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Weakly-singular kernels appear frequently in the boundary integral equation method for solving elliptic equations (see [a1]).

In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations.

Journal of Integral Equations and Applications. Publisher: Rocky Mountain Mathematics Consortium. The Journal of Integral Equations and Applications is devoted to research in the general area of integral equations and their applications. Current Issue …

01.12.2018 · Weakly singular integral equations are also result from the reformulation of partial differential equations (PDEs), such as the exterior boundary value problem for the Helmholtz equation on the two-dimensional domains which is characterized by [42] (2) where is a weakly singular kernel given by (3) where is a constant, and

of the integral equation u(t) = /£ K(t, s)u(s) ds + f(t) with a weakly singular kernel K{t, s) have been studied in papers [2]-[7].

On Weakly Singular Integral Equations of the Second Kind. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 68, Issue. 12, p. 643.

WEAKLY SINGULAR INTEGRAL EQUATIONS. LECTURE NOTES BY GENNADI VAINIKKO, HUT, MARCH-APRIL 2006. Contents. 1. Introduction 2. 2. Requisites 3. 2.1. Spaces.

On Weakly Singular Integral Equations of the Second Kind. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 68, Issue. 12, p. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 68, Issue. 12, p.

WEAKLY SINGULAR FREDHOLM INTEGRAL EQUATIONS 37 LEMMA 2. K:L2[0, l] ---f W[O, 11. Proof. Let 4 E P[O, l] and define an extension $ EL~( - co, co) of $ as follows: ?+w = w, x E [O, 11 = 0, x $ [O, 11. Now let ,8(x) = D{J-“m log 1 x - y j q(y) dy}. As shown in [2], B(X) is the Hilbert transform of 6,

Specification for Volterra integral equations 19. 7. A collocation method for weakly singular integral equations 21. 7.1. Interpolation by polynomials on a ...

approximate solution of weak singular integral equations with logarithmic Kernel. The equation is examined in a pair of spaces. The results obtained could be used for any pair of the functional spaces where the problem of finding the solution of weak singular integral equations is correctly formulated problem by Tihonovo.

PDF | We examine the differential properties of the solution of the linear integral equation of the second kind, whose kernel depends on the ...

The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory.

We consider a perturbed linear boundary-value problem for a weakly singular integral equation. Assume that the generating boundary-value problem is ...

Dec 01, 2018 · Weakly singular integral equations are also result from the reformulation of partial differential equations (PDEs), such as the exterior boundary value problem for the Helmholtz equation on the two-dimensional domains which is characterized by (2) u (x)-1 π ∫-π π K (x, y) u (y) d y = f (x),-π ⩽ x ⩽ π, where K (x, y) is a weakly singular kernel given by (3) K (x, y) = α 0 + α (x, y) sin 2 x-y 2 ln 2 sin x-y 2 + β (x, y), where α 0 is a constant, α (x, y) and β (x, y) are ...

In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operatorwhose kernel function K : R ×R → R is singularalong the diagonal x = y. Specifically, the singularity is such that |K(x, y)| is of size |x − y| asymptotically as |x − y| → 0. Since such integrals may not i…

WEAKLY SINGULAR FREDHOLM INTEGRAL EQUATIONS 33 2. HILBERT-SCHMIDT KERNELS OF DISPLACEMENT TYPE We consider here the integral equation 4 =fSK$ (1) where f~L~[0, l] and K# = si k(j x - y I) 4(y) dy, with k GL~[O, I]. We first prove the following: LEMMA 1.

Abstract. Direct function theoretic methods are developed to handle two weakly singular integral equations with their kernels having ...

of the integral equation u(t) = /£ K(t, s)u(s) ds + f(t) with a weakly singular kernel K{t, s) have been studied in papers [2]-[7]. Kahane [2] presents condi-tions under which the solution of the equation is analytical in the interior points of the domain of integration. Richter [5] submits concrete results of

weak singular integral equations is correctly formulated problem by Tihonovo. Keywords: Weak Singular Integral Equation, Trigonometric Interpolating Polynomials, incorrectly formulated problem, iterative methods. 1 Introduction The integral equations of the first kind with logarithmic kernels in the main

WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS 421 Note that the choice (2.7) for the grading exponent leads to optimal (global) convergence, in the sense that the exponent m in (2.6) cannot be replaced by m + 1. This agrees, of course, with the …

This article describes a numerical method for solving nonlinear Fredholm integral equations of the second kind with weakly singular kernels. The scheme estimates the solution by the discrete Galerkin method based on the use of moving least squares (MLS) as a local approximation.

The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives ...

THE PROPERTIES OF SOLUTIONS OF WEAKLY SINGULAR INTEGRAL EQUATIONS G. VAINIKKO and A. PEDAS (Received 22 July 1980) (Revised 5 February 1981) Abstract We examine the differential properties of the solution of the linear integral equation of the second kind, whose kernel depends on the difference of arguments and has an

In this paper, two numerical schemes for a nonlinear integral equation of Fredholm type with weakly singular kernel are studied. These numerical ...