Further Application of Double Exponential Transformation

本文研究了二阶常微分方程奇异摄动边值问题的基于双指数变换（DE变换）的sincc - galerkin和sincc -配点法。并给出了偏微分方程的近似解。结果表明，基于DE变换的这些方法的误差行为为（exp(-cN/log N)），c>0，其中N是表示Sinc近似中项数的参数。一些奇异摄动边值问题的数值算例证实了基于DE变换的Sinc方法的高效率，并且当N变大时，其数值结果比基于单指数变换的Sinc方法的数值结果效率更高。

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.