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Comparison ODE theorems related to the method of lines

Leszczyński H.

Journal of Applied Analysis

2011

Vol. 17, nr 1

137-154

We prove a comparison theorem for an ODE and DAE system which arises from the method of lines. Under a Perron comparison condition on the functional dependence and a specific Lipschitz and (W+) condition on the classical argument, we obtain strong uniqueness criteria.

Uses of new sensitivity and DAE solving methods in SMARTMOBILE for verified analysis of mechanical systems

Auer E., Luther W.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 3

455-467

Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SMARTMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features and functionalities of SMARTMOBILE. In particular, we focus on its use of newly developed methods for sensitivity analysis and DAE solving for several practically relevant mechanical systems.