DIFFERENCE-SCHEMES FOR FULLY NONLINEAR PSEUDO-PARABOLIC SYSTEMS WITH 2 SPACE DIMENSIONS

The first boundary value problem for the fully nonlinear pseudoparabol ic systems of partial differential equations with two space dimensions by the finite difference method is studied. The existence and uniquen ess of the discrete vector solutions for the difference system are est ablished by the fixed point technique. The stability and convergence o f the discrete vector solutions of the difference schemes to the vecto r solutions of the original boundary problem of the fully nonlinear ps eudoparabolic system are obtained by way of a priori estimation. Here the unique smooth vector solution of the original problem for the full y nonlinear pseudo-parabolic system is assumed. Moreover, by the metho d used here, it on be proved that analogous results hold for fully non linear pseudo-parabolic system with three space dimensions, and improv e the known results in the case of one space dimension.