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

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 L ∞-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.