Sinc-Nyström methods for Fredholm integral equations of the second kind over infinite intervals

Abstract

Efficient numerical methods using Sinc quadrature formula are proposed and analyzed for second kind Fredholm integral equations over infinite intervals. These methods are obtained by combining the infinite trapezoidal rule with two concrete families of single and double exponential transformations. In such a way, the integral equation is reduced to a set of linear algebraic equations. Furthermore, optimal error estimates of both schemes are thoroughly provided and shown to have an exponential order of convergence. Several numerical experiments are given for illustration and a comparison with well-known methods is carried out to show the outperformance of our approach in terms of accuracy and efficiency.