Difference method of fourth order accuracy for the Laplace equation with multilevel nonlocal conditions.

Abstract We consider the multipoint nonlocal boundary value problem for the two-dimensional Laplace equation in a rectangular domain. The solution of this problem is defined as a 9-point finite difference solution, with the fourth order gluing operator of the local Dirichlet boundary value problem, by constructing a special method to find a function as the boundary value on the side of the rectangle, where the nonlocal condition is given. Numerical experiments are illustrated to support the analysis made. [ABSTRACT FROM AUTHOR]