SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Efficient Implicit-Explicit Runge-Kutta methods with low storage requirements

T. Roldan and I. Higueras

Space discretization of some time-dependent PDEs gives rise to systems of ordinary differential equations in additive form $ y'=f(y)+g(y) , y(t_{0})=y_{0} , \label{eq:split} $ where $f, g:\mathbb{R}^k \to \mathbb{R}^k$ are sufficiently smooth functions with different stiffness properties. For these problems, implicit methods should be used to treat the stiff terms while efficient explicit methods can still be used for the nonstiff part of the equation. We consider different implicit-explicit Runge-Kutta methods for additive differential equations of the form \eqref{eq:split}. In the construction of Runge-Kutta methods, stability and accuracy properties should be taken into account. However, in some contexts, storage requirements of the schemes play an important role.

[1] M. Calvo, J. Franco and L. Rández, Minimum storage Runge-Kutta schemes for computational acoustics, Computers & Mathematics with Applications 45, 1 (2003), 535-545.
[2] D. I. Ketcheson, Highly efficient strong stability-preserving Runge-Kutta methods with low-storage implementations, SIAM Journal on Scientific Computing 30, 4 (2008), 2113-2136.

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