The double-exponential transformation in numerical analysis [PDF]
Journal of Computational and Applied Mathematics, 2001 The authors present a review of results to the double-exponential transformation in numerical integration and in a variety of Sinc numerical methods.
Masaaki Sugihara
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Double exponential transformation in the Sinc-collocation method for two-point boundary value problems [PDF]
Journal of Computational and Applied Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Masaaki Sugihara
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Double exponential transformation in the Sinc-collocation method for a boundary value problem with fourth-order ordinary differential equation [PDF]
Journal of Computational and Applied Mathematics, 2005 A sinc-collocation method is used for the numerical solution for two point boundary value problem of a linear fourth-order ordinary differential equation. The authors incorporate this method with the double exponential transformation and show its convergence rate. Four numerical examples are solved.
Masaaki Sugihara, Masatake Mori
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Double exponential transformation: a quick review of a Japanese tradition
Japan Journal of Industrial and Applied Mathematics, 2023 10 ...
Kazuo Murota, Takayasu Matsuo
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Journal of Computational and Applied Mathematics, 2005 Numerical solutions of linear Volterra integral equations of the first and second kind and Fredholm integral equations of the second kind are obtained by means of the sinc collocation method based on the double exponential transformation. A formula for numerical indefinite integration, developed earlier by \textit{M. Muhammad} and \textit{M.
Masaaki Sugihara, Masatake Mori
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Numerical solution of nonlinear Hammerstein integral equations via Sinc collocation method based on double exponential transformation [PDF]
Mathematical Sciences, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fariborzi Araghi, Mohammad Ali +1 more
semanticscholar +3 more sources
Discovery of the Double Exponential Transformation and Its Developments
Publications of the Research Institute for Mathematical Sciences, 2005 This article is mainly concerned how the double exponential formula for numerical integration was discovered and how it has been developed thereafter. For evaluation of I = \int_{-1}^1 f(x)dx , H. Takahasi and M.
M. Mori
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Double exponential transformation for computing three-center nuclear attraction integrals
Molecular Physics, 2019 Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively small systems, millions of these laborious calculations need to be executed.
Lovrod, Jordan, Safouhi, Hassan
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Numerical Solutions of Serrin’s Equations by Double Exponential Transformation
Publications of the Research Institute for Mathematical Sciences, 2007 We consider Serrin’s equations, which describe a steady flow of the incompressible viscous fluid caused by an interaction between a vortex filament and a planar wall. They are integro-differential equations with a singularity at an end point. By means of the double exponential transformation, we numerically solve their solutions with high accuracy, and ...
S. Hamada
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Numerical Solution of Initial Value Problems Based on the Double Exponential Transformation
Publications of the Research Institute for Mathematical Sciences, 2005 The purpose of this paper is to present a method for approximate solution of initial value problems of ordinary differential equation by the double exponential transformation. The original problem is transformed into a Volterra integral equation and it is solved via the indefinite integration formula derived by Muhammad and Mori.
Nurmuhammad, Ahniyaz +2 more
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