We propose a Conservative Front Tracking method for solving the hyperbolic systems of nonlinear conservation laws.; The algorithm presented is an explicit finite volume integration scheme, which is derived from an integral formulation of the generalized solutions of PDEs. The major issues concerned in designing the conservative tracking algorithm are (1) to obtain a space-time control volume discretization which respects the explicitly tracked front and (2) to calculate the amount of the flux flowing through the space-time surfaces of each control volume.; The algorithm is conservative. The 1D version of the algorithm is formally second-order accurate away from the interaction of the tracked waves. For the 2D version of the algorithm, we obtain a proof of formal first-order accuracy near the tracked front, which is not available in other methods. The numerical results show that the conservative tracking algorithm converges rapidly in comparison to other methods.
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