Runge-Kutta methods for quadratic ordinary differential equations |
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| Authors: | Arieh Iserles Geetha Ramaswami Mark Sofroniou |
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| Affiliation: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW Cambridge, England;(2) Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, 47005 Valladolid, Spain;(3) Wolfram Research Inc., 100 Trade Center Drive, 61820 Champaign, IL, USA;(4) Present address: Department of Mathematics, Indian Institute of Science, 560012 Bangalore, India |
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| 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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| Keywords: | 65L06 |
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