Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
On the influence of numerical boundary conditions
Applied Numerical Mathematics
Stability Analysis of Difference Methods for Parabolic Initial Value Problems
Journal of Scientific Computing
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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.