High order stable difference schemes for multipoint nonlocal boundary value problems for hyperbolic equations

In this work the multipoint nonlocal boundary value problem for hyperbolic equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The third and fourth order of accuracy difference schemes generated by the integer power of A approximately solving this abstract nonlocal boundary value problem are established. Stability estimates for the solution of these difference schemes are obtained. The theoretical statements for the solution of this difference schemes are supported by the numerical results using MATLAB.