Numerical solution of the nonlocal boundary value problem for elliptic equations

in an arbitrary Banach space E with the positive operator A and its related applications have been investigated by many researchers (see, for example, [1–3] and the references given therein). In mathematical modeling, elliptic equations are used together with local boundary conditions specifying the solution on the boundary of the domain. In some cases, classical boundary conditions cannot describe process or phenomenon precisely. Therefore, mathematical models of various physical, chemical, biological or environmental processes often involve nonclassical conditions. The well-posedness of various nonlocal boundary value problems for partial differential and difference equations has been studied extensively by many researchers (see, e.g., [4–21] and the references given therein). In the present paper the abstract nonlocal boundary value problem for differential equation of elliptic type