Numerical Methods for Fredholm Integral Equations of the First Kind

Abstract

In the engineering and scientific fields, many problems can be mathematically described by Fredholm integral equations of the first kind, which have a prominent feature called as “ill-posednessâ€. This feature makes it extremely difficult to obtain the analytical solution. In recent years, various numerical methods have been commonly developed by both international and domestic scholars to solve this kind of equations. In this paper, the mainstream of current numerical methods for Fredholm integral equations of the first kind have been reviewed and evaluated in details, then a guideline of using the intelligence algorithms to solve the Fredholm integral equations of the first kind is provided in the end.