An efficient numerical solution to the stochastic collection equation

Abstract

The SCE is converted to a set of moment equations in categories using a new analytical form of Bleck's approach. The equations are written in a form amenable to solution and to a category-by-category analysis of drop formation and removal. This method is unique in that closure of the equations is achieved using an expression relating high-order moments to any two layer order moments, thereby restricting the need for approximation of the category distribution function only to integrals over incomplete categories. Moments in categories are then expressed in terms of complete moments with the aid of linear or cubic polynomials. The method is checked for the case of the constant kernel and a linear polynomial kernel. Results show that excellent approximation to the analytical solutions for these kernels are obtained. -from Authors