A study of splitting scheme for hyperbolic conservation laws with source terms

This study deals with the convergence of a numerical scheme for conservation laws including source terms. A splitting method for source term integration is presented. More precisely, the convergence of the numerical solution towards the entropy solution is proved in the scalar case. Because of the effect of source term, the constructed scheme is total variation bounded. Numerical experiments for one-dimensional shallow water equation are presented to demonstrate the performance of the scheme.