Back Data Fitting in Partial Differential Algebraic Equations: Some Academic and Industrial Applications
K. Schittkowski: Journal of Computational and Applied Mathematics, Vol. 163, No. 1, 29-57 (2004)
The paper introduces a numerical method to estimate parameters in systems of one-dimensional partial differential algebraic equations. Proceeding from given experimental data, i.e., observation times and measurements, the minimum least squares distance of measured data from a fitting criterion is computed, which depends on the solution of the dynamical system. We present a typical black box approach that is easily implemented proceeding from some standard numerical analysis tools. Main emphasis of the paper is to present a couple of practical applications from industry and academia, to give an impression on the complexity of real life systems of partial differential equations. The domains of application are pharmaceutics, geology, mechanical engineering, chemical engineering, food engineering, and electrical engineering.
To download a preprint, click here: pde_appl.pdf