FINITE-DIFFERENCE METHOD OF FIRST BOUNDARY-PROBLEM FOR QUASI-LINEAR PARABOLIC-SYSTEMS .4. CONVERGENCE OF ITERATION

More work is done to study the explicit, weak and strong implicit diff erence solution for the first boundary problem of quasilinear paraboli c system: u(t) = (-1)(M+1) A(x, t, u, ..., u(x) M-1)u(x)2M + f(x, t, u , ..., u(x)2M-1), (x, t) is an element of Q(T) = {0 < l, 0 < t less th an or equal to T}, u(x)(k) (0, t) = (k = 0, 1, ..., M - 1), 0 < t less than or equal to T, u(x, 0) = phi(x), 0 less than or equal to x less than or equal to l, where u, phi, and f are m-dimensional vector value d functions, A is an m x m positively definite matrix, and u(t) = part ial derivative u/partial derivative t, u(x)(k) = partial derivative(k) u/partial derivative x(k). For this problem, the convergence of iterat ion for the general difference schemes is proved.