A collocation method for a class of Fredholm integral equations with highly oscillatory kernels

Abstract

In this paper, a collocation method by using Clenshaw–Curtis points is proposed to solve the Fredholm integral equations (FIEs) with highly oscillatory kernels. The collocation method is being applied to graded and uniform meshes. Due to the highly oscillatory kernels of integral equations, the discretized collocation equation will lead to the computation of the oscillatory integrals which will be computed by using the efficient Filon-type method. Finally, the effectiveness and accuracy of the proposed method are confirmed by numerical examples.