Computational methods for discrete boundary value problems, II

Abstract

For a given nonlinear discrete system together with nonlinear boundary conditions we use Newton's iterative scheme and provide sufficient conditions for its convergence to the unique solution. Then, the computational aspects of this iterative method on a floating point system are discussed. This includes necessary and sufficient conditions for the convergence of the Approximate Newton's method, an oscillatory state, and the stopping criterion. To make the analysis widely applicable all the results are proved component-wise. © 1992.