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Numerical Methods for Hyperbolic Equations
This work concerns the solution of generalized Riemann problems. To this end, we consider the ADER scheme of Titarev & Toro (2002) , which relies on a generalization of the classical Godunov scheme. Another solution method is the power series expansion of LeFloch & Raviart (1988) . We analyze the two resulting approximation schemes, where we show that for scalar 1d problems the Toro-Titarev solver and the LeFloch-Raviart expansion yield the same Taylor series expansions in time. The full analysis for the Burgers equation is finally provided.doi:10.1201/b14172-37 fatcat:bdqumxhy3zdzdoqxiubc75lupq