| Title | Logarithmic norms and nonlinear DAE stability |
| Authors | I Higueras, Gustaf Söderlind |
| Alternative Location | http://dx.doi.org/10.1023/A..., Restricted Access |
| Publication | BIT NUMERICAL MATHEMATICS |
| Year | 2002 |
| Volume | 42 |
| Issue | 4 |
| Pages | 823 - 841 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | SWETS ZEITLINGER PUBLISHERS |
| Abstract English | 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. |
| Keywords | monotonicity, nonlinear stability, error bounds, differential inequalities, differential-algebraic equations, logarithmic Lipschitz constant, logarithmic norm, difference inequalities, |
| ISBN/ISSN/Other | ISSN: 0006-3835 |
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