Asymptotic error estimate of iterative Newton-type methods and its practical application

Abstract

In the paper we present a new result for evaluating the convergence error of iterative Newton-type methods with respect to the number of iteration steps. We prove an explicit asymptotically correct estimate that provide a fruitful basis to treat many practical situations. As an example of such application, we solve three important problems arising in numerical integration of ordinary differential equations and semi-explicit index 1 differential-algebraic systems. © Springer-Verlag Berlin Heidelberg 2004.