D-splitting methods: 2N -storage embedded explicit pseudo-geometric Runge-Kutta methods using splitting methods

Sergio Blanes; Alejandro Escorihuela-Tomàs

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arXiv · 2604.03457

D-splitting methods: 2N -storage embedded explicit pseudo-geometric Runge-Kutta methods using splitting methods

Sergio Blanes·Alejandro Escorihuela-Tomàs

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Abstract

Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to their efficiency and their reduced memory requirements. We show that D-splitting methods, splitting methods on the extended phase space, can be used as high performance 2N-storage embedded explicit RK methods without a third storage register. They are pseudo-geometric methods preserving some of the qualitative properties of the exact solution up to a higher order than the order of the method. Some of their properties are analysed, to build new tailored methods, and are tested on numerical examples.

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Sergio Blanes, Alejandro Escorihuela-Tomàs. 2026-04-03. D-splitting methods: 2N -storage embedded explicit pseudo-geometric Runge-Kutta methods using splitting methods. https://arxiv.org/abs/2604.03457

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