numerical analysis operator-splitting method initial value problems iterative solver method eigenvalue problem convection-diffusion-reaction equation Operator-Splitting Methods Respecting Eigenvalue Problems for Nonlinear Equations and Applications for Burgers Equations. Juergen Geiser Geiser Juergen Lena Noack Noack Lena Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 30 pp.

Operator-Splitting Methods Respecting Eigenvalue Problems for Nonlinear Equations and Applications for Burgers Equations.

Juergen Geiser , Lena Noack

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 30 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 with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. 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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