# Calculating the Courant number for a PDE

I have a PDE, which I need to calculate the Courant number for. Does anyone have any resources on that which can help I. I do want a general way of calculating the number if that is possible, so I can use it further.

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Forgive my ignorance, but what is the Courant number? – timur Jan 9 '11 at 17:28

## 1 Answer

The wikipedia article explains it pretty clearly: http://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition

It's simply the velocity in the given direction multiplied by the time step and divided by the step size in the given direction.

In 1D that would be: vx * dt / dx.

If you're talking about the constant that the Courant number needs to be smaller than, that's dependent on your system.

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Guess I explained it badly. I was thinking of the constant the courant number must be smaller then. Is there no standard way of finding that? – martiert Jan 19 '11 at 7:24
There is some way of finding it, but it's dependent on the system you're studying. So no, there is no "general" constant you can just calculate without needing to know the specifics of the esystem. – user6003 Feb 9 '11 at 4:37