Higher-order (2,4) nonstandard finite difference scheme to improve anisotropy

Dispersion is one of the most critical topics related to finite difference methods. Although K.S. Yee´s scheme (1966) is the most popular, it is considered to be dispersive. There have been many techniques proposed to minimize this characteristic. One of the proposed techniques is to use J. Fang´s (2,4) scheme (1989), while another way is to use the nonstandard finite difference (NSFD) (Mickens, R.E., 1994; Cole, J.B., 1995, 1997). Naturally, the idea of NSFD can be directly extended to the (2,4) stencil, and we designate it as the NSFD (2,4) scheme. More recently, efforts were made to reduce the isotropic error without increasing the stencil´s size by introducing artificial anisotropic material into the simulation domain (Juntunen, J.S. and Tsiboukis, T.D., 2000; Zygiridis, T.T. and Tsiboukis, 2004). Similarly, we can introduce extra degrees-of-freedom into the NSFD (2,4) stencils to construct an isotropy-improved NSFD (2,4) scheme.