Stability Analysis of Difference Methods for Parabolic Initial Value Problems

A decomposition of the numerical solution can be defined by the normal mode representation, that generalizes further the spatial eigenmode decomposition of the von Neumann analysis by taking into account the boundary conditions which are not periodic. In this paper we present some new theoretical results on normal mode analysis for a linear and parabolic initial value problem. Fur-thermore we suggest an algorithm for the calculation of stability regions based on the normal mode theory. KEY WORDS: Convection–diffusion; finite differences; stability; normal mode analysis