ABSTRACT
The outline of this paper is as follows. In Section 2 we briefly review generalized Godunov schemes and the Toro-Titarev solver for the ADER scheme. Then, we recall well-known results on the solution of classical and generalized Riemann problems in Section 3. In Section 4, we discuss the key steps of the LeFloch-Raviart expansion, where we show that for scalar 1d problems the ToroTitarev solver and the LeFloch-Raviart expansion yield the same the Taylor series expansions in time. The full analysis for a scalar 1d example concerning Burgers equation is finally provided in Section 6.
