Further Application of Double Exponential Transformation

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In this study, the Sinc-Galerkin and the Sinc-collocation methods based on the double exponential transformation (DE transformation) for the second order singularly-perturbed boundary value problem of ordinary differential equation is considered. And the approximate solution for the partial differential equation is proposed. It is shown that the error behavior in these methods based on the DE transformation is (exp(-cN/log N)),c>0 where N is a parameter representing the number of terms in the Sinc approximation. High efficiency of the Sinc method based on the DE transformation is confirmed by some numerical examples of singularly-perturbed boundary value problem, and the numerical result exhibits higher efficiency than the one obtained by the Sinc method based on the single exponential (SE) transformation as N becomes large.