Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number

Table 1

Analysis of the number of elements needed for a dispersion error of .

	Second-order scheme	Fourth-order scheme
	(, ) approx.	(, ) approx.
10	(, )	(, )	10.00008889
	(, )	(, )	100.0000970
	(, )	(, )	1000.000099