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OverviewThe 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. Full Product DetailsAuthor: Klaus SchittkowskiPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2002 ed. Volume: 77 Dimensions: Width: 15.50cm , Height: 2.30cm , Length: 23.50cm Weight: 0.879kg ISBN: 9781402010798ISBN 10: 1402010796 Pages: 396 Publication Date: 31 December 2002 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1 Introduction.- 2 Mathematical Foundations.- 3 Data Fitting Models.- 4 Numerical Experiments.- 5 Case Studies.- Appendix A: Software Installation.- 1 Hardware and Software Requirements.- 2 System Setup.- 3 Packing List.- Appendix B: Test Examples.- 1 Explicit Model Functions.- 2 Laplace Transforms.- 3 Steady State Equations.- 4 Ordinary Differential Equations.- 5 Differential Algebraic Equations.- 6 Partial Differential Equations.- 7 Partial Differential Algebraic Equations.- Appendix C: The PCOMP Language.- Appendix D: Generation of Fortran Code.- 1 Model Equations.- 1.1 Input of Explicit Model Functions.- 1.2 Input of Laplace Transformations.- 1.3 Input of Systems of Steady State Equations.- 1.4 Input of Ordinary Differential Equations.- 1.5 Input of Differential Algebraic Equations.- 1.6 Input of Time-Dependent Partial Differential Equations.- 1.7 Input of Partial Differential Algebraic Equations.- 2 Execution of Generated Code.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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