Finite difference schemes for a size structured coagulation-fragmentation model in the space of Radon measures

Abstract

Abstract We study a size-structured coagulation-fragmentation model formulated in the space of Radon measures. We reformulate this model as a mass conservation law on this space and establish its well-posedness. We develop and compare multiple finite difference schemes. In particular, we develop a fully explicit scheme and a semi-implicit scheme for the structured coagulation-fragmentation model, and we develop an explicit scheme based on the conservation law formulation. We prove convergence for each scheme and test the schemes against multiple well-known examples. We analyze and compare important properties of each scheme, such as mass conservation, order of convergence and computation time.