Approximate solution for the Duffing-harmonic oscillator by the enhanced cubication method

DOI10.1155/2012/618750zbMath1264.34067OpenAlexW1970752761WikidataQ58912317 ScholiaQ58912317MaRDI QIDQ1954999

René K. Córdoba-Díaz, Alex Elías-Zúñiga, Oscar Martínez-Romero

Publication date: 11 June 2013

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/618750

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

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Cites Work

• Unnamed Item
• Iterative homotopy harmonic balancing approach for conservative oscillator with strong odd-nonlinearity
• On the solution of strong nonlinear oscillators by applying a rational elliptic balance method
• An accurate closed-form approximate solution for the quintic Duffing oscillator equation
• Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators
• An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
• Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method
• An equivalent nonlinearization method for strongly nonlinear oscillations
• ``Cubication of non-linear oscillators using the principle of harmonic balance
• MATHEMATICAL AND NUMERICAL STUDY OF THE DUFFING-HARMONIC OSCILLATOR
• Improved Lindstedt–Poincaré method for the solution of nonlinear problems
• Analytical study on a Duffing-harmonic oscillator
• Solution of a quadratic nonlinear oscillator by the method of harmonic balance
• Higher accuracy analytical approximations to the Duffing-harmonic oscillator
• A weighted mean-square method of “cubication” for non-linear oscillators
• ON THE UNIQUENESS OF ANGULAR FREQUENCY USING HARMONIC BALANCE FROM THE EQUATION OF MOTION AND THE ENERGY RELATION
• Cubication of conservative nonlinear oscillators
• Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He's homotopy methods
• A weighted mean square method of linearization in non-linear oscillations

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