Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators

DOI10.1016/j.cpc.2011.04.001zbMath1262.65077OpenAlexW2039943333MaRDI QIDQ1943121

Yonghui Zhang, Jinxi Zhao, Xiong You

Publication date: 15 March 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2011.04.001

zbMATH Keywords

stabilitynumerical experimentsRunge-Kutta methodlinear operatorsperturbed oscillatorstrigonometrically-fitted methodsG-functionScheifele two-step methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Cites Work

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• Stability of explicit ARKN methods for perturbed oscillators
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• Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
• Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)
• New methods for oscillatory systems based on ARKN methods
• Scheifele two-step methods for perturbed oscillators
• On numerical integration of perturbed linear oscillating systems
• A class of explicit two-step hybrid methods for second-order IVPs
• Multistep Numerical Methods Based on the Scheifele G-Functions with Application to Satellite Dynamics
• Order conditions for a class of two-step methods for y = f (x, y)
• A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS

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