An asymptotically stable scheme for diffusive coagulation-fragmentation models

TL;DR

This paper introduces a finite volume numerical scheme for diffusive coagulation-fragmentation models that guarantees positivity, conservation, and stability, with numerical simulations exploring long-term behavior.

Contribution

A new finite volume scheme for spatially diffusive coagulation-fragmentation equations that preserves key physical properties and stability.

Findings

Scheme preserves positivity and total volume.

Scheme maintains global steady states.

Numerical simulations reveal long-term solution behavior.

Abstract

This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous coagulation-fragmentation model, it is shown that the scheme preserves positivity, total volume and global steady states. Finally, several numerical simulations are performed to investigate the long time behavior of the solution.