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He’s frequency formulation for the relativistic harmonic oscillator. (English) Zbl 1189.65162
Summary: He’s frequency formulation is used to solve the nonlinear differential equation that governs the oscillation of the relativistic oscillator. The obtained solution with high accuracy shows that He’s frequency formulation is a simple but promising method without any requirement for advanced calculus.
MSC:
65L99Numerical methods for ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)
70H40Relativistic dynamics
References:
[1]Beléndez, A.; Pascual, C.; Márquez, A.; Méndez, D. I.: Application of he’s homotopy perturbation method to the relativistic (an) harmonic oscillator. I: comparison between approximate and exact frequencies, International journal of nonlinear of science and numerical simulation 8, No. 4, 483-491 (2007)
[2]He, J. -H.: Some asymptotic methods for strongly nonlinear equations, International journal of modern physics B 20, No. 10, 1141-1199 (2006) · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[3]J.-H. He, Nonperturbative methods for strongly nonlinear problems, Dissertation.de-Verlag im Internet GmbH. 2006
[4]He, J. -H.: Comment on ’he’s frequency formulation for nonlinear oscillators’, European journal of physics 29, L1-L4 (2008)
[5]He, J. -H.: An improved amplitude-frequency formulation for nonlinear oscillators, International journal of nonlinear sciences and numerical simulation 9, No. 2, 211-212 (2008)
[6]Geng, Lei; Cai, Xu-Chu: He’s frequency formulation for nonlinear oscillators, European journal of physics 28, 923-931 (2007) · Zbl 1162.70019 · doi:10.1088/0143-0807/28/5/016