A finite-difference scheme of second-order accuracy for elliptic equations with discontinuous coefficients

2000 ◽  
Vol 36 (6) ◽  
pp. 928-930 ◽  
Author(s):  
O. P. Iliev
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Elliptic Equations ◽  
Finite Difference Scheme ◽  
Discontinuous Coefficients ◽  
Second Order ◽  
Order Accuracy

scholarly journals Generalized finite difference solution for the Motz Problem

2020 ◽  
Vol 36 (4) ◽  
Author(s):  
C. Chávez ◽  
F. Domíngez ◽  
S. Lucas-Martínez ◽  
J. Tinoco-Martínez ◽  
D. Santana
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Optimality Condition ◽  
Finite Difference Scheme ◽  
Second Order ◽  
Order Accuracy ◽  
Numerical Examples ◽  
Finite Difference Solution ◽  
General Difference ◽  
Difference Solution

In this paper, it is presented a formulation of a generalized finite difference scheme to solve the Motz problem. It is based on a general difference scheme defined by an optimality condition, which has been developed to solve Poisson-like equations whose domains are approximated by a wide variety of grids over general regions. Numerical examples showing second-order accuracy of the calculated solutions are presented.

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

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