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Data fitting in partial differential algebraic equations: Some academic and industrial applications. (English) Zbl 1046.65079

Summary: The author 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.

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35R10 Partial functional-differential equations
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