Sinc-Galerkin method with the double exponential transformation for the two-point boundary value problems

摘要

The Sinc-Galerkin method developed by Stenger [5], when applied to two-point boundary value problems, converges at the rate exp(-κN~(1/2)), where N is the number of basis functions. This paper presents a method obtained by combining the Sinc-Galerkin method with the double exponential transformation technique, which was proposed for numerical integration by Takahasi and Mori [10]. It is shown that the presented method, when applied to two-point boundary value problems that satisfy stronger conditions than the original Sinc-Galerkin method requires, converges at the rate exp(-κ'N/log N).