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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 nonstiff systems. The modified schemes also fall in the class of central schemes, all of which can be viewed as based on the wellknown LaxFriedrichs (LxF) schemes. The schemes are Riemannsolver 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 blackbox solvers for general conservation laws and related equations governing the evolution of large gradient phenomena. Their capabilities for both shorttime and longtime scheme integrations are assessed. These modified schemes yields results similar to those of splitting, LaxWendroff MacCormack, ENO and the Riemann solver schemes. Numerical studies performed on relaxation systems indicate the accuracy and robustness of the modified schemes. In addition, their application to the plasma fluid equations constitutes a novel approach to the numerical integration of such systems.
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