Abstract
In this article, we consider the problem of parameter estimation for an integrodifferential population balance equation model which describes the crystal size distribution for a continuous crystallizer at steady state with random growth dispersion and particle agglomeration. In order to obtain a physically meaningful positive solution to the problem, we formulate the model as a boundary value problem (BVP) on [0, L], and apply a modified shooting method to obtain its solution. We then couple the shooting method with an optimization scheme in order to estimate the constant parameters. To test this optimization scheme, we generate a synthetic data set from the physically meaningful part of an analytical solution and then show that it is possible to recapture the values of the parameters used to generate the data by solving the inverse BVP.
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