An ancient Chinese mathematical algorithm and its application to nonlinear oscillators

DOI10.1016/j.camwa.2010.08.073zbMath1219.65002OpenAlexW1984479875WikidataQ56875114 ScholiaQ56875114MaRDI QIDQ636631

Hui-Li Zhang, Li Juan Qin

Publication date: 28 August 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.08.073

zbMATH Keywords

nonlinear oscillatorancient chinese mathematicsHe's amplitude-frequency formulation

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) History of numerical analysis (65-03) History of ordinary differential equations (34-03) Numerical methods for ordinary differential equations (65L99) History of Chinese mathematics (01A25)

Related Items (2)

Solitary-solution formulation for differential-difference equations using an ancient Chinese algorithm ⋮ He's max-min approach to a nonlinear oscillator with discontinuous terms

Cites Work

• Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method
• Periodic solutions for some strongly nonlinear oscillations by He's variational iteration method
• Application of He's amplitude-frequency formulation to a nonlinear oscillator with discontinuity
• He's frequency formulation for the relativistic harmonic oscillator
• Application of He Chengtian's interpolation to Bethe equation
• Exact solution for nonlinear Schrödinger equation by He's frequency formulation
• He's frequency-amplitude formulation for the Duffing harmonic oscillator
• He's frequency-amplitude formulation for nonlinear oscillators with an irrational force
• Ancient Chinese algorithm: The ying buzu shu (method of surplus and deficiency) vs Newton iteration method
• Solution of nonlinear equations by an ancient Chinese algorithm.
• Some interpolation formulas in Chinese ancient mathematics
• He Chengtian's inequality and its applications
• Zu-Geng's axiom vs Cavalieri's theory
• Rebuild of King Fang 40 BC musical scales by He's inequality
• AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING
• Application of He's amplitude–frequency formulation to nonlinear oscillators with discontinuities
• He's frequency formulation for nonlinear oscillators
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS

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