Abstract
Many systems of ordinary differential equations are quadratic: the derivative can be expressed as a quadratic function of the dependent variable. We demonstrate that this feature can be exploited in the numerical solution by Runge-Kutta methods, since the quadratic structure serves to decrease the number of order conditions. We discuss issues related to construction design and implementation and present a number of new methods of Runge-Kutta and Runge-Kutta-Nyström type that display superior behaviour when applied to quadratic ordinary differential equations.
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Communicated by Gustaf Söderlind.
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Iserles, A., Ramaswami, G. & Sofroniou, M. Runge-Kutta methods for quadratic ordinary differential equations. Bit Numer Math 38, 315–346 (1998). https://doi.org/10.1007/BF02512370
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DOI: https://doi.org/10.1007/BF02512370