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A mono-implicit Runge-Kutta-Nyström modification of the Numerov method

✍ Scribed by T. Van Hecke; M. Van Daele; G. Vanden Berghe; H. De Meyer


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
675 KB
Volume
78
Category
Article
ISSN
0377-0427

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On the generation of mono-implicit Runge
✍ H De Meyer; G Vanden Berghe; T Van Hecke; M Van Daele 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 1017 KB

Mono-implicit Runge-Kutta methods can be used to generate implicit Runge-Kutta-Nystr6m (IRKN) methods for the numerical solution of systems of second-order differential equations. The paper is concerned with the investigation of the conditions to be fulfilled by the mono-implicit Runge-Kutta (MIRK)

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We consider collocation-based Runge-Kutta-Nyström methods with symmetric points and derive a three-stage method which results exact in phase for second order linear ODEs having a periodic or an oscillatory solution. We assume that the dominant frequency k can be estimated in advance; then the result