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A 5(3) pair of explicit Runge–Kutta–Nyström methods for oscillatory problems

✍ Scribed by Hans Van de Vyver

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
309 KB
Volume
45
Category
Article
ISSN
0895-7177

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✦ Synopsis

New Runge-Kutta-Nyström methods especially designed for the numerical integration of periodic initial value problems are presented in this paper. They are able to integrate exactly the harmonic oscillator. Here we analyze the construction of an embedded 5(3) RKN pair with four stages. Numerical experiments indicate that the new pair is more efficient than some previously derived RKN pairs.

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A symplectic exponentially fitted modifi
A symplectic exponentially fitted modified Runge–Kutta–Nyström method for the numerical integration of orbital problems
✍ Hans Van de Vyver 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 244 KB

A symplectic exponentially fitted modified Runge-Kutta-Nystro ¨m method is derived in this paper. It is a two-stage second-order method with FSAL-property. An application to some well known orbital problems shows the properties of the developed method.