Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
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Higher order: IMEX <strong>schemes</strong> can be considered as a particular case of additive <strong>Runge</strong>-<br />
<strong>Kutta</strong> methods and there<strong>for</strong>e higher order conditions can be derived as well using a<br />
generalization of Butcher 1-trees to 2-trees. However the number of coupling conditions<br />
increase dramatically with the order of the <strong>schemes</strong>.<br />
IMEX-RK Number of coupling conditions<br />
order General case ˜wi = wi ˜c = c ˜c = c and ˜wi = wi<br />
1 0 0 0 0<br />
2 2 0 0 0<br />
3 12 3 2 0<br />
4 56 21 12 2<br />
5 252 110 54 15<br />
6 1128 528 218 78<br />
9
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