Developments of DE-Sinc Methods

最近的研究表明，当与Takahasi和Mori提出的求积公式的双指数变换相结合时，Stenger和他的同事们发展的SINC数值方法可以产生高效的数值方法(称为DE-SINC方法)。在这里，我们发展了积分方程组、常微分方程组和泊松方程的DE-SINC方法及其理论分析。此外，与它们相关的，我们发展了一个新的大型线性方程组的快速求解器。

Recently it has turned out that, when incorporated with the double exponential transformation proposed by Takahasi and Mori for quadrature formulae, the Sinc numerical methods developed by Stenger and his colleagues, yield highly efficient numerical methods (which are referred to as DE-Sinc methods). We here develop the DE-Sinc methods for integral equations, ordinary differential equations and Poisson equation together with their theoretical analyses. Further, related to them, we develop a new fast solver for a large system of linear equations.