Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
Copyright © 2009 Jürgen Geiser. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This article proposes a new approach to the construction of a linearization method based on the
iterative operator-splitting method for nonlinear differential equations. The convergence properties
of such a method are studied. The main features of the proposed idea are the linearization
of nonlinear equations and the application of iterative splitting methods. We present an iterative
operator-splitting method with embedded Newton methods to solve nonlinearity. We confirm
with numerical applications the effectiveness of the proposed iterative operator-splitting method
in comparison with the classical Newton methods. We provide improved results and convergence rates.