scholarly journals Fredholm-Stieltjes integral equations with linear constraints: duality theory and Green's function

1979 ◽  
Vol 104 (4) ◽  
pp. 357-369
Author(s):  
Milan Tvrdý
Keyword(s):  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Duality Theory ◽  
Linear Constraints ◽  
Stieltjes Integral

scholarly journals Green's Function for A Piecewise Continous Potential via Integral Equations Method

2018 ◽  
Vol 24 (2) ◽  
pp. 20-35
Author(s):  
Benali Brahim ◽  
Mohammed Tayeb Meftah ◽  
Rai Vandana
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Hamiltonian Operator ◽  
Potential Part ◽  
Piecewise Continuous ◽  
Discrete Spectra

The aim of this work is to provide Green's function for the Schrodingerequation. The potential part in the Hamiltonian is piecewise continuous operator.It is a zero operator on a disk of radius "a" and a constant V0 outside this disk (intwo dimensions). We have used, to construct the Green's function, the technique ofthe integral equations. We have respected the boundary conditions of the problem.The discrete spectra of the Hamiltonian operator have been also derived.

Integral equations and relations for Lamé functions and ellipsoidal wave functions

1968 ◽  
Vol 64 (1) ◽  
pp. 113-126 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Wave Function ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Function Theory ◽  
Natural Generalization ◽  
Wave Functions ◽  
Linear Integral ◽  
First Time ◽  
Linear Integral Equations

AbstractNon-linear integral equations and relations, whose nuclei in all cases is the ‘potential’ Green's function, satisfied by Lamé polynomials and Lamé functions of the second kind are discussed. For these functions certain techniques of analysis are described and these find their natural generalization in ellipsoidal wave-function theory. Here similar integral equations are constructed for ellipsoidal wave functions of the first and third kinds, the nucleus in each case now being the ‘free space’ Green's function. The presence of ellipsoidal wave functions of the second kind is noted for the first time. Certain possible generalizations of the techniques and ideas involved in this paper are also discussed.

scholarly journals On the condition number of integral equations in linear elasticity using the modified Green's function

2003 ◽  
Vol 44 (3) ◽  
pp. 431-446
Author(s):  
E. Argyropoulos ◽  
D. Gintides ◽  
K. Kiriaki
Keyword(s):  
Fundamental Solution ◽  
Green’S Function ◽  
Optimal Condition ◽  
Integral Equations ◽  
Green's Function ◽  
Condition Number ◽  
Linear Elasticity ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Function Technique

AbstractIn this work the modified Green's function technique for an exterior Dirichlet and Neumann problem in linear elasticity is investigated. We introduce a modification of the fundamental solution in order to remove the lack of uniqueness for the solution of the boundary integral equations describing the problems, and to simultaneously minimise their condition number. In view of this procedure the cases of the sphere and perturbations of the sphere are examined. Numerical results that demonstrate the effect of increasing the number of coefficients in the modification on the optimal condition number are also presented.

Integral equation approach to the problem of scattering by a number of fixed scatterers

1977 ◽  
Vol 55 (16) ◽  
pp. 1442-1452
Author(s):  
M. Hron ◽  
M. Razavy
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inhomogeneous Term ◽  
Integral Equation Approach ◽  
An Array Of Cylinders

In the derivation of the Lippmann–Schwinger integral equation for scattering of a wave ψ(r) by the potential ν(r), one constructs the Green's function for the operator [Formula: see text], and treats νψ as the inhomogeneous term. However, in certain cases, it is desirable to formulate the scattering problem in terms of an integral equation by obtaining the Green's function for the operator [Formula: see text], and by considering (−k2ψ) as the inhomogeneous term. An important aspect of this formulation is that the resulting integral equation can be used to generate a low energy expansion of the wave function for some separable and nonseparable systems. For two-dimensional scattering, if the geometry of the scatterers is simple enough, the Laplace equation with the prescribed boundary conditions on the surface of the scatterers is separable in a certain coordinate system, then one can write the solution of the wave equation as an inhomogeneous integral equation. In this way the problems of scattering by two cylinders, an array of cylinders, and a grating can be formulated in terms of integral equations. For three-dimensional scattering, one can consider either the spherically symmetric cases or nonseparable problems. In the former case, for certain types of force laws, a Volterra integral equation in one variable can be found for the wave function. In the latter case, integral equations in two or three variables can be obtained for scattering by two spheres or by a torus.

scholarly journals Integral Equations and the Determination of Green's Functions in the Theory of Potential

1912 ◽  
Vol 31 ◽  
pp. 71-89 ◽  
Author(s):  
H. S. Carslaw
Keyword(s):  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Closed Surface ◽  
Second Derivatives

In the Theory of Potential the term Green's Function, used in a slightly different sense by Maxwell, now denotes a function associated with a closed surface S, with the following properties:—(i) In the interior of S, it satisfies ∇2V = 0.(ii) At the boundary of S, it vanishes.(iii) In the interior of S, it is finite and continuous, as also its first and second derivatives, except at the point (x1, y1,z1).

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