## PDEFIT: A FORTRAN Code for Data Fitting in Partial Differential Equations

K. Schittkowski: Optimization Methods and Software, Vol. 10, 539-582 (1999)

**Abstract:**
PDEFIT is a computer program to estimate parameters in a
system of one-dimensional differential equations and coupled
ordinary differential equations.
Equations without time-dependent derivatives are permitted.
The model allows arbitrary transition conditions between
separate integration areas for functions and derivatives,
switching conditions and dynamic constraints.
Proceeding from
given experimental data, e.g. observation times and measurements,
the distance of these measured data from the
solution of a system of differential equations at designated
spatial values is to be minimized in the L_2-, L_1-, or max-norm.
The method of lines is used to discretize the partial differential
equation with respect to polynomial approximation, difference formulae
and several special upwind and related formulae for hyperbolic PDE's.
The original system is transformed into a set of ordinary
differential equations or, alternatively, into a set of differential
algebraic equations, that is solved then by standard
ODE or DAE solvers.
We describe program organization and outline the usage of the
corresponding Fortran code.
A few examples are added to prove the feasibility of the
proposed approach.