numerical analysis operator-splitting method initial value problems iterative solver method Iterative operator-splitting methods for nonlinear differential equations and applications of deposition processes. Juergen Geiser Geiser Juergen Lena Noack Noack Lena Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 20 pp.

Iterative operator-splitting methods for nonlinear differential equations and applications of deposition processes.

Juergen Geiser , Lena Noack

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 20 pp.

MSC 2000

35J60 Nonlinear PDE of elliptic type
35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE

Abstract
In this article we consider iterative operator-splitting methods for nonlinear differential equations. The main feature of the proposed idea is the embedding of Newton's method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator-splitting methods by providing improved results and convergence rates. We apply our results to deposition processes.

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