PDEFIT: A FORTRAN code for data fitting in partial differential equations

Optimization Methods and Software

Volumn 10, Issue 3, 1999, Pages 539-582

  Schittkowski, K ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; CURVE FITTING; DIFFERENCE EQUATIONS; FORTRAN (PROGRAMMING LANGUAGE); INTEGRATION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR PROGRAMMING; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

DATA FITTING; LINE METHOD; SOFTWARE PACKAGE PDEFIT;

COMPUTER SOFTWARE;

EID: 0032666365     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556789908805727     Document Type: Article

References (28)

1. F. Andersson and B. Olsson (eds.) (1985): Lake Gådsjön. An acid forest lake and its catchment, Ecological Bulletins, Vol. 37, Stockholm.
2. P. Boderke, K. Schittkowski, M. Wolf and H.P. Merkle (1997): A mathematical model for diffusion and concurrent metabolism in metabolically active tissue, submitted for publication.
3. S.R. Chakravarthy and S Osher (1984): High resolution schemes and the entropy condition, SIAM Journal on Numerical Analysis, 21(5), 955-984.
4. S.R. Chakravarthy and S. Osher (1984): Very high order accurate TVD schemes, ICASE Report No. 84-44.
5. S.R. Chakravarthy and S. Osher (1985): Computing with high resolution upwind schemes for hyperbolic equations, Lectures in Applied Mathematics, 22, 57-86.
6. J.E. Dennis, Jr., D.M. Gay and R.E. Welsch (1993): Algorithm 573: NL2SOL - An adaptive nonlinear least-squares algorithm, ACM Transactions on Mathematical Software, 7(3), 369-383.
7. M. Dobmann, M. Liepelt and K. Schittkowski (1995): Algorithm 746: PCOMP: A FORTRAN code for automatic differentiation, ACM Transactions on Mathematical Software, 21(3), 233-266.
8. M. Dobmann, M. Liepelt, K. Schittkowski and C. Traßl (1995): PCOMP: A FORTRAN code for automatic differentiation - language description and user's guide, Technical Report, Department of Mathematics, University of Bayreuth.
9. E. Hairer, S.P. Norsett and G. Wanner (1991): Solving Ordinary Differential Equations I. Nonstiff Problems, Series Computational Mathematics, Springer.
10. E. Hairer and G. Wanner (1991): Solving Ordinary Differential Equations II. Stiff and Differential Algebraic Problems, Series Computational Mathematics, Springer.
11. P. Lindström (1983): A general purpose algorithm for nonlinear least squares problems with nonlinear constraints, Report UMINF-103.83, Institute of Information Processing, University of Umea, Umea, Sweden.
12. M. Molander (1990): Computer aided modelling of distributed parameter processes, Technical Report No. 193, School of Electrical and Computer Engineering, Chalmers University of Technology, Göteborg, Sweden.
13. B. Nickel (1995): Parameterschätzung basierend auf der Levenberg-Marquardt-Methode in Kombination mit direkter Suche, Diploma Thesis, Department of Mathematics, University of Bayreuth.
14. J.R. Dormand and P.J. Prince (1981): High order embedded Runge-Kutta formulae, Journal on Computational Applied Mathematics, 7, 67-75.
15. W.E. Schiesser (1991): The numerical method of lines, Academic Press Inc., San Diego.
16. K. Schittkowski (1985/86): NLPQL: A FORTRAN subroutine solving constrained nonlinear programming problems, Annals of Operations Research, 5, 485-500.
17. K. Schittkowski (1988): Solving nonlinear least squares problems by a general purpose SQP-method, In: Trends in Mathematical Optimization, K.-H. Hoffmann, J.-B. Hiriart-Urruty, C. Lemarechal, J. Zowe (eds.), International Series of Numerical Mathematics, Vol. 84, Birkhäuser.
18. K. Schittkowski (1994): MODFIT: A FORTRAN subroutine for estimating parameters in systems of ordinary differential equations, Technical Report, Department of Mathematics, University of Bayreuth.
19. K. Schittkowski (1994): Parameter estimation in systems of nonlinear equations, Numerische Mathematik, 68, 129-142.
20. K. Schittkowski (1995): Parameter Estimation in Differential Equations, WSSIAA 5, World Scientific Publishing Company, 353-370.
21. K. Schittkowski (1996): EASY-FIT: Parameter estimation in dynamical systems, User's Guide, Department of Mathematics, University of Bayreuth.
22. K. Schittkowski (1997): Parameter estimation in one-dimensional time-dependent partial differential equations, Optimization Methods and Software, 7(3-4), 165-210.
23. I. Steingässer (1994): The organized HaCaT cell culture sheet: A model approach to study epidermal peptide drug metabolism, Dissertation, Pharmaceutical Institute, ETH Zürich.
24. P.K. Sweby (1984): High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM Journal on Numerical Analysis, 21(5), 995-1011.
25. M.T. Van Genuchten and P.J. Wierenga (1976): Mass transfer studies in sorbing porous media. 1. Analytical solutions, Soil Sci. Soc. Am. Journal, 44, 892-898.
26. Z. Wang and B.E. Richards (1991): High resolution schemes for steady flow computation, Journal of Computational Physics, 97, 53-72.
27. H.Q. Yang and A.J. Przekwas (1992): A comparative study of advanced shock-capturing schemes applied to Burgers'equation, Journal of Computational Physics, 102, 139-159.
28. H.C. Yee (1985): Construction of a class of symmetric TVD schemes, Lectures in Applied Mathematics, 22, 381-395.