Nonlocal boundary value problem for elliptic-schrödinger differential equations

The abstract nonlocal boundary value problem for differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces with a weight is established. The coercivity inequalities for the solutions of the boundary value problems for elliptic-Schrödinger equations are obtained. The first and the second order accuracy difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The well-posedness of these difference schemes in Hölder spaces is established. In applications, the coercivity inequalities for the solutions of difference schemes for elliptic-Schrödinger equation are obtained. The Matlab implementation of these difference schemes for elliptic-Schrödinger equation is presented.