On order-interval methods for bounding zeros of order convex operators

摘要

Let f: X→X be an order convex operator, where X is partially ordered Banach space. The purpose of this paper is to describe a method which, under frequently satisfied hypotheses, permits two-sided bounds on zero of f to be obtained using any member of a wide class of procedures for determining one-sided bounds. The method is illustrated for systems of nonlinear algebraic equations which arise from the discretization of nonlinear two-point boundary-value problems. Numerical results for two such systems are given.