Parallel multisplitting explicit AOR methods for numerical solutions of semilinear elliptic boundary value problems

A class of parallel multisplitting explicit AOR methods for a large scale system of nonlinear algebraic equations, which is a finite difference approximation of a semilinear elliptic boundary value problem, are presented. This class of methods avoid the inner iteration and are shown to converge monotonically either from above or from below to a solution of the system without the monotonicity property of nonlinearity. Moreover, this class of methods are applicable to the pure Neumann boundary value problems. A sufficient condition for the uniqueness of the solutions is provided. The global convergence of the methods and the influence of the acceleration factor on the convergence rate are considered. The applications and numerical results are given.