Abstract: Some sufficient conditions are considered, under which the solutions of a class of incompletely exponentially fitted difference schemes converge uniformly in e, with orders one and two, to the solution of the singular perturbation problem: eu"+a(x)u’-b(x)u=f(x), for 0<x<1, u(0), u(1) given. ε∈(0,l],a(x)>a>0, b(x)≥0. From these conditions.an incompletely exponentially fitted second-order scheme is derived. Finally, the results of some numerical experiments are given.

Key words: global attractor, plate equation, regularity, finite dimensionality, unbounded domain