  In this paper, an improvement of the finite difference time domain (FDTD)
method using a non-standard finite difference scheme is presented. The standard
numerical scheme for the second derivative in the spatial domain is replaced by
a non-standard numerical scheme. In order to apply the non-standard FDTD
(NSFDTD), first estimates of eigen-energies of a system are needed and computed
by the standard FDTD method. These first eigen-energies are then used by the
NSFDTD method to obtain improved eigen-energies. The NSFDTD method can be
performed iteratively using the resulting eigen-energies to obtain accurate
results. In this paper, the NS-FDTD method is validated for infinite square
well, harmonic oscillator and Morse potentials.
