A Note on the Stability of Multi-Level Difference Schemes

Abstract:

      In this note we discuss how to use finite Fourier method correctly to analysis the stability of mult-level difference schemes. As an example, we have showed that the classical explicit scheme with usual initial data for the initial-boundary problem of wave equation is not stable when the mesh ratio r = l and have also showed that we can modify one of the initial data to get stability when r=1.