Fast high order ADER schemes for linear hyperbolic equations

A reformulation of the ADER approach (Arbitrary high order schemes using DERivatives) for linear hyperbolic PDEʹs is presented. This reformulation leads to a drastic decrease of the computational effort. A formula for the construction of ADER schemes that are arbitrary high order accurate in space and time is given. The accuracy for some selected schemes is shown numerically for the two-dimensional linearized Euler equations as a mathematical model for noise propagation in the time domain in aeroacoustics.