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A novel analytic approximation method with a convergence acceleration parameter for solving nonlinear problems
Zhang Xiaolong
Zou Li
Liang Songxin
Liu Cheng
Communications in Nonlinear Science & Numerical Simulation, 2018, 56: 354-364.
Summary
In this paper, a new analytic approximation method with a convergence acceleration parameter c is first proposed. The parameter c is used to adjust and control the convergence region and rate of the resulting series solution. It turns out that the convergence region and rate can be greatly enlarged by choosing a proper value of c. Furthermore, a numerical approach for finding the optimal value of the convergence acceleration parameter is given. At the same time, it is found that the traditional Adomian decomposition method is only a special case of the new method. The effectiveness and applicability of the new technique are demonstrated by several physical models including nonlinear heat transfer problems, nano-electromechanical systems, diffusion and dissipation phenomena, and dispersive waves.
Keywords
Adomian decomposition method; Convergence acceleration parameter; Series solution; Nonlinear differential equation
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