Results 281 to 290 of about 29,720 (316)

SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS

Acta Mathematica Scientia, 1998
Abstract In this paper, the author discusses some singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, and obtain some useful properties for them. These results improve both the classical theory of singular integral equation and the classical theory of ...
Jinyuan Du
exaly   +2 more sources

Singularities of Solutions of Singular Integral Equations

Ukrainian Mathematical Journal, 2002
This paper deals with a singular integral equation \[ Sq+Tq=f,\tag{1} \] where \(q(x)\) is an unknown function, \[ Sq(x):=aq(x)+\frac{1}{\pi }\text{v.p.} \int_{-1}^{1} \frac{q(\tau)}{\tau -x} d\tau,\;Tq(x):=\int_{-1}^{1}K(x,\tau)q(\tau) d\tau. \] It is assumed that the functions \(f\) and \(K\) smoothly depend on additional parameters.
Kapustyan, V. E., Il'man, V. M.
openaire   +1 more source

Approximate solution of singular integral equations

Applied Mathematics Letters, 2004
An approximate method is developed for solving singular integral equations of the first kind, over a finite interval. The singularity is assumed to be of the Cauchy type, and the four basically different cases of singular integral equations of practical ...
G Vanden Berghe
exaly   +2 more sources

Oscillatory Singular Integrals

Mathematische Nachrichten, 1987
L 2 boundedness is proved for a class of oscillatory singular integrals of the form \[ Tf(x)=\int_{{\mathbb{R}}\quad n}e^{iB(x)\cdot y} K(x- y)f(y)dy,\quad x\in {\mathbb{R}}\quad n,\quad f\in C^{\infty}_ 0({\mathbb{R}}\quad n) \] (suitable assumptions are made about B and K).
openaire   +1 more source

Hierarchical Quadrature for Singular Integrals

Computing, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Steffen Börm, Wolfgang Hackbusch
openaire   +1 more source

Singular Integral Equations

Journal of Mathematical Physics, 1966
The integral equation P ∫ cK(ζ′,ζ)ζ′−ζφ(ζ′) dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.
openaire   +3 more sources

Product Integration for Singular Integrals and Singular Integral Equations

1979
Integral equations with weakly singular kernels often have solutions which have derivative singularities at the end points of the range of integration. The error analysis of a product integration method for such integral equations depends on the error analysis of the product integration method applied to integrals of the form \(\int\limits_0^1 {g\left(
openaire   +1 more source

On a "Singular" Integration Technique of Poisson

The American Mathematical Monthly, 2005
(2005). On a “Singular” Integration Technique of Poisson. The American Mathematical Monthly: Vol. 112, No. 3, pp. 270-272.
openaire   +2 more sources

On the numerical integration of certain singular integrals

Computing, 1992
For singular integrals in the sense of Hadamard new numerical approximations are derived. Error estimates and numerical results are given.
H. W. Stolle, Raimond Strauss
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Repeated singular integrals

Journal of the London Mathematical Society, 1977
openaire   +2 more sources