A convenient technique for solving integral equations of the first kind by the Adomian decomposition method

Abstract

Purpose

In this paper, Fredholm integral equations of the first kind, the Schlomilch integral equation, and a class of related integral equations of the first kind with constant limits of integration are transformed in such a manner that the Adomian decomposition method (ADM) can be applied. Some examples with closed‐form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient. The purpose of this paper is to develop a new iterative procedure where the integral equations of the first kind are recast into a canonical form suitable for the ADM. Hence it examines how this new procedure provides the exact solution.

Design/methodology/approach

The new technique, as presented in this paper in extending the applicability of the ADM, has been shown to be very efficient for solving Fredholm integral equations of the first kind, the Schlomilch integral equation and a related class of nonlinear integral equations with constant limits of integration.

Findings

By using the new proposed technique, the ADM can be easily used to solve the integral equations of the first kind, the Schlomilch integral equation, and a class of related integral equations of the first kind with constant limits of integration.

Originality/value

The paper shows that this new technique is easy to implement and produces accurate results.

Citation

Bougoffa, L., Al‐Haqbani, M. and Rach, R.C. (2012), "A convenient technique for solving integral equations of the first kind by the Adomian decomposition method", Kybernetes, Vol. 41 No. 1/2, pp. 145-156. https://doi.org/10.1108/03684921211213179