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- H. Takahasi, Masatake Mori
- 1973

A family of numerical quadrature formulas is introduced by application of the trapezoidal rule to infinite integrals which result from the given integrals f b \ f(x)dx by suitable variable… (More)

In this paper we derive a formula for indefinite integration of analytic functions over (-1,s) where -1 > s > 1, by means of the double exponential transformation and the Sinc method. The integrand… (More)

Abstract The double exponential formula is known to be very powerful for evaluation of various kinds of integrals, in particular integrals with end point singularities or integrals over the half… (More)

The double-exponential transformation was first proposed by Takahasi and Mori in 1974 for the efficient evaluation of integrals of an analytic function with end-point singularity. Afterwards, this… (More)

Numerical solution of linear integral equations by means of the Sinc collocation method based on the double exponential transformation, abbreviated the DE transformation, is considered. We first… (More)

Abstract A double exponential transformation is presented to obtain a quadrature formula for Fourier-type integrals ∫ 0 ∞ f(x) sin ωx d x or ∫ 0 ∞ f(x) cos ωx d x where f ( x ) is a slowly decaying… (More)

- H. Takahasi, Masatake Mori
- 1973

AbstractQuadrature formulas suitable for evaluation of improper integrals such as
$$\int\limits_{ - 1}^1 {f(x)(1 - x)^{ - \alpha } (1 + x)^{ - \beta } dx,\alpha ,\beta< 1} $$
are obtained by means… (More)

A method, called “the discrete variational method”, has been recently presented by Furihata and Matsuo for designing finite difference schemes that inherit energy dissipation or conservation property… (More)

AbstractA formula for numerical evaluation of two dimensional iterated integrals of the formI = ∫abdx ∫a′q(x)f(x,y)dy whereq(a) =a’,q(b) =b’ (a <x <b) is derived by means of the sinc approximation… (More)

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… (More)