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When a high dimension system of ordinary differential equations is solvednumerically, the computer memory capacity may be compromised. Thus, for suchsystems, it is important to incorporate low memory usage to some otherproperties of the scheme. In the context of strong stability preserving (SSP)schemes, some low-storage methods have been considered in the literature. Inthis paper we study 5-stage third order 2N* low-storage SSP explicitRunge-Kutta schemes. These are SSP schemes that can be implemented with 2Nmemory registers, where N is the dimension of the problem, and retain theprevious time step approximation. This last property is crucial for a variablestep size implementation of the scheme. In this paper, first we show that theoptimal SSP methods cannot be implemented with 2N* memory registers. Next, twonon-optimal SSP 2N* low-storage methods are constructed; although their SSPcoefficients are not optimal, they achieve some other interesting properties.Finally, we show some numerical experiments.

New third order low-storage SSP explicit Runge-Kutta methods