Dissipativity of linear θ-methods for integro-differential equations

被引：20

作者：

Gan, Siqing ^{[1
]}

机构：

[1] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2006年 / 52卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

dissipativity; integro-differential equation; theta-method; A-stability;

D O I：

10.1016/j.camwa.2006.02.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the analytic and numerical dissipativity of nonlinear integro-differential equations (IDEs). A dissipativity criteria for IDEs is given. It is shown that any A-stable linear theta-method for the systems is dissipative. Numerical examples are given to confirm the theoretical results. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：449 / 458

页数：10

共 20 条

[1] STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR VOLTERRA INTEGRAL-EQUATIONS OF THE 2ND KIND [J].

BELLEN, A ;

JACKIEWICZ, Z ;

VERMIGLIO, R ;

ZENNARO, M .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1990, 10 (01) :103-118

[2]

Bellen A., 2003, Numerical methods for delay differential equations, numerical mathematics and scientific computation

[3] STABILITY OF NUMERICAL-METHODS FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS [J].

BRUNNER, H ;

LAMBERT, JD .

COMPUTING, 1974, 12 (01) :75-89

[4]

Burrage K., 1980, BIT (Nordisk Tidskrift for Informationsbehandling), V20, P185, DOI 10.1007/BF01933191

[5]

HALE JK, 1986, P 9 DUND C ORD PART

[6] Dissipativity of Runge-Kutta methods in Hilbert spaces [J].

Hill, AT .

BIT NUMERICAL MATHEMATICS, 1997, 37 (01) :37-42

[7] Global dissipativity for A-stable methods [J].

Hill, AT .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (01) :119-142

[8]

Huang Chengming, 2000, Mathematica Numerica Sinica, V22, P501

[9] Dissipativity of one-leg methods for dynamical systems with delays [J].

Huang, CM .

APPLIED NUMERICAL MATHEMATICS, 2000, 35 (01) :11-22

[10] Dissipativity of Runge-Kutta methods for dynamical systems with delays [J].

Huang, CM .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2000, 20 (01) :153-166

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