Numerical expansion methods for solving Fredholm‐Volterra type linear integral equations by interpolation and quadrature rules

Abstract

Purpose

This paper sets out to introduce a numerical method to obtain solutions of Fredholm‐Volterra type linear integral equations.

Design/methodology/approach

The flow of the paper uses well‐known formulations, which are referenced at the end, and tries to construct a new approach for the numerical solutions of Fredholm‐Volterra type linear equations.

Findings

The approach and obtained method exhibit consummate efficiency in the numerical approximation to the solution. This fact is illustrated by means of examples and results are provided in tabular formats.

Research limitations/implications

Although the method is suitable for linear equations, it may be possible to extend the approach to nonlinear, even to singular, equations which are the future objectives.

Practical implications

In many areas of mathematics, mathematical physics and engineering, integral equations arise and most of these equations are only solvable in terms of numerical methods. It is believed that the method is applicable to many problems in these areas such as loads in elastic plates, contact problems of two surfaces, and similar.

Originality/value

The paper is original in its contents, extends the available work on numerical methods in the solution of certain problems, and will prove useful in real‐life problems.

Citation

Yusufoğlu, E. and Erbaş, B. (2008), "Numerical expansion methods for solving Fredholm‐Volterra type linear integral equations by interpolation and quadrature rules", Kybernetes, Vol. 37 No. 6, pp. 768-785. https://doi.org/10.1108/03684920810876972