numerical analysis operator-splitting method initial value problems iterative solver method nonlinear equations Modified Jacobian Newton Iterative Method with Embedded Domain Decomposition Method Juergen Geiser Geiser Juergen Christos Kravvaritis Kravvaritis Christos Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 16 pp.

Modified Jacobian Newton Iterative Method with Embedded Domain Decomposition Method

Juergen Geiser , Christos Kravvaritis

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 16 pp.

MSC 2000

35K45 Initial value problems for parabolic systems
35K90 Abstract parabolic evolution equations

Abstract
In this article a new approach is proposed for constructing a domain decomposition method based on the iterative operator-splitting method for nonlinear differential equations. The convergence properties of such a method are studied. The main feature of the proposed idea are the linearization of the nonlinear equations and the application of iterative splitting methods. We present iterative operator-splitting method with embedded Newton methods to solve the 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.

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