013, PT II, 2013, 392 : 242 - +
[46] SINGLY-IMPLICIT RUNGE-KUTTA METHODS FOR RETARDED AND ORDINARY DIFFERENTIAL-EQUATIONS
CLAUS, H
COMPUTING, 1990, 43 (03) : 209 - 222
[47] Dissipativity of Runge-Kutta methods for neutral delay differential equations with piecewise constant delay
Wang, Wan-Sheng
Li, Shou-Fu
APPLIED MATHEMATICS LETTERS, 2008, 21 (09) : 983 - 991
[48] Continuous two-step Runge-Kutta methods for ordinary differential equations
D'Ambrosio, Raffaele
Jackiewicz, Zdzislaw
NUMERICAL ALGORITHMS, 2010, 54 (02) : 169 - 193
[49] Runge-Kutta methods for linear ordinary differential equations
Zingg, DW
Chisholm, TT
APPLIED NUMERICAL MATHEMATICS, 1999, 31 (02) : 227 - 238
[50] The development of Runge-Kutta methods for partial differential equations
vanderHouwen, PJ
APPLIED NUMERICAL MATHEMATICS, 1996, 20 (03) : 261 - 272

← 1 2 3 4 5 →