D-CONVERGENCE AND STABILITY OF A CLASS OF LINEAR MULTISTEP METHODS FOR NONLINEAR DDES

被引：0

作者：

Cheng-jian Zhang

Xiao-xin Liao (Department of Mathematics

机构：

来源：

Journal of Computational Mathematics | 2000年 / 02期

基金：

中国国家自然科学基金;

关键词：

D-Convergence; Stability; Multistep methods; Nonlinear DDEs;

D O I：

暂无

中图分类号：

O241 [数值分析];

学科分类号：

070102 ;

摘要：

This paper deals with the error behaviour and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation (LMLMs) as applied to the nonlinear delay differential equations (DDEs). It is shown that a LMLM is generally stable with respect to the problem of class D_σγ, and a p-order linear multistep method together with a q-order Lagrangian interpolation leads to a Dconvergent LMLM of order min{p, q + 1}.

引用

页码：199 / 206

页数：8

共 50 条

[1] D-convergence and stability of a class of linear multistep methods for nonlinear DDES
Zhang, CJ
Liao, XX
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2000, 18 (02) : 199 - 206
[2] Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
Zhang, CJ
Zhou, SZ
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 85 (02) : 225 - 237
[3] D-convergence and GDN-stability of Runge-Kutta methods for a class of delay systems
Zhang, CJ
Zhou, SZ
Liao, XX
APPLIED NUMERICAL MATHEMATICS, 2001, 37 (1-2) : 161 - 170
[4] D-convergence of general linear methods for stiff delay differential equations
Huang, CM
Chen, GN
Li, SF
Fu, HY
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 41 (5-6) : 627 - 639
[5] Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations
Yuan, Haiyan
Zhao, Jingjun
Xu, Yang
ABSTRACT AND APPLIED ANALYSIS, 2012,
[6] Convergence and stability of multistep methods solving nonlinear initial value problems
Iavernaro, F.
Mazzia, F.
SIAM Journal of Scientific Computing, 1997, 18 (01): : 270 - 285
[7] Convergence and stability of multistep methods solving nonlinear initial value problems
Iavernaro, F
Mazzia, F
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1997, 18 (01): : 270 - 285
[8] Stability of linear multistep methods and applications to nonlinear parabolic problems
Ostermann, A
Thalhammer, M
Kirlinger, G
APPLIED NUMERICAL MATHEMATICS, 2004, 48 (3-4) : 389 - 407
[9] STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR NONLINEAR DISSIPATIVE EVOLUTION EQUATIONS IN BANACH SPACE
Wang, Wansheng
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2024, 42 (02): : 337 - 354
[10] Asymptotic stability of a class of linear multistep methods for delay differential equations
Yu, Yue-Xin
Wen, Li-Ping
Changsha Dianli Xueyuan Xuebao/Journal of Changsha University of Electric Power, 2003, 18 (03):

← 1 2 3 4 5 →