scholarly journals The solution of a singular integral equation with some applications in potential theory

1998 ◽  
Vol 21 (1) ◽  
pp. 189-196
Author(s):  
N. T. Shawagfeh
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Singular Integral Equation ◽  
Boundary Value Problems ◽  
Potential Theory ◽  
Singular Integral ◽  
Boundary Value ◽  
Region Exterior

An analytical solution is derived for a singular integral equation which governs some twodimensional potential boundary value problems in a region exterior ton-infinite co-axial circular strips. An application in electrostatics is discussed.

Analysis of the Relaxation of Wall Electrons in a Plasma

1975 ◽  
Vol 30 (8) ◽  
pp. 937-946
Author(s):  
G. Ecker ◽  
K.-U. Riemann ◽  
A. Scholz
Keyword(s):  
Integral Equation ◽  
Kinetic Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Singular Integral ◽  
Boundary Value ◽  
Iteration Process ◽  
Standard Technique ◽  
Inelastic Collisions ◽  
Zeroth Order

Abstract A procedure is developed which renders the simultaneous description of angular and energy relaxation of wall electrons in a plasma possible. The plasma is assumed to be field free, allowance is made for elastic and inelastic collisions with neutrals, as well as for electron-electron encounters. The procedure is based on an expansion in terms of the eigenfunctions of a suitable part of the kinetic equation. In the zeroth order, the problem is reduced to a boundary value problem of the Sturm type, and subsequent solution of a singular integral equation by standard technique. To account for the rest of the kinetic equation, we construct a Green′s function which forms the basis for an iteration process. The application of the procedure is illustrated with an example.

scholarly journals On solution of the integral equations for the potential problems of two circular-strips

1988 ◽  
Vol 11 (4) ◽  
pp. 751-762 ◽  
Author(s):  
C. Sampath ◽  
D. L. Jain
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Potential Theory ◽  
Singular Integral ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Two Dimensional ◽  
Potential Problems ◽  
Physical Quantities ◽  
Quantities Of Interest

Solutions are given to some singular integral equations which arise in two-dimensional Dirichlet and Newmann boundary value problems of two equal infinite coaxial circular strips in various branches of potential theory. For illustration, these solutions are applied to solve some boundary value problems in electrostatics, hydrodynamics, and expressions for the physical quantities of interest are derived.

On an approximate solution of a class of surface singular integral equations of the first kind

2020 ◽  
Vol 27 (1) ◽  
pp. 97-102 ◽  
Author(s):  
Elnur H. Khalilov
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Value Problems

AbstractIn this work, a method for calculating an approximate solution of a singular integral equation of first kind is presented for the Neumann boundary value problems for the Helmholtz equation.

scholarly journals Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity

2008 ◽  
Vol 2008 ◽  
pp. 1-27 ◽  
Author(s):  
A. V. Balakrishnan ◽  
M. A. Shubov
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Singular Integral ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Normal Velocity ◽  
Initial Boundary Value ◽  
Slender Wing

The present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing (downwash). In spite of the importance of the Possio equation, the question of the existence of its solution has not been settled yet. We provide a rigorous reduction of the initial boundary value problem involving a partial differential equation for the velocity potential and highly nonstandard boundary conditions to a singular integral equation, the Possio equation. The question of its solvability will be addressed in our forthcoming work.

scholarly journals On a boundary value problem for the heat equation and a singular integral equation associated with it

2021 ◽  
Vol 399 ◽  
pp. 126009
Author(s):  
Meiramkul Amangaliyeva ◽  
Muvasharkhan Jenaliyev ◽  
Sagyndyk Iskakov ◽  
Murat Ramazanov
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Singular Integral ◽  
Boundary Value

Integral equation methods in potential theory. I

1963 ◽  
Vol 275 (1360) ◽  
pp. 23-32 ◽  
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Potential Theory ◽  
Boundary Value ◽  
Fredholm Integral Equations ◽  
Integral Equation Methods

This paper makes a short study of Fredholm integral equations related to potential theory and elasticity, with a view to preparing the ground for their exploitation in the numerical solution of difficult boundary-value problems. Attention is drawn to the advantages of Fredholm ’s first equation and of Green’s boundary formula. The latter plays a fundamental and hitherto unrecognized role in the integral equation formula of biharm onic problems.

scholarly journals On the solvability of some operators with several moved and fixed

2020 ◽  
pp. 10-25
Author(s):  
Д.М. Одинабеков
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problems ◽  
Bounded Domain ◽  
Singular Integral ◽  
Elliptic Systems ◽  
Two Dimensional ◽  
Systems Of Equations ◽  
Singular Coefficients ◽  
Work First

В работе рассматриваются двумерные сингулярные интегральные операторы по ограниченной области с коэффициентами при интегралах, содержащими в нескольких точках существенный разрыв и операторы с ядрами, имеющими в нескольких точках фиксированные особенности типа однородных функций порядка -2. Такие операторы широко применяются при изучении различных краевых задач для эллиптических систем уравнений первого и второго порядка с сингулярными коэффициентами на плоскости (см. напр. [1]-[4]). Одно из таких приложений приведено в конце настоящей работы. Сначала излагаются результаты исследования разрешимости (нетеровости) двумерного сингулярного интегрального уравнения с коэффициентом при интеграле, содержащим в одной точке существенный разрыв. In this paper we consider two-dimensional singular operators over a bounded domain with coefficients of the integrals, containing an essential discontinuity at several points and operators with kernels having fixed singularities at several points of the type of homogeneous functions order -2. Such operators are widely used in various boundary value problems for elliptic systems of equations of the first and second order with singular coefficients on the plane (see eg. [1]-[4]). One such application is given at the end of this work. First of all set out the results of studying the solvability (Noethericity) of a two-dimensional singular integral equation with a coefficient of the integral containing an essential discontinuity at one point.

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

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