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

•A convergence acceleration parameter is introduced to enlarge the convergence rate and region.•A novel method is always valid no matter there exist small parameters or not in the problems.•A numerical method for choosing the optimal value of convergence acceleration parameter is given. 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.