Logarithmic Norms and Nonlinear DAE Stability |
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Authors: | Inmaculada Higueras Gustaf Söderlind |
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Affiliation: | (1) Departamento de Matemática e Informática, Universidad Pública de Navarra, ES-31006 Pamplona, Spain;(2) Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden |
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Abstract: | Logarithmic norms are often used to estimate stability and perturbation bounds in linear ODEs. Extensions to other classes of problems such as nonlinear dynamics, DAEs and PDEs require careful modifications of the logarithmic norm. With a conceptual focus, we combine the extension to nonlinear ODEs [15] with that of matrix pencils [10] in order to treat nonlinear DAEs with a view to cover certain unbounded operators, i.e. partial differential algebraic equations. Perturbation bounds are obtained from differential inequalities for any given norm by using the relation between Dini derivatives and semi-inner products. Simple discretizations are also considered. |
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Keywords: | Logarithmic norm logarithmic Lipschitz constant monotonicity nonlinear stability error bounds differential-algebraic equations differential inequalities difference inequalities |
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