Convergence of a non conservative finite difference scheme for a system of hyperbolic conservation laws (Q756387)

The purpose of the paper is to construct a finite difference approximation to the system \((1)\quad u_ t+(ug(u,v))_ x=0,\) \(v_ t+(vg(u,v))_ x=0,\) where (u,v) denotes the unknown state vector and g is a given smooth scalar function, and to prove convergence of the approximate solution generated by a non-conservative first order finite difference scheme to a weak solution of the system of hyperbolic conservation laws (1). This finite difference method is used also to prove some results on the qualitative behaviour of a weak solution of the system (1) The authors establish that the finite difference schemes may be a powerful tool for the analysis of systems of hyperbolic conservation laws.