A Godunov-Ryabenkii Instability for a Quickest Scheme
نویسنده
چکیده
We consider a finite difference scheme, called Quickest, introduced by Leonard in 1979, for the convection-diffusion equation. Quickest uses an explicit, Leith-type differencing and third-order upwinding on the convective derivatives yielding a four-point scheme. For that reason the method requires careful treatment on the inflow boundary considering the fact that we need to introduce numerical boundary conditions and that they could lead us to instability phenomena. The stability region is found with the help of one of the most powerful methods for local analysis of the influence of boundary conditions – the Godunov-Ryabenkii theory.
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