A finite difference method for self-adjoint elliptic equations in three dimensions

摘要

In this article, we present a fourth-order finite difference method for the three-dimensional, second-order, self-adjoint elliptic partial differential equations subject to Dirichlet boundary conditions. A 19-point uniform cubic grid of size h is used to derive the method. The resulting system of algebraic equations could be solved by iterative methods. Numerical results of some test problems are given.