D-splitting methods: 2N -storage embedded explicit Runge-Kutta methods at any order using splitting methods
This work provides a new approach to low-storage Runge-Kutta methods for solving time-dependent PDEs, offering memory efficiency and pseudo-geometric properties.
The authors propose D-splitting methods as 2N-storage embedded explicit Runge-Kutta schemes that require only two storage registers, preserving qualitative properties of the exact solution to higher order than the method's order. Numerical tests demonstrate their effectiveness.
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.