Parameter Estimation in One-Dimensional Time-Dependent Partial
K. Schittkowski: Optimization Methods and Software, Vol. 7, No. 3-4, 165-210 (1997)
We consider an approach to determine parameters in a
system of one-dimensional time-dependent parabolic differential equations
and coupled ordinary differential equations.
The model allows transmission conditions between
separate integration areas for functions and derivatives.
given experimental data, e.g. observation times and measurements,
the minimum least squares distance of the measured data from the
solution of the dynsmical system at designated
space values is to be computed.
The method of lines is used to discretize the partial differential
equation with respect to polynomials of arbitrary odd order, and
to transform the original system into a sequence of ordinary
differential equations, that can be solved then by any available
Numerical test results are included to show the efficiency of different
ODE solvers and optimization routines based on a collection of 20 test
To download the report, click here: reportPDE1D.pdf
(Acrobat Reader version)