On the convergence of a certain class of difference schemes for the equations of unsteady gas motion in a disperse medium (Q1571250)

The paper is concerned with the convergence of a one-parameter class of difference schemes for solving linear transport equations with sources. It is established that stability and local approximation of the family of schemes considered do not imply convergence. Therefore, the approximation is considered as a property of difference problem that leads to a well-posed differential problem as a result of a passage to limit. For the equation of unsteady gas motion in a disperse medium, a necessary condition for convergence of a four-parameter class of schemes with splitting according to physical processes is found.