Abstract
We introduce a generalized version of the front tracking algorithm for the full ultra-relativistic Euler system. The construction and analysis of this algorithm are somewhat simpler than other algorithms. Moreover, this scheme leads to a more robust and efficient result. The scheme also satisfies positivity. This scheme is compared with other two schemes by two numerical test cases. Furthermore we give another application of this scheme, namely we check the explicit formula of interaction of two generalized shocks, by further numerical test case.