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

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.