This article reviews the application of various notions from the theory of dy-namical systems to the analysis of numerical approximation of initial value problems over long time intervals. Standard error estimates comparing individual trajectories are of no direct use in this context since the error constant typically grows like the exponential of the time interval under consideration. Instead ...

The area of numerical analysis interacts with the area of control and systems theory in a number of ways, some of which are widely recognized and some of which are not fully appreciated or understood. Many of these topics were part of the presentations at the 2000 Mathematical Theory of Networks and Systems Conference held in Perpignan, France. Several of these contributions are included in the...

Complexity theory of numerical analysis is the study of the number of arithmetic operations required to pass from the input to the output of a numerical problem. To a large extent this requires the (global) analysis of the basic algorithms of numerical analysis. This analysis is complicated by the existence of ill-posed problems, conditioning and roundoff error. A complementary aspect (“lower b...

Numerous technological innovations, including material and process changes such as high–k gate dielectrics and metal gate electrodes, are investigated to meet the upcoming scaling requirements while keeping the gate leakage current within tolerable limits [1]. To overcome the technological problems, further theoretical and experimental research is needed which requires an extensive use of compu...

The aim of this paper is to present the numerical resolution of suction muffler configurations (by means of a tridimensional, unstructured, parallel and object oriented CFD&HT TermoFluids code (Lehmkuhl, et al. 2007) specially adapted to low Mach models (Lopez et al. 2012), coupled with the numerical resolution of the whole compressor domain (by means of a modular, unstructured and object orien...

There is growing recognition in the last few years that Lie groups and homogeneous spaces are often the right connguration space for the dis-cretization of time-dependent diierential equations. In this paper we review brieey recent advances in Lie-group calculations, concentrating mainly on approximation methods that advance a trivialised version of the diierential equation in a Lie algebra in ...