On the convergence of a coupling successive approximation method for solving Duffing equation

Dao Huy Bich, Nguyen Dang Bich

Abstract


General Duffing equations occur in many problems of Mechanics and Dynamics. These equations include nonlinear terms of second and third order, their coefficients are finite but not small parameters. For finding analytical approximate solutions of the general Duffing equation the coupling successive approximation method (CSAM) has been proposed by the authors.In the present paper the convergence of mentioned method is proven and a condition relating coefficients of Duffing equation to provide the convergence procedure is formulated. Emphasize that the assumption of small parameters is not used in the proving.Some examples are presented to illustrate the proposed method, particularly exact solutions of some problems are compared with analytical approximate ones found by CSAM.

Keywords


General Duffing equation; coupling successive approximation method; convergence; complex valued solution; chaotic solution

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DOI: https://doi.org/10.15625/0866-7136/36/3/4843 Display counter: Abstract : 42 views. PDF : 25 views.

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