Comment on numerical solution of potential problems by integral equations without Green’s function

1977 ◽  
Vol 20 (17) ◽  
pp. 619-620
Author(s):  
W. Squire
Keyword(s):  
Green’S Function ◽  
Numerical Solution ◽  
Integral Equations ◽  
Green's Function ◽  
Potential Problems

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.

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