Time: tradeoff

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Choosing a timestep that is short enough to be accurate and yet not take too long to compute

There is a tradeoff between speed and the accuracy with which the equation solver can solve the equations. This is feature of all numerical modelling. Continuous time is approximated by a series of short intervals or steps (dt). With steps that are too long the mesh will grow more than about 2% - an acceptable limit. Very short steps take a long time to compute and can also suffer rounding problems. This is an example of subdividing a rectangular mesh in the region in which curves will develop.

Step size (dt) is 10. Is the 'S' shape correct? Simple mesh of 382 elements equally spaced vertices. Superimposed are the polarity arrows (pointing bottom left) and purple and blue factors that control local growth rates.

Step size (dt) is 1. Is the 'S' shape correct? It is different so we reduce it again...

Step size (dt) is 0.1. This shape is very similar to the previous one so we might conclude that it is not necessary to make the stepsize this short, a stepsize of 1 is OK.

It still might not be correct because the mesh might be too coarse, See mesh tradeoffs
It still might not be correct because the tolerances might be too large, See tolerance tradeoffs