ADER and DeC: Arbitrarily High Order Explicit Time Integration Methods
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When we think about high order time integration, Runge–Kutta (RK) is the most known class of schemes that comes to mind, for historical reasons. Nevertheless, many other techniques have been developed during these years to improve these techniques and to get a generalized form of them.
In particular, we aim to have an arbitrarily high order without computing all the order condition equations, typical of the RK schemes, and we still want to have an explicit method, otherwise implicit RK and implicit collocation methods would be available.
The hyperbolic PDE community has used, in the last years, two powerful techniques that provide such schemes: ADER (arbitrary derivative) schemes and Deferred Correction (DeC) schemes.
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.