Results 11 to 20 of about 7,891,501 (248)

Uniform convergence results for Cauchy principal value integrals [PDF]

Mathematics of Computation, 1991
A general uniform convergence theorem for numerical integration of Cauchy principal value integrals is proved. Seven special instances of this theorem are given as corollaries.
Philip Rabinowitz
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On quadrature for Cauchy principal value integrals of oscillatory functions [PDF]

Journal of Computational and Applied Mathematics, 2003
Based on a quadrature suggested by \textit{G. E. Okecha} [Math. Comput. 49, 259--268 (1987; Zbl 0634.65013)] the authors deal with the numerical evaluation of Cauchy principal value integrals \[ H^\omega(g; t)= \lim_{\varepsilon\to 0^+}\,\int_{| x-t|\geq \varepsilon} {g(x)\over x- t} e^{i\omega x} \,dx\qquad (t\in (-1,1)).
M. R. CAPOBIANCO, CRISCUOLO, GIULIANA
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Efficient Quadrature Rules for Cauchy Principal Value Integrals with Highly Oscillatory Bessel Kernel

Mathematics
In this paper, we address the fast computation of highly oscillatory Bessel transforms involving algebraic-type singularities and Cauchy principal value integrals.
Bin Li, Yibo Liu, Jinjun Yong
doaj   +2 more sources

On the evaluation of Cauchy principal value integrals of oscillatory functions [PDF]

Journal of Computational and Applied Mathematics, 2010
The authors are concerned with the numerical evaluation of the Cauchy principal value integrals of oscillatory functions \[ \begin{aligned} I_{\omega}(f;\tau) :=&\displaystyle{\int_{-1}^1e^{i\omega x}\frac{f(x)}{x-\tau}dx}\\ =&\displaystyle{\lim_{\epsilon\to 0^{+}}\int_{|x-\tau|\geq\epsilon}e^{i\omega x}\frac{f(x)}{x-\tau}dx ...
Haiyong Wang, Shuhuang Xiang
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A sinc-Hunter quadrature rule for Cauchy principal value integrals [PDF]

Mathematics of Computation, 1990
A Sinc function approach is used to derive a new Hunter type quadrature rule for the evaluation of Cauchy principal value integrals of certain analytic functions. Integration over a general arc in the complex plane is considered. Special treatment is given to integrals over the interval
Bernard Bialecki
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A stable Gauss-Kronrod algorithm for cauchy principal-value integrals [PDF]

Computers & Mathematics with Applications, 1986
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rabinowitz, P.
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Numerical evaluation of Cauchy principal value integrals with singular integrands [PDF]

Mathematics of Computation, 1990
Convergence results are proved for sequences of interpolatory integration rules for Cauchy principal value integrals of the form \[ ∮
Philip Rabinowitz
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Uniform approximation to Cauchy principal value integrals with logarithmic singularity [PDF]

Journal of Computational and Applied Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Takemitsu Hasegawa, Hiroshi Sugiura
core   +4 more sources

A sinc quadrature subroutine for Cauchy principal value integrals [PDF]

Journal of Computational and Applied Mathematics, 1999
The aim of this paper is to present a subroutine for the evaluation of Cauchy principal value integrals. The method is based on a truncated sum of a Sinc function series. A nested sequence of approximation algorithm is proposed. Numerical results prove that the proposed algorithm works well on analytic functions with endpoint singularities ...
Bialecki, B, Keast, P
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Gauss-Kronrod integration rules for Cauchy principal value integrals [PDF]

Mathematics of Computation, 1983
Kronrod extensions to two classes of Gauss and Lobatto integration rules for the evaluation of Cauchy principal value integrals are derived. Since in one frequently occurring case, the Kronrod extension involves evaluating the derivative of the integrand, a new extension is introduced using
Philip Rabinowitz
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