APPLYING DISPERSION CORRECTION TO NUMERICAL APPROXIMATIONS OF THE 2-DIMENSIONAL WAVE-EQUATION - EIGENPROBLEMS

A technique is presented whereby numerical calculations of vibration m odes 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 corre ction method. In general the numerical dispersion is dependent upon bo th the frequency and the direction of a wave, but if a 9-point formula is used the directional dependence is much reduced. This enables corr ection 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.