  In this paper, a new analytic method with a convergence-control 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-control 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. Moreover, the ideas proposed in this paper may offer us
possibilities to greatly improve current analytic and numerical techniques.
