Numerical Data Fitting in Dynamical Systems

The main objective of the volume is to give an overview of numerical methods that are needed to compute parameters of a dynamical model by a least squares fit. The mathematical equations under consideration are explicit model functions or steady state systems in the simplest case, or responses of dynamical systems defined by ordinary differential equations, differential algebraic equations, and one-dimensional partial differential equations. Many different mathematical disciplines must be combined, and the intention is to present some fundamental ideas of the numerical methods needed. Possible pitfalls are outlined to illustrate failures obtained by insufficient numerical modeling. Remedies are proposed to overcome instabilities and deficiencies of model formulations. We discuss how to check the validity of mathematical models, and present numerical results of comparative test runs of least squares codes. To analyze these questions in a quantitative way, 945 test examples are attached together within an interactive software system running under MS-Windows. Moreover, 12 real life case studies show how mathematical models and data fitting algorithms are effectively used in practical situations.