Results 1 to 10 of about 3,430 (271)
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
openaire +2 more sources
On the numerical evaluation of certain 2-D singular integrals
Journal of Numerical Analysis and Approximation Theory, 2000 The problem of approximating certain two-dimensional Cauchy principal value integrals is here considered, product integration formulas with multiple nodes are presented and the behaviour of the remainder is analyzed.
Laura Gori +2 more
doaj +2 more sources
The Elementary Theory of Cauchy's Principal Values
Proceedings of the London Mathematical Society, 1901 n ...
openaire +1 more source
International Journal of Mathematics and Mathematical Sciences, 1983 A numerical technique, first reported in 1979 in refs.[1] and [2], for the numerical evaluation of two-dimensional Cauchy-type principal-value integrals, is extended in this paper to include several cubature formlas of the Radau and Lobatto types.
P. S. Theocaris
doaj +1 more source
Journal of Numerical Analysis and Approximation Theory, 1983 It is shown how the construction of Gaussian quadrature rules for Cauchy type principal value integrals, as well as for finite-part integrals with an algebraic singularity, can be based on the theory of Gaussian quadrature rules for ordinary integrals ...
N. I. Ioakimidis
doaj +2 more sources
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
openaire +2 more sources
The Asymptotics of Solutions of a Singularly Perturbed Equation with a of Fractional Turning Point
Известия Иркутского государственного университета: Серия "Математика", 2017 We develop the classical Vishik – Lyusternik – Vasil’eva – Imanaliev boundary-value method for constructing uniform asymptotic expansions of solutions of singularly perturbed equations with singular points.
D. A. Tursunov, K. G. Kozhobekov
doaj +1 more source
PRACTICAL ASPECTS IN SOME NOT CLASSICAL METHODS FOR THE NUMERICAL EVALUATION OF CPV- INTEGRALS
Ratio Mathematica, 1995 Two different not classical approaches are given for the numerical evaluation of weighted Cauchy principal value integrals, The first approach is an interpolatory Gaussian integration over the unit half disc.The second method is a quasi interpolatory ...
Franca Caliò, Elena Marchetti
doaj
Shock and Vibration, 2018 A simple model for vertical dynamic interactions among a group of strip footings rested on half-space is presented in this paper. An analytical method is presented to obtain the contact pressures and the impedance matrix for a group of surface strip ...
Jue Wang, Ding Zhou
doaj +1 more source