(untitled) (Journal of Computational Mathematics, 1991)
In this paper, we deal with the finite difference method for the initial boundary value problem of the nonlinear pseudo-parabolic system (-1)^Mu_t+A(x,t,u,u_x,…,u_x 2M-1)u_x2M_t=F(x,t,u,u_x,…,u_x 2M),u_xk(o,t)=ψ_0k(t), u_xk(L,t)=ψ_1k(t),k=0,1,…,M-1,u(x,0)=φ (x) in the rectangular domain D=[0≤ X≤ L,0≤ t≤ T], where u(x,t)=(u_1(x,t),u_2(x,t),…,u_m(x,t)),φ (x),ψ_0k(t),ψ_1k(t),F(x,t,u,u_x,…,u_x 2M) are m-dimensional vector functions, and A(x,t,u,u_x,…,u_x2M-1) is an m× m positive definite matrix. The existence and uniqueness of solution for the finite difference system are proved by fixed-point theory. Stability, convergence and error estimates are derived.