Logarithmic norms and nonlinear DAE stability - Higueras, I; Söderlind, Gustaf (BIT Numerical Mathematics, 2002)
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.
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
Keywords: monotonicity; nonlinear stability; error bounds; differential inequalities; differential-algebraic equations; logarithmic Lipschitz constant; logarithmic norm; difference inequalities