Abstract
In enviromental pollution problems, the contamination is predicted by the convective diffusion equation (CDE) as a mathematical model. Nowadays many discretized schemes are proposed for solving the CDE exactly. Then the stability analysis as a necessary condition is firstly implemented to formulate the selection criteria for their schemes. Even though the schemes are stable, there are probably some cases which produce innegligible numerical errors. Therefore the error analysis of numerical solution is necessary for the next step of the stability analysis. The purpose of this studies is to apply the system control theory to the error analysis and then to analize the wave number transfer properties of the several schemes by taking the influence of the initial value into consideration. In this paper the one-dimensional unsteady CDE is employed for the simplicity of discussion and a new error estimation index is proposed. This index is related to both the amplification factor and the initial value, and its availability is investigated by a simple example.
