Numerical methods based on rational variable substitution for Wiener–Hopf equations of the second kind

This paper considers numerical methods for Wiener–Hopf equations of the second kind: y(t)+∫0∞k(t−s)y(s)ds=g(t),0≤t<∞. By applying rational variable substitution to integrals on the semi-infinite interval [0,∞)[0,∞) and using the well-known Clenshaw–Curtis quadrature to the resulted integral, we get a Clenshaw–Curtis-Rational (CCR) quadrature rule. We then apply the CCR quadrature to Wiener–Hopf equations. The reduction of singularities in the transformed equation is considered. Numerical examples are given to illustrate the efficiency of the numerical methods proposed in this paper.