  In this paper we present a numerical scheme for the approximation of singular
shock solutions of the Keyfitz-Kranzer model system. Consistence in the sense
of distributions is studied. As long as some numerical properties are verified
when the space step tends to 0, we prove that the scheme provides a numerical
solution that satisfies the equations in the sense of distributions with an
approximation that tends to 0 when h \rightarrow 0. We also show that this
scheme adapts to degenerate systems. This is illustrated by two examples: the
system presenting delta wave solutions originally studied by Korchinski and
another system studied by Keyfitz-Kranzer that models elasticity. Consistence
of the scheme in the sense of distributions is fully proved in the case of the
Korchinski model.

Numerical Analysis