FINITE-DIFFERENCE METHOD OF 1ST BOUNDARY-PROBLEM FOR QUASI-LINEAR PARABOLIC-SYSTEMS

In this paper, we consider the existence, uniqueness and convergence of weak and strong implicit difference solution for the first boundary problem of quasilinear parabolic system: [GRAPHICS] where u, phi and f are m-dimensional vector valued functions, A is an m x m positively definite matrix and u(x)k denotes partial k(u)/partial x(k). For this problem, the estimations of the difference solution are obtained. As h-->0, DELTA-t-->0, the difference solution converges weakly in W2(2M,1) (Q(T)) to the unique generalized solution u(x,t) is-an-element-of W2(2M,1)(Q(T)) of problems (1), (2), (3). Especially, a favorable restriction condition to the step lengths DELTA-t and h for explicit and weak implicit schemes is found.