Regions of stability, equivalence theorems and the Courant-Friedrichs- Lewy condition
The Courant-Friedrichs-Lewy condition for the discretization of hyperbolic partial differential equations is shown to be equivalent to some results of Jeltsch and Nevanlinna concerning the regions of stability of k-step, m-stage methods for the integration of ordinary differential equations. New equivalence theorems between stability and convergence are provided, which improve on classical results. The paper also characterizes the methods for the numerical integration of the model equation \(u_ t=u_ x\) which are weakly stable when the mesh-ratio takes the maximum value allowed by the CFL condition.
scientific article; zbMATH DE number 3917627
scientific article