  We present a variational study of employing the trigonometric basis functions
satisfying periodic boundary condition for the accurate calculation of
eigenvalues and eigenfunctions of quartic double-well oscillators. Contrary to
usual Dirichlet boundary condition, imposing periodic boundary condition on the
basis functions results in the existence of an inflection point with vanishing
curvature in the graph of the energy versus the domain of the variable. We show
that this boundary condition results in a higher accuracy in comparison to
Dirichlet boundary condition. This is due to the fact that the periodic basis
functions are not necessarily forced to vanish at the boundaries and can
properly fit themselves to the exact solutions.
