The method of moments is an alternative to the direct discretization approaches for the numerical solution of fragmentation equation. Due to its rather small computational requirements, it is ideally suited for the simulation of fragmentation processes exhibiting spatial variation. A survey of the application of several methods of moments to the fragmentation equation was recently presented [Power Technol. 127 (2002) 116]. In that work, only the case of homogeneous fragmentation functions was considered and several methods were tested for various cases. In the present work, which is a sequel of the previous one, methods are chosen that can be used for arbitrary fragmentation functions, and are generalized/adjusted for best performance by taking into account the scope of a particular simulation. The results obtained are quite concrete; i.e. specific methods are proposed which are proven to be appropriate through rather extensive comparisons with exact solutions under several realistic conditions. The methods proposed can serve as the basic module in computational tools for the numerical solution of complicated spatially distributed fragmentation problems. (C) 2004 Elsevier B.V. All rights reserved.