  The paper begins with a novel variational formulation of Duffing equation
using the extended framework of Hamilton's principle (EHP). This formulation
properly accounts for initial conditions, and it recovers all the governing
differential equations as its Euler-Lagrange equation. Thus, it provides
elegant structure for the development of versatile temporal finite element
methods. Herein, the simplest temporal finite element method is presented by
adopting linear temporal shape functions. Numerical examples are included to
verify and investigate performance of non-iterative algorithm in the developed
method.
