What is the relation between stability criterion and time step?

[t0mm02]

Homework Statement:: time step must be greater than stability criterion
Relevant Equations:: stability criterion= h^2/4 x alpha

Hello. I have had to do 2 MATLAB codes based on the 2D Heat diffusion equation using the Explicit Finite Method. In those codes, the time step must be greater or equal to the stability criterion. I do not understand the relationship between the time step and the stability criterion or why the time step must be equal to the stability criterion.

 

[Filip Larsen]

If this is homework perhaps you will get more feedback here if you provide a specific question with clear reference to what part of your textbook or notes you are stuck on.

If its not homework and you seek general understanding you should probably prepare to invest some time studying regions of stability as it is used as a general tool in analysis of numerical methods, and then return here with specific questions if needed.

A few links that may be relevant for stability of ODE solvers (mayby others here can provide better links for PDE's):
https://en.wikipedia.org/wiki/Euler_method#Numerical_stability
https://en.wikipedia.org/wiki/Stiff_equation
http://folk.ntnu.no/leifh/teaching/tkt4140/._main025.html