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Strong Stability Preserving Properties of Composition Runge–Kutta Schemes

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Abstract

In this paper strong stability preserving (SSP) properties of Runge–Kutta methods obtained by composing k different schemes with different step sizes are studied. The SSP coefficient of the composition method is obtained and an upper bound on this coefficient is given. Some examples are shown. In particular, it is proven that the optimal \(n^2\)-stage third order explicit Runge–Kutta methods obtained by Ketcheson (SIAM J Sci Comput 30(4):2113–2136, 2008) are composition of first order SSP schemes.

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  1. Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, Campus de Arrosadia, 31006, Pamplona, Spain

    I. Higueras & T. Roldán

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  1. I. Higueras
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  2. T. Roldán
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Correspondence to T. Roldán.

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Supported by Ministerio de Economía y Competividad (Spain), Project MTM2016-77735-C3-2-P.

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Higueras, I., Roldán, T. Strong Stability Preserving Properties of Composition Runge–Kutta Schemes. J Sci Comput 80, 784–807 (2019). https://doi.org/10.1007/s10915-019-00956-9

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