Logarithmic norms and nonlinear DAE stability
The authors discuss the use of logarithmic norms for the stability analysis of nonlinear differential algebraic equations (DAEs). The main idea is to introduce (restricted) least upper bound logarithmic Lipschitz constants defined with respect to the left and right semi-inner products in a Banach space. The definition is made in such a way that it also covers unbounded operators with a view towards the application to problems in partial differential equations. The case of nonlinear index 1 differential algebraic equations is studied in detail including an analysis of the discretised equations for some simple discretisations. For Runge-Kutta methods the relation to B-stability is studied.
scientific article; zbMATH DE number 1876914