The selection of mesh size for computation of waves over long times (Q1319096)

The numerical errors in finite difference schemes for a linear wave propagation problem are studied from the point of view of how the propagation time influences the choice of the mesh size. It is shown that for a difference scheme with order of accuracy \(p\) and a long propagation time \(t\), the mesh size should be of order \(O(t^{-1/p})\).