The author presents the FORTRAN computer program PDEFIT to estimate parameters in a system of one-dimensional partial differential equations. Using a method of lines, the partial differential equations are discretized and transformed into a set of ordinary differential equations that are solved then by standard ODE or DAE solvers.\parProceeding from given experimental data the distance of these measured data from the solution of the differential equations is to be minimized in different $L$-norms. Some examples are presented to prove the feasibility of the given approach.

References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Bergou, El Houcine; Diouane, Youssef; Kungurtsev, Vyacheslav; Royer, Clément W.: A nonmonotone matrix-free algorithm for nonlinear equality-constrained least-squares problems (2021)
  2. Hassani, H.; Machado, J. A. Tenreiro; Naraghirad, E.; Sadeghi, B.: Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials (2020)
  3. Liu, Chongyang; Gong, Zhaohua; Teo, Kok Lay: Robust parameter estimation for nonlinear multistage time-delay systems with noisy measurement data (2018)
  4. Mohd Mahali, Shalela; Wang, Song; Lou, Xia: Estimation of effective diffusion coefficients of drug delivery devices in a flow-through system (2014)
  5. Chudej, K.; Bauer, Marco; Pesch, H. J.; Schittkowski, K.: Numerical simulation of a Molten carbonate fuel cell by partial differential algebraic equations (2008)
  6. Schittkowski, Klaus: Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery (2008)
  7. Schittkowski, K.: Parameter identification in one-dimensional partial differential algebraic equations (2007)
  8. Androshchuk, Taras: Regularity conditions and the maximum likelihood estimation in dynamical systems with small fractional Brownian noise (2006)
  9. Müller, T. G.; Faller, D.; Timmer, J.; Swameye, I.; Sandra, O.; Klingmüller, U.: Tests for cycling in a signalling pathway (2004)
  10. Müller, T. G.; Timmer, J.: Parameter identification techniques for partial differential equations. (2004)
  11. Schittkowski, K.: Data fitting in partial differential algebraic equations: Some academic and industrial applications. (2004)
  12. Voss, Henning U.; Timmer, Jens; Kurths, Jürgen: Nonlinear dynamical system identification from uncertain and indirect measurements. (2004)
  13. Müller, T. G.; Noykova, N.; Gyllenberg, M.; Timmer, J.: Parameter identification in dynamical models of anaerobic waste water treatment (2002)
  14. Frías, Jesús M.; Oliveira, Jorge C.; Schittkowski, Klaus: Modeling and parameter identification of a maltodextrin DE 12 drying process in a convection oven (2001)
  15. Blatt, M.; Schittkowski, K.: Optimal control of one-dimensional partial differential algebraic equations with applications (2000)
  16. Schittkowski, K.: PDEFIT: A FORTRAN code for data fitting in partial differential equations (1999)
  17. Schittkowski, K.: Parameter estimation in one-dimensional time-dependent partial differential equations (1997)
  18. Schittkowski, K.: Parameter estimation in differential equations (1995)