This paper deals with the numerical approximation of weak solutions of the first initial, boundary value problem for the higher order, nonlinear parabolic equation $$\sum\limits_{|\alpha | , |\beta | \leqq p} {D^\alpha (a_{\alpha \beta } (x,t)) \leqq D^\beta u - \partial u/\partial t = f} $$ wheref=f(x, t, D v u), |v|≤p−1, p≥1 is an integer and α, β,v are multi-indices.