A novel analytic approximation method with a convergence acceleration parameter for solving nonlinear problems

作者：Zhang, Xiaolong^*; Zou, Li; Liang, Songxin; Liu, Cheng

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 56: 354-364.

DOI：10.1016/j.cnsns.2017.08.025

• Adomian decomposition method
• Convergence acceleration parameter
• Series solution
• Nonlinear differential equation

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.

• 出版日期2018-3
• 单位工业装备结构分析国家重点实验室; 大连理工大学; 南京林业大学