Sinc-type approximations in H1-norm with applications to boundary value problems

摘要

Sinc functions are used for approximation on a general arc Γ in the complex plane. It is proved that for certain functions analytic in a domain containing the arc Γ, the error of an N-term approximation converges to zero, in the Sobolev space H1(Γ), at the rate O(e−γN12), as N → ∞. Special attention is given to the important case of Γ = (a, b), where a and b are finite real numbers. An application is also considered of the approximate result to the numerical solution of two-point boundary value problems. It is shown that the classical Sinc—Galerkin method with N basis functions has O(e−γN12) convergence rate in the H1-norm.