The Dirichlet Problem for an Elliptic Equation with Several Singular Coefficients in an Infinite Domain

2021 ◽  
Vol 65 (7) ◽  
pp. 71-80
Author(s):  
T. G. Ergashev ◽  
Z. R. Tulakova
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Infinite Domain ◽  
Singular Coefficients

scholarly journals The Dirichlet problem for elliptic equation with several singular coefficients

2018 ◽  
Vol 1 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Tuhtasin G. Ergashev
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Hypergeometric Function ◽  
Unique Solution ◽  
Explicit Form ◽  
Fundamental Solutions ◽  
Singular Elliptic Equation ◽  
Singular Coefficients

AbstractRecently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. When finding a solution, we use decomposition formulas and some adjacent relations for the Lauricella hypergeometric function in many variables.

Method of corrections by higher order differences for elliptic equations with variable coefficients

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Givi Berikelashvili ◽  
Bidzina Midodashvili
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Convergence Rate ◽  
Difference Scheme ◽  
Elliptic Equations ◽  
Variable Coefficients ◽  
Order Accuracy ◽  
Corrected Scheme

AbstractWe consider the Dirichlet problem for an elliptic equation with variable coefficients, the solution of which is obtained by means of a finite-difference scheme of second order accuracy. We establish a two-stage finite-difference method for the posed problem and obtain an estimate of the convergence rate consistent with the smoothness of the solution. It is proved that the solution of the corrected scheme converges at rate

Sign in / Sign up

Export Citation Format

Share Document