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DOE OSTI · 1870469

Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

Fekete, Imre·Conde, Sidafa·Shadid, John N.
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Abstract

We construct a family of embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods of order 2 ≤ p ≤ 4 to be used to obtain numerical solution of spatially discretized hyperbolic PDEs. In this construction, the goals include non-defective property, large stability region, and small error values as defined in Dekker and Verwer (1984) and Kennedy et al. (2000). The new family of embedded pairs offer the ability for strong stability preserving (SSP) methods to adapt by varying the step-size. Through several numerical experiments, we assess the overall effectiveness in terms of work versus precision while also taking into consideration accuracy and stability.

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97 MATHEMATICS AND COMPUTINGEmbedded pairsHyperbolic problemsRunge–Kutta methodsStep-size controlStrong stability preserving methodsVariable step-size

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Fekete, Imre, Conde, Sidafa, Shadid, John N.. 2022-04-14. Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods. https://doi.org/10.1016/j.cam.2022.114325

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