Convenient Total Variation Diminishing Conditions for Nonlinear Difference Schemes

Convenient conditions for nonlinear difference schemes to be total variation diminishing (TVD) are derived. It is shown that such schemes share the TVD property, provided their numerical fluxes meet a certain positivity condition at local extreme values but can be arbitrary otherwise. Local TVD conditions are invariant under different incremental representations of the nonlinear schemes, and thus provide a simplified generalization of the global TVD conditions established by previous work.