Transient Heat Flow: Consider time dependent heat flow on a square, heat conducting sheet of material. Two edges of the square are held at temperature 100 and the other two at temperature 0. The initial termperature on the interior of the square is 50.

The algorithm used is the explicit forward-in-time method. For this method to be stable on this grid, the time increment must be less than 0.25.

Experiment with time increments larger than 0.25 and then see if you can regain control of the algorithm once an instability has manifested itself. Note: Subsequent to the appearance of an instability, time-accuracy of the model is lost. You may still be able to get the algorithm to reach a valid steady state temperature distribution.