D-splitting methods: 2N -storage embedded explicit Runge-Kutta methods at any order using splitting methods
Numerical Analysis
2026-04-07 v1 Numerical Analysis
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.
Cite
@article{arxiv.2604.03457,
title = {D-splitting methods: 2N -storage embedded explicit Runge-Kutta methods at any order using splitting methods},
author = {Sergio Blanes and Alejandro Escorihuela-Tomàs},
journal= {arXiv preprint arXiv:2604.03457},
year = {2026}
}