The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical
schemes with low dispersion and low dissipation errors. A technique has recently been devised
in a Computational Fluid Dynamics framework which enables optimal parameters to be chosen so
as to better control the grade and balance of dispersion and dissipation in numerical schemes
(Appadu and Dauhoo, 2011; Appadu, 2012a; Appadu, 2012b; Appadu, 2012c). This technique
has been baptised as the Minimized Integrated Exponential Error for Low Dispersion and Low
Dissipation (MIEELDLD) and has successfully been applied to numerical schemes discretising the
1-D, 2-D, and 3-D advection equations. In this paper, we extend the technique of MIEELDLD to the
field of computational aeroacoustics and have been able to construct high-order methodswith Low
Dispersion and Low Dissipation properties which approximate the 1-D linear advection equation.
Modifications to the spatial discretization schemes designed by Tam and Webb (1993), Lockard et
al. (1995), Zingg et al. (1996), Zhuang and Chen (2002), and Bogey and Bailly (2004) have been
obtained, and also a modification to the temporal scheme developed by Tam et al. (1993) has
been obtained. These novel methods obtained using MIEELDLD have in general better dispersive
properties as compared to the existing optimised methods.