Investigations of the monotony of difference schemes for diffusion equations

The aim of this study is to develop a general theory of the monotony of difference schemes for a certain class of diffusion equations. It is shown that this problem is contained in the more comprehensive general boundary value problem for parabolic differential equations. It was thus possible to enlist and adapt the known estimates for weakly coupled systems of diffusion equations. A similar method can be applied to prove the monotony of strongly coupled systems of diffusion equations. To ensure its validity, the set of solutions has to be restricted. The estimates obtained were checked on a system of strongly coupled diffusion equations from plasma physics. As already discussed elsewhere in the literature, it was found that a certain amount of caution should be exercised in choosing the step sizes. (orig.)