INTEGRAL EQUATION FORMULATION OF THE BOUNDARY VALUE PROBLEMS OF ELASTICITY

1963 ◽  
Author(s):  
Robert P. Banaugh
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Equation Formulation ◽  
Integral Equation Formulation

scholarly journals A unified boundary integral equation method for a class of second order elliptic boundary value problems

1984 ◽  
Vol 25 (4) ◽  
pp. 501-517 ◽  
Author(s):  
M. Rezayat ◽  
F. J. Rizzo ◽  
D. J. Shippy
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Second Order ◽  
Elliptic Type ◽  
Integral Equation Formulation

AbstractA generalized integral equation formulation and a systematic numerical solution procedure are presented for a class of boundary value problems governed by a general second-order differential equation of elliptic type. Diverse numerical examples include problems of plane-wave scattering, three-dimensional fluid flow, and plane heat transfer for a body with a moving flame boundary. The last example employs certain representation functions useful to increase solution effectiveness in problems with an isolated integrable singularity.

scholarly journals Integral Equation Formulation of some Three Part Boundary Value Problems

1963 ◽  
Vol 13 (4) ◽  
pp. 317-323 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Fredholm Integral Equation ◽  
Simple Form ◽  
Boundary Value ◽  
Outer Radius ◽  
Electrostatic Problem ◽  
Circular Annulus ◽  
Inner Radius ◽  
Integral Equation Formulation

One of the simplest three part boundary value problems is the electrostatic problem for the circular annulus and, at present, there seems to be no method available for obtaining the solution in a closed form. It has recently been shown by the author (1) and Cooke (2) that this problem can be reduced to the solution of a Fredholm integral equation of the second kind. The equation obtained in (1, 2) is fairly simple and is suitable for obtaining a numerical solution but, unfortunately, it cannot be solved iteratively to give a simple form of solution valid for small values of the ratio (inner radius/outer radius).

scholarly journals On the solutions of mixed plane problems that are unbounded where the boundary conditions change

2001 ◽  
Vol 32 (3) ◽  
pp. 173-180
Author(s):  
M. G. El-Sheikh ◽  
V. N. Gavdzinski ◽  
A. E. Radwan
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Infinite System ◽  
Original Method ◽  
Plane Boundary ◽  
Algebraic Equations ◽  
Typical Problem ◽  
Equation Formulation ◽  
Integral Equation Formulation

In this paper, we apply a modification to the method of the integral equation formulation of mixed plane boundary value problems so that it enables us to obtain the solutions unbounded at the points where the boundary conditions change. Such solutions are of great physical interest. The modification is illustrated by means of a typical problem. As is it the case in the original method proposed by Cherskii [1], the problem is reduced to an infinite system of algebraic equations. The justification of the truncation of such systems has been established.

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

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