HIGH ORDER DIFFERENCE GROUP EXPLICIT (HODGE) METHODS.

Point iterative methods at which, at any one time only a single equation of the linear system is treated are well known. However, in recent times block (or line) iterative methods, in which a group of equations (or points on the grid mesh) are treated implicitly and solved directly by a specialized algorithm+ have become the standard techniques for solving the sparse linear systems derived from the finite difference/element discretization of a self-adjoint elliptic partial differential equation on a two-dimensional grid. The main concern of this paper is to construct new groupings of the mesh points of the network into four and nine points using the high order accurate nine-point finite difference equations and to investigate their advantages when used explicitly in the standard iterative methods. [ABSTRACT FROM AUTHOR]