2011
DOI: 10.1016/j.camwa.2010.07.053
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Numerical solutions of Duffing equations involving both integral and non-integral forcing terms

Abstract: a b s t r a c tIn this paper, an improved variational iteration method is presented for solving Duffing equations involving both integral and non-integral forcing terms. The main advantage of this modification over the standard variational iteration method (VIM) is that it can avoid unnecessary repeated computation in determining the unknown parameters in the initial solution. Numerical results reveal that the improved method is simple and efficient.

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Cited by 10 publications
(10 citation statements)
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“…For instance, the [15][16][17][18][19][20]. Some of the above mentioned methods were employed to investigate the dynamical behaviour of a large variety of physical systems that are described by the various forms of the homogeneous Duffing equation.…”
Section: Introductionmentioning
confidence: 99%
“…For instance, the [15][16][17][18][19][20]. Some of the above mentioned methods were employed to investigate the dynamical behaviour of a large variety of physical systems that are described by the various forms of the homogeneous Duffing equation.…”
Section: Introductionmentioning
confidence: 99%
“…For the purpose of comparison, in Table II, we compare the absolute error of our method with n D 12 and n D 16 together with the VIM given in [13] and an iterative reproducing kernel method given in [14]. In Table II, y n represent the nth term approximation obtained using VIM.…”
Section: Examplementioning
confidence: 99%
“…The literature of numerical analysis contains little on the solutions of Duffing equations such as Equation (1). Geng [13] improved variational iteration method (VIM) for solving Equation (1). Also, Yao [14] presented an iterative reproducing kernel method for solving Equation (1).…”
Section: Introductionmentioning
confidence: 99%
“…In [23], the authors presented the existence and uniqueness of the solution of the Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions by using a generalized quasilinearization technique. However, as mentioned in [24] there is little literature on the solution of equations ( 3) and (4).…”
Section: Form 2: the Duffing Equation Involving Both Integral And Non...mentioning
confidence: 99%
“…Numerical solutions of the Duffing equation with two-point boundary conditions have been investigated by many researchers [18][19][20][21][22]. However, there are few references on the solution for the forced Duffing equation with integral boundary conditions [23] and the Duffing equation involving both integral and non-integral forcing terms [24]. In this paper, we consider the following two forms of the Duffing equation.…”
Section: Introductionmentioning
confidence: 99%