High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures

Abstract

In this paper, we develop explicit and semi-implicit second-order high-resolution finite difference schemes for a structured coagulation-fragmentation model formulated on the space of Radon measures. We prove the convergence of each of the two schemes to the unique weak solution of the model. We perform numerical simulations to demonstrate that the second order accuracy in the Bounded-Lipschitz norm is achieved by both schemes.

Keywords

• coagulation-fragmentation equation
• size structured populations
• radon measures equipped with bounded-lipschitz norm
• finite difference schemes
• high resolution methods