Summary of Sinc Numerical Methods

Contents Abstract Sinc approximation methods excel for problems whose solutions may have singularities, or innnite domains, or boundary layers. This article summarizes results obtained to date, on Sinc numerical methods of computation. Sinc methods provide procedures for function approximation over bounded or unbounded regions, encompassing interpolation, approximation of derivatives, approximate deenite and indeenite integration, solving initial value ordinary diierential equation problems, approximation and inversion of Fourier and Laplace transforms, approximationof Hilbert transforms, and approximation of indeenite convolutions, the approximate solution of partial diieren-tial equations, and the approximate solution of integral equations, methods for constructing conformal maps, and methods for analytic continuation. Indeed, Sinc are ubiquitous for approximating every operation of calculus.