Finite Difference Scheme for the Heat Equation
![](/img/demonstrations-branding.png)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
We apply a finite difference scheme to the heat equation, , and study its convergence. The rate of convergence (or divergence) depends on the problem data and the inhomogeneous function
.
Contributed by: Igor Mandric and Ecaterina Bunduchi (March 2011)
(Moldova State University)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Consider the finite difference scheme
,
,
,
,
,
,
,
.
This Demonstration shows how the convergence of this finite difference scheme depends on the initial data, the boundary values, and the parameter that defines the scheme for the heat equation
. If
, then the scheme is called explicit; if
, it is called implicit. If
, then the scheme is stable, so the approximate solution converges to the exact solution. If
, the scheme diverges.
The three pairs of snapshots 1–2, 3–4, and 5–6 show the dependence of the convergence on .
Reference
[1] A. A. Samarskii and A. V. Goolin, Numerical Methods (in Russian), Moscow: Science, 1989.
Permanent Citation