## ADER: Arbitrary high-order Godunov approach.(English)Zbl 1024.76028

The ADER Toro approach is extended to the case of nonlinear scalar hyperbolic conservation laws. In this approach, which is related to the ENO/WENO methodology, a generalized Riemann problem is solved as a sequence of conventional Riemann problems for the $$k$$-th derivatives of the solution. The presented schemes enjoy very high order of accuracy in space and time and, while being explicit one-step methods, show optimal stability properties.

### MSC:

 76M12 Finite volume methods applied to problems in fluid mechanics 76M20 Finite difference methods applied to problems in fluid mechanics
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