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A phase-fitted collocation-based Runge–Kutta–Nyström method

✍ Scribed by B. Paternoster

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
275 KB
Volume
35
Category
Article
ISSN
0168-9274

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✦ Synopsis

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 resulting method depends on the parameter θ = kh, where h is the stepsize. Due to its stability properties, the method is suitable to integrate systems which exhibits a moderate stiffness. The procedure can be easily generalized to derive phase-fitted RKN methods with an arbitrary high order.

📜 SIMILAR VOLUMES

High-order zero-dissipative Runge-Kutta-
High-order zero-dissipative Runge-Kutta-Nyström methods
✍ Ch. Tsitouras 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 247 KB

A new Runge-Kutta-Nystr6m pair of orders eight and six is presented here. Its main advantage is that it is of zero dissipation so it possesses an interval of periodicity. Numerical results over a set of problems demonstrate the superiority of the method in problems with periodic solution. (~) 1998 E