On a high-accuracy difference scheme for an elliptic equation with several space variables

1963 ◽  
Vol 3 (6) ◽  
pp. 1373-1382 ◽  
Author(s):  
A.A. Samarskii ◽  
V.B. Andreyev
Keyword(s):  
Elliptic Equation ◽  
Difference Scheme ◽  
High Accuracy ◽  
Accuracy Difference

The Comparison for Several Difference Methods in Heat Conduction Equations

2011 ◽  
Vol 282-283 ◽  
pp. 399-402
Author(s):  
Fan Lei Meng
Keyword(s):  
Heat Conduction ◽  
Difference Scheme ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
High Accuracy ◽  
Third Order ◽  
Numerical Experimentation ◽  
Valuable Method ◽  
Accuracy Difference ◽  
Initial Boundary Value

In this paper, one-dimensional heat conduction equations is studied, many difference Schemes have been proposed to solve it. In order to find a high accuracy difference scheme in all the methods, we give a numerical experimentation in this paper. by numerical experimentation, a high accuracy difference scheme for solving Heat conduction equations initial boundary value problem is found, according to the truncation error and stability analysis ,we find its accuracy is better-then- third-order in time and space direction. this is a valuable method and better then the others this is a high accuracy difference Scheme. this scheme is a valuable method in Heat conduction and Fluid mechanics.

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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