Synchronous Multi-splitting Two-stage TOR Methods for Systems of Weakly Nonlinear Equations

Abstract

For the large sparse systems of weakly nonlinear equations arising in the discretizations of many classical differential and integral equations, this paper presents a class of synchronous parallel multi-splitting two-stage two-parameter over-relaxation (TOR) methods for getting their solutions by the high-speed multiprocessor systems. Under suitable assumptions, we study the global convergence properties of these synchronous multi-splitting two-stage TOR methods.