Finite difference method of first boundary problem for quasilinear parabolic systems (III)——Stability

The explicit, weak and strong implicit difference solution for the first boundary problem ofquasilinear parabolic system is considered:where u,, and f are m-dimensional vector valued functions, A is an m x m positively definite matrix, andFor this problem, the absolute and relative stability for the general difference schemes is justifiedin the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems.