A multiple scale time domain collocation method for solving non-linear dynamical system

Dai, Honghua; Yue, Xiaokui; Liu, Chein‐Shan

doi:10.1016/j.ijnonlinmec.2014.10.001

Cited by 8 publications

(1 citation statement)

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“…Chen [4] has used a target function method for the solution of the Duffing oscillator, while the Laplace decomposition methods were introduced by Yusufoglu [5] and Khuri [6]. Yue et al [7] have applied the optimal scale polynomial interpolation technique to obtain the periodic solutions of the Duffing equation, and Dai et al [8] have used the multiple scale time domain collocation method for solving nonlinear dynamical systems. The power series method (PSM) is a classical one to solve ordinary differential equations (ODEs), which is closely related to the Taylor series method, but does not need an elaborate differential process to derive the expansion coefficients.…”

Section: Introductionmentioning

confidence: 99%

A multiple-scale power series method for solving nonlinear ordinary differential equations

Liu¹,

Kuo²,

Jhao³

2016

Communications in Numerical Analysis

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The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales R k in the power term (t/R k ) k is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.

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