Abstract
Nonlocal boundary value problems for elliptic equations arise in many applied models; however, their numerical analysis in Banach spaces, particularly under the Samarskii–Ionkin condition, remains insufficiently studied. Motivated by this gap, the present work develops first- and second-order two-step difference schemes for the numerical solution of nonlocal boundary value problems associated with elliptic equations involving a positive definite operator in a Banach space. Coercive stability estimates for the proposed schemes are established. Furthermore, the abstract results are applied to the construction of stable difference schemes for multidimensional elliptic partial differential equations. Numerical experiments for two- and three-dimensional problems confirm the efficiency and applicability of the proposed method.