Ri. Mackie, APPLYING DISPERSION CORRECTION TO NUMERICAL APPROXIMATIONS OF THE 2-DIMENSIONAL WAVE-EQUATION - EIGENPROBLEMS, Communications in numerical methods in engineering, 10(9), 1994, pp. 735-742
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.