In the present paper, the finite difference method for the initial value problem for the first order partial differential equation with the nonlocal boundary condition is investigated. The positivity of the difference analogy of the space operator generated by this problem in the space C with maximum norm is established. The structure interpolation spaces generated by this difference operator is studied. The positivity of this difference operator in Holder spaces is established. In applications, the stability estimates for the solution of the difference scheme for the first order partial differential equation with the nonlocal boundary condition are obtained. A numerical experiment is given.