PDEFIT

Parameter estimation in time-dependent, one-dimensional partial differential equations

PDEFIT solves parameter estimation problems where the parameters are part of a time-dependent partial differential equation system in one spatial variable e.g. of parabolic, hyperbolic or any mixed type. The system may possess coupled ordinary differential equations, transition conditions between different integration areas, and arbitrary smooth equality or inequality constraints.

The line method is applied to discretize the system w.r.t. the spatial variable, to get a system of ordinary differential equations. Polynomial approximation, difference formulae and special upwind techniques for hyperbolic equations are applied. The usually large system of ordinary differential equations can be integrated by six available ODE-solvers, e.g. the Hairer and Wanner codes for stiff and non-stiff systems, where band structures are exploited. The resulting nonlinear least squares problem is solved by DFNLP or related algorithms.

Special features of PDEFIT are

• non-continous transition conditions,
• coupled ordinary differential equations,
• dynamic constraints depending on state variables,
• switching points for non-continuous model changes, either constant or variable,
• exploiting band structure,
• separate definition of flux possible,
• more than one fitting criterion allowed,
• various scaling options,
• generation of 3D-plot data and TEX reports,
• full documentation by initial comments,
• FORTRAN source code or executable code with interpretation of ASCII model file and automatic differentiation.

PDEFIT is a double precision FORTRAN-77 subroutine and all parameters are passed through arguments. An additional main program takes over some organizational ballast and reads in all problem data. A user provided subroutine is required to define initial values, constraints, the partial differential equation system together with suitable boundary conditions, coupled ordinary equations and fitting criteria. There exists a convenient user interface for PDEFIT called EASY-FIT running under MS-Windows 95/NT.

Need more info?

Take a look at the author's home page, or contact

Prof. K. Schittkowski 
Dept. of Mathematics
University of Bayreuth 
95440 Bayreuth, Germany 

klaus.schittkowski@uni-bayreuth.de

Reference:

M. Dobmann, K. Schittkowski, PDEFIT: A FORTRAN code for constrained parameter estimation in partial differential equations, Report, Dep. of Mathematics, University of Bayreuth (1995),

K. Schittkowski, Parameter estimation in one-dimensional time-dependent partial differential equations, Optimization Methods and Software, Vol. 7, No. 3-4, 165-210 (1997).

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