Developments of DE-Sinc Methods

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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.