Results 11 to 20 of about 488 (225)

Cauchy Principal Value Contour Integral with Applications [PDF]

Entropy, 2017
Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity.
Matilde Legua, Luis M. Sánchez-Ruiz
doaj   +5 more sources

Spline approximation for Cauchy principal value integrals

Journal of Computational and Applied Mathematics, 1990
The author considers the problem of numerical evaluation of Cauchy principal value integrals of the form \(I(f^{(k)};y)=\oint^{b}_{a}w(x)f^{(k)}(x)/(x-y)dx\quad (k=0,1,...).\) She examines quadrature rules of the form: \(I(f^{(k)};y)\approx I_ n(f^{(k)};y)=\sum^{n}_{i=0}w_ i^{(k)}(y)f(x_ i),\) where \(a=x_ ...
exaly   +2 more sources

Nested quadrature rules for Cauchy principal value integrals

Journal of Computational and Applied Mathematics, 1989
Starting from ideas of \textit{G. Monegato} [Computing 29, 337-354 (1982; Zbl 0485.65017)] and \textit{P. Rabinowitz} [Math. Comput. 41, 63-78 (1983; Zbl 0545.65012)], the author builds new cubature formulae to numerically evaluate integrals of Cauchy type \(\int^{b}_{a}f(x)/(x-\lambda)dx\), \(-\infty
exaly   +3 more sources

A Class of Quadrature Rules for Complex Cauchy Principal Value Integrals [PDF]

International Journal of Mathematical, Engineering and Management Sciences, 2023
This article is fully devoted to the numerical approximation of Cauchy-type integrals in the complex plane. A class of degree eight quadrature rules is formulated from a family of Gauss-type two-point rules based on the method of extrapolation. The basic
Arup Kumar Saha, Manoj Kumar Hota, Prasant Kumar Mohanty   +2 more
doaj   +1 more source

OPERATOR METHOD IN THE PROBLEM OF THE H-POLARIZED WAVE DIFFRACTION BY TWO SEMI-INFINITE GRATINGS PLACED IN THE SAME PLANE [PDF]

Radio Physics and Radio Astronomy, 2021
Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper
M. E. Kaliberda, L. M. Lytvynenko, S. A. Pogarsky   +2 more
doaj   +1 more source

An automatic quadrature for Cauchy principal value integrals [PDF]

Mathematics of Computation, 1991
An automatic quadrature is presented for computing Cauchy principal value integrals Q ( f ; c
Takemitsu Hasegawa, Tatsuo Torii
openaire   +1 more source

Rational Transformations for Evaluating Singular Integrals by the Gauss Quadrature Rule

Mathematics, 2020
In this work we introduce new rational transformations which are available for numerical evaluation of weakly singular integrals and Cauchy principal value integrals.
Beong In Yun
doaj   +1 more source

Extended Error Expansion of Classical Midpoint Rectangle Rule for Cauchy Principal Value Integrals on an Interval

Journal of Mathematics, 2021
The classical composite midpoint rectangle rule for computing Cauchy principal value integrals on an interval is studied. By using a piecewise constant interpolant to approximate the density function, an extended error expansion and its corresponding ...
Chunxiao Yu, Lingling Wei
doaj   +1 more source

A Green’s function-based approach to the concentration tensor fields in arbitrary elastic microstructures

Frontiers in Materials, 2023
Computational homogenization based on FEM models is the gold standard when it comes to homogenization over a representative volume element (RVE), of so-called complex material microstructures, i.e., such which cannot be satisfactorily represented by an ...
Nabor Jiménez Segura, Nabor Jiménez Segura, Bernhard L. A. Pichler, Christian Hellmich   +3 more
doaj   +1 more source

Noninterpolatory integration rules for Cauchy principal value integrals [PDF]

Mathematics of Computation, 1989
Let w ( x ) w(x)
Rabinowitz, P., Lubinsky, D. S.
openaire   +2 more sources