ABSTRACT
This chapter deals with boundary equations with projections and the method of difference potentials. The method of difference potentials is a technique for the numerical solution of interior and exterior boundary value problems for linear partial differential equations. The method of finite differences is most efficient when using regular grids for solving problems with simple boundary conditions on domains of simple shape (e.g., a square, circle, cube, ball, annulus, torus, etc.). For curvilinear domains, the method of finite differences may encounter difficulties, in particular, when approximating boundary conditions. The chapter introduces five model problems, for which their respective approximate solutions is obtained using the method of difference potentials. It also presents difference approximation and spectral approximation of the boundary condition.
