A stable numerical method for Volterra integral equations with discontinuous kernel

被引：21

作者：

Messina, E. ^{[1
]}

Russo, E. ^{[1
]}

Vecchio, A. ^{[2
]}

机构：

[1] Univ Naples Federico II, Dipartimento Math & Applicaz, I-80126 Naples, Italy

[2] CNR, Sede Napoli, Ist Appl Calcolo M Picone, I-80131 Naples, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 337卷 / 02期

关键词：

Volterra integral equations; trapezoidal method; direct quadrature methods; discontinuous kernel; constant delay;

D O I：

10.1016/j.jmaa.2007.04.059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Numerical methods for Volterra integral equations with discontinuous kernel need to be tuned to their peculiar form. Here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations. In order to delineate its stability properties, we first investigate about the behavior of the solution of a suitable (basic) test equation and then we find out under which hypotheses the trapezoidal direct quadrature method provides numerical solutions which inherit the properties of the continuous problem. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：1383 / 1393

页数：11

共 16 条

[1]

Alsnar M.H., 2004, INT J COMPUT MATH, V81, P1257

[2] CONVERGENCE AND STABILITY OF QUADRATURE METHODS APPLIED TO VOLTERRA-EQUATIONS WITH DELAY [J].

BAKER, CTH ;

DERAKHSHAN, MS .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1993, 13 (01) :67-91

[3]

Bellman R., 1963, DIFFERENTIAL DIFFERE

[4]

BREDA D, 204 UDMI

[5] COLLOCATION AND CONTINUOUS IMPLICIT RUNGE-KUTTA METHODS FOR A CLASS OF DELAY VOLTERRA INTEGRAL-EQUATIONS [J].

BRUNNER, H .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1994, 53 (01) :61-72

[6]

Brunner H., 1986, CWI MONOGR, V3

[7] Stability criteria for certain delay integral equations of Volterra type [J].

Cahlon, B ;

Schmidt, D .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 84 (02) :161-188

[8]

Cahlon B., 1995, Neural, Parallel & Scientific Computations, V3, P281

[9]

Corduneanu C., 1991, Integral Equations and Applications

[10] Stability of difference Volterra equations: Direct Liapunov method and numerical procedure [J].

Crisci, MR ;

Kolmanovskii, VB ;

Russo, E ;

Vecchio, A .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 36 (10-12) :77-97

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