Finite difference method for multipoint nonlocal elliptic–parabolic problems

A finite difference method for solving the multipoint elliptic–parabolic partial differential equation with a nonlocal boundary condition is considered. Stable difference schemes accurate to first and second orders for this problem are presented. Stability, almost coercive stability and coercive stability for the solution of these difference schemes are obtained. The theoretical statements for the solution of these difference schemes are supported by numerical examples.