Numerical solution of multi-variable cell population balance models. II. Spectral methods

Several Galerkin, Tau and Collocation (pseudospectral) approximations have been developed for the solution of the multi-variable cell population balance model in its most general formulation, i.e. for any set of single-cell physiological state functions. Time-explicit methods were found to be more efficient than time-implicit methods for the time integration of the system of ordinary differential equations that results after the spectral approximation in space. The Legendre and Tchebysheff polynomials that were used in Tau algorithms were shown to have significantly worse convergence and stability properties than the Galerkin and collocation algorithms that were applied with sinusoidal trial functions. The collocation method that was implemented with discrete fast Fourier transforms was found to be the most efficient from all the Galerkin and Tau algorithms that were developed. However, the method was inferior to the best finite difference algorithm that was presented in our earlier work.