Results 11 to 20 of about 7,832,039 (286)

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   +3 more sources

Extrapolation Algorithm for Computing Multiple Cauchy Principal Value Integrals [PDF]

Mathematical Problems in Engineering, 2020
In this paper, the computation of multiple (including two dimensional and three dimensional) Cauchy principal integral with generalized composite rectangle rule was discussed, with the density function approximated by the middle rectangle rule, while the singular kernel was analytically calculated.
Jin Li, Yongling Cheng
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Investigation of the solution of a boundary value problem with variable coefficients whose principal part is the Cauchy–Riemann equation

Қарағанды университетінің хабаршысы. Математика сериясы
This study is devoted to obtaining an analytical expression for the solution of a non-local boundary value problem for a linear inhomogeneous differential equation with variable coefficients, which principle part is the Cauchy–Riemann equation.
M. Rasulov, N. Aliyev, B. Sinsoysal
doaj   +3 more sources

Principal values for the Cauchy integral and rectifiability [PDF]

Proceedings of the American Mathematical Society, 2000
We give a geometric characterization of those positive finite measures μ \mu
Xavier Tolsa
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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
openaire   +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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The Trapezoidal Rule for Computing Cauchy Principal Value Integral on Circle [PDF]

Mathematical Problems in Engineering, 2015
The composite trapezoidal rule for the computation of Cauchy principal value integral with the singular kernelcot((x-s)/2)is discussed. Our study is based on the investigation of the pointwise superconvergence phenomenon; that is, when the singular point coincides with some a priori known point, the convergence rate of the trapezoidal rule is higher ...
Jin Li
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The superconvergence of the Newton–Cotes rule for Cauchy principal value integrals

Journal of Computational and Applied Mathematics, 2010
The authors study the superconvergence phenomenon for the Newton-Cotes quadrature rule for Cauchy principal values integrals. Necessary and sufficient conditions satisfied by the superconvergence point, the given superconvergence estimate and properties of the superconvergence points are investigated. Numerical examples are given.
Dongjie Liu, Jiming Wu, Dehao Yu
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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
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