NUMERICAL ANALYSIS Why is the order of convergence not the o

NUMERICAL ANALYSIS: Why is the order of convergence not the only important criteria in assessing the speed of convergence of an algorithm?

Solution

CONVERGENCE: means that the solution to the finite difference approximation approaches the true solution of the p.d.e. we the mesh is refined. off course the finite difference formulation must have the same set of ICs and BCs.

The important Lax Equivalence Theorem says that a finite difference approximation for a properly posed p.d.e. satisfying consistency ( meaning truncation error --> zero when time step size and mesh size goes to zero) and stability (meaning error goes on diminishing from time step to time step possesses necessary and sufficient conditions for convergence