On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems

Abstract

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem -d(2)u(t)/dt(2) + Au(t) = g(t), (0 <= t <= 1), du(t)/dt -Au(t) = f(t), (-1 <= t <= 0), u(1) = u(-1) + mu for differential equations in a Hilbert space H with a self-adjoint positive definite operator A is considered. The well posedness of this difference scheme in Holder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained and a numerical example is presented.