Results 51 to 60 of about 145 (135)

Multi-Component BEM for the Helmholtz Equation: A Normal Derivative Method

Shock and Vibration, 2012
We describe a multi-component boundary element method for predicting wave energy distributions in a complex built-up system with material properties changing discontinuously at boundaries between sub-components.
H.A.M. Ben Hamdin, G. Tanner
doaj   +1 more source

Kolmogorov-type inequalities for hypersingular integrals with homogeneous characteristics

Researches in Mathematics
In this article we obtain sharp Kolmogorov-type inequalities that estimate the uniform norm of a hypersingular integral operator $$ D^{w,\Omega}_K f(x): = \int_{C} w(|t|_K) (f(x+t) - f(x))\Omega(t)dt, x\in C, $$ using the uniform norm of the ...
V.F. Babenko, O.V. Kovalenko, N.V. Parfinovych   +2 more
doaj   +1 more source

BPX Preconditioner for Hypersingular Integral Equations

Journal of Integral Equations and Applications, 1998
The BPX preconditioner [cf. \textit{J. H. Bramble, J. E. Pasciak} and \textit{J. Xu}, Math. Comput. 55, No. 191, 1-22 (1990; Zbl 0703.65076)] for the Galerkin approximation of hypersingular integral equations is presented. The condition number of the preconditioned matrix is shown to behave as \(O(h^{-\varepsilon})\) where \(\varepsilon\) is small and ...
openaire   +2 more sources

Transformation of hypersingular integrals and black-box cubature [PDF]

Mathematics of Computation, 2000
In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals.
Sauter, S A, Lage, C
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Hypersingular integro-differential equations with power factors in coefficients

Журнал Белорусского государственного университета: Математика, информатика, 2019
The linear hypersingular integro-differential equation of arbitrary order on a closed curve located on the complex plane is considered. A scheme is proposed to study this equation in the case when its coefficients have some particular structure.
Andrei P. Shilin
doaj   +1 more source

Exact radially symmetric solutions to n-dimensional space–time fractional diffusion equations: Resolution of singularities via generalized Hankel transforms [PDF]

AIP Advances
We present, for the first time, exact radially symmetric solutions to the n-dimensional space–time fractional diffusion equation with point source initial conditions, employing the most general fractional framework: the Riemann–Liouville temporal ...
Farrukh A. Chishtie
doaj   +1 more source

Taming hypersingular integrals using dimensional continuation

Physical Review E, 2012
We use the method of dimensional continuation to isolate singularities in integrals containing products of Green's functions or their derivatives. Rules for the extraction of the finite part of so-called hypersingular integrals are developed, which should be useful in methods based on boundary integral techniques in science and engineering.
Zehao, Li, L R, Ram-Mohan
openaire   +3 more sources

Numerical evaluation of hypersingular integrals

Journal of Computational and Applied Mathematics, 1994
The paper is motivated by the occurrence of singular and hypersingular integrals in applied mathematics, for example Cauchy principal value and Hadamard finite-part integrals in boundary integral equations. Attention is concentrated on the less familiar two-dimensional Cauchy principal value integrals and one- and two-dimensional integrals with ...
openaire   +2 more sources

Boundary Integral Equations Approach for a Scattering Problem of a TE-Wave on a Graphene-Coated Slab

Photonics
This paper focuses on a transmission problem describing the scattering of a TE-wave on a slab having an absolutely conducting wall at the bottom and covered with graphene at the top, accounting for the optical nonlinearity of graphene.
Yury Smirnov, Stanislav Tikhov
doaj   +1 more source

A Quadrature Method for the Hypersingular Integral Equation on an Interval [PDF]

Journal of Integral Equations and Applications, 1995
Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
openaire   +5 more sources