Method of moments over orthogonal polynomial bases

• A numerical scheme based on the method of moments and characteristics is derived.
• It is suitable for a wide class of PBEs with size-dependent growth rate.
• It represents an enhancement to an earlier scheme based on Taylor approximation.
• This is accomplished by introducing least square approximation instead.
• The method is generalized to multivariate particulate systems.

A method for the design of approximate models in the form of a system of ordinary differential equations (ODE) for a class of first-order linear partial differential equations of the hyperbolic type with applications to monovariate and multivariate population balance systems is proposed in this work. We develop a closed moment model by utilizing a least square approximation of spatial-dependent factors over an orthogonal polynomial basis. A bounded hollow shaped interval of convergence with respect to the order of the approximate ODE model arises as a consequence of the structural and finite precision computation numerical errors. The proposed modeling scheme is of interest in model-based control and optimization of processes with distributed parameters.