Stability analysis for a family of space one dimensional convection diffusion difference schemes (Q1894992)

The author considers the numerical solution of the one dimensional convection diffusion equation. They develop a difference scheme involving five points for the spatial derivatives and a forward difference for the time derivative. These schemes involve a number of parameters, and diagrams are given to illustrate the stability regions of the schemes for various values of the parameters. The satisfaction of the von Neumann condition is discussed and the toughness of the scheme is investigated.