Convergence and error estimation of weighted finite volume scheme for coagulation‐fragmentation equation

Abstract

This article is dedicated to analyze a finite volume scheme for solving coagulation and multiple fragmentation equation. The rates of coagulation and fragmentation are chosen locally bounded and unbounded (singularity near the origin), respectively. It is shown that using weak L 1 compactness method, the numerically approximated solution tends to the weak solution of the continuous problem under a stability condition on the time step for non-uniform mesh. Further, considering a uniform mesh, first order error approximation is demonstrated when kernels are in W 1,∞ loc space. The accuracy of the scheme is also authenticated numerically for several test problems.