It is useful to compare the partial differential equation scheme evolution for several steps lengths for a better convergence.

In practice it is possible and interesting to program the varying steps lengths when using the first order function derivatives and coupled second order function derivatives in a partial differential equation during an analysis.

In this case, one pivot may becomes zero. The matrix conditioning can then be numerically tested.

It is important to numerically detect this element and to give a solution during this solving process while it isn't aborted.