2. Consistency, precision or order, stability of a DF diagram

To be usable, a finite-difference diagram must satisfy at least two conditions.

• The scheme must be consistent, i.e. the approximated equation must resemble the continuous equation we want to solve. It is hoped that this property leads to the scheme being convergent, i.e. that the discrete solution U _h converges, when the discretization is refined (h → 0) to the exact solution U. The consistency of a scheme is, as we shall see 2.1 , a property that is easy to verify by elementary calculations, whereas proving the convergence...