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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 307298, 24 pages
Research Article

Modified Jacobian Newton Iterative Method: Theory and Applications

Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany

Received 3 September 2008; Revised 10 November 2008; Accepted 4 December 2008

Academic Editor: José Roberto Castilho Piqueira

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.