On a nonlinear iterative method in applied mechanics-part 1

Abstract

A particular iterative method that has proven effective for finite difference solution of nonlinear membrane and plate problems is studied. The iteration is shown to belong to a general class of iterations termed SOR-Newton mk step iteration and corresponds to the choice mk = 1. As a result of this characterization we proceed to give the theoretical basis for studying convergence of the iteration. From this standpoint one is better able to evaluate the utility and limitations of the iterative scheme and compare it with alternative competitive schemes for various classes of problems and nonlinear systems in applied mechanics. © 1981.