Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software - Brossura

Brossura

ISBN 10: 1441957634 ISBN 13: 9781441957634

Riassunto

The main objective of the book is to give an overview of numerical methods to compute parameters of a dynamical model by a least squares fit of experimental data. 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, partial differential equations, and partial differential algebraic equations (1D). Many different mathematical disciplines must be combined to find a solution, for example nonlinear programming, least squares optimization, systems of nonlinear equations, ordinary differential equations, discretization of partial differential equations, sensitivity analysis, automatic differentiation, and statistics.

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Contenuti

Preface. 1: Introduction. 2. Mathematical Foundations. 1. Optimality Criteria. 2. Sequential Quadratic Programming Methods. 3. Least Squares Methods. 4. Numerical Solution of Ordinary Differential Equations. 5. Numerical Solution of Differential Algebraic Equations. 6. Numerical Solution of One-Dimensional Partial Differential Equations. 7. Laplace Transforms. 8. Automatic Differentiation. 9. Statistical Interpretation of Results. 3: Data Fitting Models. 1. Explicit Model Functions. 2. Laplace Transforms. 3. Steady State Equations. 4.Ordinary Differential Equations. 5. Partial Differential Equations. 6. Optimal Control Problems. 4: Numerical Experiments. 1. Test Environment. 2. Numerical Pitfalls. 3. Testing the Validity of Models. 4. Performance Evaluation. 5: Case Studies. 1. Linear Pharmacokinetics. 2. Receptor-Ligand Binder Study. 3. Robot Design. 4. Multibody System of a Truck. 5. Binary Distillation Column. 6. Acetylene Reactor. 7. Transdermal Application of Drugs. 8. Groundwater Flow. 9. Cooling a Hot Strip Mill. 10. Drying Maltodextrin in a Convection Oven. 11. Fluid Dynamics of Hydro Systems. 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. 2. Execution of Generated Code. References. Index.

Dettagli dell?edizione

• ISBN 10: 1441957634
• ISBN 13: 9781441957634
• Rilegatura: Copertina flessibile
• Lingua: Inglese