ADER and DeC: Arbitrarily High Order Explicit Methods for hyperblic PDEs and ODEs

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The hyperbolic PDE community has used, in the last years, two powerful techniques that provide arbitrarily high order explicit schemes: ADER (arbitrary derivative) schemes and Deferred Correction (DeC) schemes.

They are often combined with high order space discretizion methods (DG, FV, FEM, RD), but they can also be studied alone as time integration methods.

In this talk, we will show that they are based on the same iterative process and that they just differ by the choice of test functions.

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