New interpretation to variational iteration method

Convolution iteration method based on duhamel's principle for dynamic system analysis

Yunhua Li, Yunze Li, Chieh-Li Chen, Cha'o Kuang Chen

Research output: Contribution to journalArticle

Abstract

Addressing the identification problem of the general Lagrange multiplier in the He's variational iteration method, this paper proposes a new kind of method based on Duhamel's principle for the dynamic system response analysis. In this method, we have constructed an analytical iteration formula in terms of the convolution for the residual error at the nth iteration, and have given a new interpretation to He's variational iteration method. The analysis illustrates that the computational result of this method is equal to that of He's variational iteration method on the assumption of considering the impulse response of the linear parts, or equal to that of Adomian's method on the assumption of considering the only the impulse response of the highest-ordered differential operator, respectively. However, new convolution iteration method doesn't need to solve the complicated Euler-Poisson variation equation. Some test examples for showing the application procedure of the convolution iteration method are provided.

Original language English 1-13 13 CMES - Computer Modeling in Engineering and Sciences 58 1 Published - 2010 Jun 2

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Variational Iteration Method
Iteration Method
Systems Analysis
Convolution
Dynamic Analysis
Dynamic Systems
Dynamical systems
Systems analysis
Impulse Response
Impulse response
Iteration
Lagrange multipliers
Poisson equation
Identification Problem
Mathematical operators
Euler
Differential operator
Computational Results
Identification (control systems)

All Science Journal Classification (ASJC) codes

• Software
• Modelling and Simulation
• Computer Science Applications

Cite this

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abstract = "Addressing the identification problem of the general Lagrange multiplier in the He's variational iteration method, this paper proposes a new kind of method based on Duhamel's principle for the dynamic system response analysis. In this method, we have constructed an analytical iteration formula in terms of the convolution for the residual error at the nth iteration, and have given a new interpretation to He's variational iteration method. The analysis illustrates that the computational result of this method is equal to that of He's variational iteration method on the assumption of considering the impulse response of the linear parts, or equal to that of Adomian's method on the assumption of considering the only the impulse response of the highest-ordered differential operator, respectively. However, new convolution iteration method doesn't need to solve the complicated Euler-Poisson variation equation. Some test examples for showing the application procedure of the convolution iteration method are provided.",
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New interpretation to variational iteration method : Convolution iteration method based on duhamel's principle for dynamic system analysis. / Li, Yunhua; Li, Yunze; Chen, Chieh-Li; Chen, Cha'o Kuang.

In: CMES - Computer Modeling in Engineering and Sciences, Vol. 58, No. 1, 02.06.2010, p. 1-13.

Research output: Contribution to journalArticle

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