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

Abstract EN

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem −d2u(t)/dt2+Au(t)=g(t), (0≤t≤1), du(t)/dt−Au(t)=f(t), (−1≤t≤0), u(1)=u(−1)+μ 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 Hölder 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.