DISCRETE OPTIMIZATION MODEL FOR THE 2-DIMENSIONAL ENERGIZED WAVES

Energized waves are waves characterized by diffusion effects [Odio et al, 1997, Pain, 2005] and such waves are common in acoustics, ocean waves and many other wave propagation phenomena that involve propagation of energy. [Reju, 1995] was the first to apply the Extended Conjugate Gradient Method (ECGM) to the optimal control of classical wave propagation problem and with a specific extension to energized waves by [Waziri, 2006]. Computational procedures of Reju and Waziri are semi-analytic in nature utilizing in each case a direct methodology that is finally employed in the implementation of the ECGM. This paper however employs a discretization procedure via the 4 th order Runge-Kutta algorithm to the search of optimal solutions of the 2-dimensional energised wave propagation problem and so contributing to the unified theory of the foregoing diffusive and kinetic Hamiltonian approach [Reju et al, 1999] preceding the implementation of the various versions of ECGM [Reju, et al, 2001; Waziri and Reju, 2006]. Moreover, the paper compares the discrete model optimal results with the semi-analytic approach of [Waziri and Reju, 2006] with its associated microscopic phenomena.