(eng): An unconditionally stable finite difference scheme for systems whose dynamics are described by a fourth-order partial differential equation is developed using a regular hexagonal grid. The scheme is motivated by the well-known Crank-Nicolson discretization that was originally developed for second order systems and it is used in this paper to develop a discrete in time and space model of a deformable mirror as a basis for control law design. As one example, the resulting model is used for iterative learning control law design and supporting numerical simulations are given.