Uniform dispersion reduction schemes for the one dimensional wave equation in isotropic media

Finite difference (FD) methods for the wave equation in general suffer from numerical dispersion. Although FD methods based on accuracy give good dispersion at low frequencies, waves tend to disperse for higher wavenumber. In this work, we will give a unified methodology to derive dispersion reduction FD schemes for the one dimensional wave equation, and this new method can reduce dispersion error uniformly for all wavenumbers up to the Nyquist. Stability criteria are given, and stability analysis is done for each generated scheme.