Abstract
In this work we consider interpolants for Nyström methods, i.e., methods for solving second order initial value problems. We give a short introduction to the theory behind the discrete methods, and extend some of the work to continuous, explicit Nyström methods. Interpolants for continuous, explicit Runge-Kutta methods have been intensively studied by several authors, but there has not been much effort devoted to continuous Nyström methods. We therefore extend some of the work by Owren.
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Marthinsen, A. Continuous extensions to Nyström methods for second order initial value problems. Bit Numer Math 36, 309–332 (1996). https://doi.org/10.1007/BF01731986
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DOI: https://doi.org/10.1007/BF01731986