On the Regularization-Homotopy Analysis Method for Linear and Nonlinear Fredholm Integral Equations of the First Kind
Ibrahim Issaka
Department of Mathematics, College of Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
William Obeng-Denteh *
Department of Mathematics, College of Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Isaac Owusu Mensah
Department of Science Education, University of Education, Winneba, Mampong-Ashanti, Ghana.
Edward Prempeh
Department of Mathematics, College of Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Patrick Akwasi Anamuah Mensah
Department of Mathematics, College of Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
*Author to whom correspondence should be addressed.
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.
Keywords: Regularization method, Homotopy analysis method, ill-posed problem, Fredholm integral equation of the first kind, Linear and nonlinear