On the solution of statistical models of cell populations

Abstract The solution of integropartial differential equations resulting from statistical formulations of the behavior of cell populations has been investigated. In particular, a statistical model that views the microbial population as distributed according to its mass has been analyzed in detail. Solutions were obtained for growth in a well-stirred vessel for batch and continuous systems by the method of weighted residuals. The trial solutions were expressed as linear combinations of basic functions from a set complete in L 2 [ 0 , ∞) and the coefficients of the expansion determined by weighting the residual with functions also from a set complete in L 2 [ 0 , ∞). The solutions obtained by the method of weighted residuals were found to be sufficiently accurate in most cases. By using them as initial approximations to a successive approximation scheme, increased accuracy could be obtained within a short number of iterations. Various choices of basic and weighting functions were considered. The method used in this work may be pertinent to other particle fission processes.