On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations-Reference-Cited by-同舟云学术

On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations

Published:2010 Issue: Volume:2010 Page:1-18
ISSN:1026-0226
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Messina E.¹^ORCID,Muroya Y.²,Russo E.¹,Vecchio A.³

Affiliation:

1. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy

2. Department of Mathematics, Waseda University, 3-4-1 Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan

3. Istituto per le Applicazioni del Calcolo “M.Picone”, Sede di Napoli, CNR, Via P. Castellino, 80131 Napoli, Italy

Abstract

Here we investigate the behavior of the analytical and numerical solution of a nonlinear second kind Volterra integral equation where the linear part of the kernel has a constant sign and we provide conditions for the boundedness or decay of solutions and approximate solutions obtained by Volterra Runge-Kutta and Direct Quadrature methods.

Publisher

Hindawi Limited

Subject

Modeling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2010/862538.pdf

Reference13 articles.

1. Encyclopedia of Mathematics and Its Applications,1990

2. Mathematics Lecture Note Series,1971

3. On the Asymptotic Behavior of the Bounded Solutions of a Nonlinear Volterra Equation

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