Numerical study of finite volume scheme for coagulation–fragmentation equations with singular rates

Abstract

This paper deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks to the Dunford–Pettis and De La Vall[Formula: see text]e-Poussin theorems, we establish that numerical solution is converging to the weak solution of the continuous model using a weak [Formula: see text] compactness argument. A suitable stable condition on time step is taken to achieve the result. Furthermore, when kernels are in [Formula: see text] space, first-order error approximation is demonstrated for a uniform mesh. It is numerically validated by taking four test problems of coupled coagulation–fragmentation models.