Abstract
Explicit Runge-Kutta methods provide a popular way to solve the initial value problem for a system of nonstiff ordinary differential equations. On the other hand, for these methods, there is no a natural way to approximate the solution at any point within a given integration step. Scaled Runge-Kutta methods have been developed recently which determine the solution of the differential system at non-mesh points of a given integration step. We propose some new such algorithms based upon well known explicit Runge-Kutta methods, and we verify their advantages by applying them to the Magnetic-Binary Problem.
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Papageorgiou, G., Simos, T. & Tsitouras, C. Some new Runge-Kutta methods with interpolation properties and their application to the Magnetic-Binary Problem. Celestial Mechanics 44, 167–177 (1988). https://doi.org/10.1007/BF01230713
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DOI: https://doi.org/10.1007/BF01230713