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Monotonicity for Runge–Kutta Methods: Inner Product Norms

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Abstract

An important class of ordinary differential systems is that whose solutions satisfy a monotonicity property for a given norm. For these problems, a natural requirement for the numerical solution is the reflection of this monotonicity property, perhaps under certain stepsize restriction. For Runge–Kutta methods, when the applied norm is an arbitrary one, the stepsize restrictions depend on the radius of absolute monotonicity. However for many problems, monotonicity holds for inner product norms and therefore it makes sense to restrict the analysis to this class of norms to obtain, if possible, less restrictive results. In this paper, we consider monotonicity issues for Runge–Kutta methods when the applied norm is an inner product norm.

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

    Inmaculada Higueras

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  1. Inmaculada Higueras
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Higueras, I. Monotonicity for Runge–Kutta Methods: Inner Product Norms. J Sci Comput 24, 97–117 (2005). https://doi.org/10.1007/s10915-004-4789-1

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