Numerical data fitting in dynamical systems. A practical introduction with applications and software. With CD-ROM The book is the outcome of the research activities of the author in the area of numerical methods for optimization problems that are needed to compute parameters of a dynamical model by a least square fit. The mathematical configurations that must be provided by the system analyst are defined by ordinary differential equations, differential algebraic equations, or one-dimensional partial differential equations which we can meet in real life phenomena, as in engineering, natural or medical sciences.par The mathematical models and data fitting calculations are illustrated by case studies from pharmaceutics, mechanical, electrical, chemical engineering and ecology.par The book contains a CD with numerical algorithms presented in the book giving to the reader the opportunity to make applications with algorithms, data, and solution tolerances of the program that run under Windows 95/98/NT4.0/2000. (Source:

References in zbMATH (referenced in 28 articles , 1 standard article )

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  1. Aydogmus, Ozgur; Tor, Ali Hakan: A modified multiple shooting algorithm for parameter estimation in ODEs using adjoint sensitivity analysis (2021)
  2. Carey, M.; Ramsay, J. O.: Fast stable parameter estimation for linear dynamical systems (2021)
  3. Dattner, Itai; Ship, Harold; Voit, Eberhard O.: Separable nonlinear least-squares parameter estimation for complex dynamic systems (2020)
  4. Huang, Hanwen; Handel, Andreas; Song, Xiao: A Bayesian approach to estimate parameters of ordinary differential equation (2020)
  5. Chen, Nan; Majda, Andrew J.: A new efficient parameter estimation algorithm for high-dimensional complex nonlinear turbulent dynamical systems with partial observations (2019)
  6. Gonçalves, Douglas S.; Santos, Sandra A.: A globally convergent method for nonlinear least-squares problems based on the Gauss-Newton model with spectral correction (2016)
  7. Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats: Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements (2014)
  8. Chowdhury, Souma; Tong, Weiyang; Messac, Achille; Zhang, Jie: A mixed-discrete particle swarm optimization algorithm with explicit diversity-preservation (2013)
  9. Rafajłowicz, Ewaryst; Rafajłowicz, Wojciech: Control of linear extended (n)-D systems with minimized sensitivity to parameter uncertainties (2013)
  10. Burdakov, Oleg; Kapyrin, Ivan; Vassilevski, Yuri: Monotonicity recovering and accuracy preserving optimization methods for postprocessing finite element solutions (2012)
  11. Exler, Oliver; Lehmann, Thomas; Schittkowski, Klaus: A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization (2012)
  12. Rafajłowicz, Ewaryst; Styczeń, Krystyn; Rafajłowicz, Wojciech: A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics (2012)
  13. Schlüter, Martin; Gerdts, Matthias; Rückmann, Jan-J.: A numerical study of MIDACO on 100 MINLP benchmarks (2012)
  14. Schittkowski, Klaus: Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery (2008)
  15. Wang, Xiaoqiang; Du, Qiang: Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches (2008)
  16. Gerdin, Markus; Schön, Thomas B.; Glad, Torkel; Gustafsson, Fredrik; Ljung, Lennart: On parameter and state estimation for linear differential--algebraic equations (2007)
  17. Schittkowski, K.: Parameter identification in one-dimensional partial differential algebraic equations (2007)
  18. Uciński, Dariusz; Bogacka, Barbara: A constrained optimum experimental design problem for model discrimination with a continuously varying factor (2007)
  19. Patan, Maciej: Optimal activation policies for continuous scanning observations in parameter estimation of distributed systems (2006)
  20. Pintér, János D.; Kampas, Frank J.: MathOptimizer Professional: key features and illustrative applications (2006)

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