The relationship of degenerate kernel and projection methods on Fredholm integral equations of the second kind

Abstract

In this paper, we show that the degenerate kernel method for some cases, on the condition that the source function is approximated by the same way of producing degenerate kernel, becomes as a projection method. We consider two ways, including Lagrange interpolation and best approximation methods, of producing degenerate kernel approximations of more general Fredholm integral equation of the second kind. For these two ways, we show that the degenerate kernel method becomes as a Lagrange-collocation method and Galerkin method respectively.