Copyright © 2013 A. R. Appadu and A. A. I. Peer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO)
scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration
scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative
properties when used to approximate the 1D linear advection equation and use a technique of
optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments
dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some
different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation,
and lower errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.