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Research Article Open access CC BY 4.0

On the Regularization-Homotopy Analysis Method for Linear and Nonlinear Fredholm Integral Equations of the First Kind

Ibrahim Issaka, William Obeng-Denteh, Isaac Owusu Mensah, Edward Prempeh, Patrick Akwasi Anamuah Mensah

Asian Research Journal of Mathematics · pp. 1–13 · Published 9 May 2017

10.9734/ARJOM/2017/32585

Abstract

Fredholm integral equations of the first kind are considered by applying regularization method and the homotopy analysis method. This kind of integral equations are considered as an ill-posed problem and for this reason needs an effective method in solving them. This method first transforms a given  Fredholm integral equation of the first kind to the second kind by the regularization method and then solves the transformed equation using homotopy analysis method. Approximation of the solution will be of much concern since it is not always the case to get the solution to converge and the existence of the  solution is not always guaranteed as this kind of Fredholm integral equation is not well-posed.

Regularization method Homotopy analysis method ill-posed problem Fredholm integral equation of the first kind Linear and nonlinear

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