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; and Cha'o-Kuang Chen;

doi:10.3970/cmes.2010.058.001
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 58, No. 1, pp. 1-14, 2010
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Keywords Adomian decomposition method, convolution, integral transformation, nonlinear differential equation, variational iteration method.
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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