A high order of accuracy of difference schemes for the nonlocal boundary value Schrödinger problem

In this study, nonlocal boundary value Schrödinger type problem in a Hilbert space with the self-adjoint positive definite operator is investigated. Single step stable third and fourth order of accuracy difference schemes for the numerical solution of this problem are presented. The main theorems on the stability of these difference schemes are established. In application, theorem on the stability of difference schemes for nonlocal boundary value problems for Schrödinger equations is proved. Numerical results are given.