Three methods to solve two classes of integral equations of the second kind

Abstract

Three methods to solve two classes of integral equations of the second kind are introduced in this paper. Firstly, two Kantorovich methods are proposed and examined to numerically solving an integral equation appearing from mathematical modeling in biology. We use a sequence of orthogonal nite rank projections. The rst method is based on general grid projections. The second one is established by using the shifted Legendre polynomials. We establish a new convergence analysis and we prove the associated theorems. Secondly, a new Nystrom method is introduced for solving Fredholm integral equation of the second kind.