Projection Methods for Integral Equations on the Half-Line

Convergence results are proved for projection methods for integral equations of the form$y(t)=f(t)+∫0∞k(t,s)y(s)ds$ are such that Wiener-Hopf integral equations are included in our analysis. The convergence results indicate that the iterated-projection solution may exhibit superconvergence. The case of collocation using piecewise-constant basis functions applied to an integral equation with kernel $k(t,s)=e−∣t−s∣$ is discussed in detail, and numerical results are given. For this example superconvergence of the iterated solution, and hence also of the collocation solution at the collocation points, is both proved theoretically and observed numerically.