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International. Mathematical. Forum, 2, 2001, no. 33, 1625 -1635. A Taylor. Polynomial. _L\pproach for Solving. Volterra-Hammerstein. Integral. Equations. of Mixed. Type. Ronak Azizi, Naser Azizi and Esmaeil Yousefi. Department of Mathematics, Faculty of Science.

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Presentation Transcript

International

Mathematical

Forum, 2, 2001, no. 33, 1625 -1635

A Taylor

Polynomial

_L\pproach for Solving

Volterra-Hammerstein

Integral

Equations

of Mixed

Type

Ronak Azizi, Naser Azizi and Esmaeil Yousefi

Department of Mathematics, Faculty of Science

P.O. Box 31485-313,

Karaj, Iran

Abstract

Integral equations of mixed Voltera-Fredholm type arise in various

physical and biological problems. I!l the present paper, we obtain the

approximate solution of the nonlin~ar Volterra-Hammerstein integral

equations of mixed type in terms cf Taylor polynomial. The reliabil-

ity and efficiency of the proposed s:heme are demonstrated by some

numerical experiments.

Keywords:

Taylor polynomials, \"clterrarHammerstein integral equations

of mixed ty-pe

1

Introduction

In this paper, we will consider the approximate solution of the nonlinear

VolterrarHammerstein integral equation of mixed type

y(x) = f(x) + f 1%KI'(x, t) 9",(t,

y(t))dt,

a ~ x ~ x,

(1)

1'=1 a