Implicit, Three Layered Difference Schemes for the Heat Conduction Equation
by
Hrant Hovhannissian
The Engineering State University of Armenia

In this work is considered the heat conduction equation in the case of the given initial and boundary conditions. The problem is solved by the method of grids, with the help of three layer difference schemes.

The following nodes are used in the applied difference schemes:

1 (i, k-1)-(i, k)-(i-1, k+1)-(i, k+1)-(i+1, k+1)
2 (i, k-1)-(i-1, k)-(i, k)-(i+1, k)-(i-1, k+1)-(i, k+1)-(i+1, k+1)
3 (i-1, k-1)-(i, k-1)-(i+1, k-1)-(i-1, k)-(i, k)-(i+1, k)-(i-1, k+1)-(i, k+1)-(i+1, k+1)
4 (i, k-1)-(i, k)-(i-2, k+1)-(i-1, k+1)-(i, k+1)-(i+1, k+1)-(i+2, k+1)

For the considered difference schemes are given the orders of approximation and the conditions of convergence.

On the basis of suggested difference schemes was created a package of programs, which includes the algorithms of realization of the all used difference schemes.

Date received: March 30, 1999