Operator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations |
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Authors: | Jürgen Geiser |
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Institution: | Department of Mathematics, Humboldt Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany |
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Abstract: | In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main focus of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. On the basis of the approximated eigenvalues of such linearized systems we choose the order of 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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Keywords: | 35J60 35J65 65M99 65N12 65Z05 74S10 76R50 |
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