TABLE OF CONTENTS Alexander Ostermann
Institut f r Technische Mathematik, Geometrie und Bauinformatik, Universit t Innsbruck
Summary. When studying a mathematical model it is not enough to compute individual solutions. It is equally important to determine systematically the influence of parameter variations on these solutions. This is particularly true in engineering applications where parameters of the underlying model are often only imprecisely known. The main task of sensitivity analysis is to identify critical parameter dependences. In this short article, we review the basic ideas of sensitivity analysis for deterministic models. We emphasize the use of internal numerical differentiation which is a reliable and robust method. A greater part of the paper is devoted to typical applications, illustrated by numerical examples.
Sensitivity analysis is concerned with the propagation of uncertainties in mathematical models. Its main task is to assess the influence of parameters on the state of the system. The term parameter is used here in a broad sense. For example, if the underlying problem consists in calculating the shape of a rod under loading, then the length of the rod itself can be considered as a parameter and the purpose of sensitivity analysis could be to determine the influence of the length on the deformation of the rod.
In this paper we will model parameter dependent systems with the help of nonlinear functions. Within this framework, sensitivity can be defined as the Fr chet derivative of the function with respect to the parameters. It thus describes the variations of the output values for...
