Applying dispersion correction to numerical approximations of the two‐dimensional wave equation ‐ eigenproblems

A technique is presented whereby numerical calculations of vibration modes can be improved. The paper looks at the classical two‐dimensional wave equation using finite difference approximations. Analysis of the numerical dispersion of the approximations is used to develop a correction method. In general the numerical dispersion is dependent upon both the frequency and the direction of a wave, but if a 9‐point formula is used the directional dependence is much reduced. This enables correction factors to be obtained using only the frequency of a vibration mode. The method was tested on the vibration of a square membrane and of an L‐shaped region; in both cases a marked improvement in accuracy was obtained, at very little computational cost.