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Characterizing Strong Stability Preserving Additive Runge-Kutta Methods

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Abstract

Space discretization of some time dependent partial differential equations give rise to ordinary differential equations containing additive terms with different stiffness properties. In these situations, additive Runge-Kutta (additive RK) methods are used.

For additive RK methods the curve of absolute monotonicity gives stepsize restrictions for monotonicity. Necessary conditions for nontrivial curves of absolute monotonicity are the nonnegativity of the additive RK coefficients and some inequalities on some incidence matrices. In this paper we characterize strong stability preserving additive Runge-Kutta methods giving some order barriers and structural properties.

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  1. Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Pamplona, 31006, Navarra, Spain

    Inmaculada Higueras

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  1. Inmaculada Higueras
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Correspondence to Inmaculada Higueras.

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Research supported by the Ministerio de Educación y Ciencia, Project MTM2005-03894.

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Higueras, I. Characterizing Strong Stability Preserving Additive Runge-Kutta Methods. J Sci Comput 39, 115–128 (2009). https://doi.org/10.1007/s10915-008-9252-2

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  • DOI: https://doi.org/10.1007/s10915-008-9252-2

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