A generalization of the continuous Euler transformation and its application to numerical quadrature
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摘要
The continuous Euler transformation, which was proposed by the present author to accelerate the convergence of integrals of Fourier-type, is an analogue of the well-known Euler transformation for series. In this paper, we propose new continuous transformations including a generalization of the continuous Euler transformation. We show that the generalized continuous Euler transformation is applicable to not only a Fourier-type integral but also an oscillatory integral with an algebraically decaying integrand. We also show some numerical examples using the generalized continuous Euler transformation.
论文关键词:Continuous Euler transformation,Numerical quadrature,Oscillatory integral with algebraically decaying integrand
论文评审过程:Received 13 May 2002, Revised 27 November 2002, Available online 4 July 2003.
论文官网地址:https://doi.org/10.1016/S0377-0427(03)00378-9