Mathematical models for diffusion processes like heat propagation, dispersion of pollutants etc., are normally partial differential equations involving unknown parameters. For practical use, one has to estimate these parameters. In this paper we consider a simple case of heat propagation in a homogeneous wall. The resulting partial differential equation is solved using numerical techniques and tools of system identification are used to estimate the unknown parameters. In particular we examine the effect of model order selection when a Chebyshev collocation method is applied for solving partial differential equations.
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