Recent second and third order finite difference schemes for the computation of weak solution of hyperbolic conservation laws are modified resulting in methods for stiff or non-stiff systems. The modified schemes also fall in the class of central schemes, all of which can be viewed as based on the well-known Lax-Friedrichs (LxF) schemes. The schemes are Riemann-solver free high resolution schemes and therefore not tied to any Eigen- structure of the problem. They can be implemented in a straight forward manner as black-box solvers for general conservation laws and related...