Accurate evaluation of modal attenuation and complex axial wavenumbers in lined ducts with shear flow requires solving either the Pridmore-Brown equation or the Linearised Euler Equations. This study systematically compares two distinct approaches: the collocation method applied to the Linearised Euler Equations

and the Galerkin method applied to the Pridmore-Brown equation. We demonstrate that the collocation method for the Linearised Euler Equations is affected by the velocity and its derivatives. Moreover

the quantity of modes is tied to the number of collocation points

leading to either modal redundancy or insufficient accuracy

and it necessitates additional mode-selection

filtering

and sorting procedures. In contrast

the Galerkin method for the Pridmore-Brown equation

based on a weak formulation

avoids explicit velocity derivatives and accommodates the Ingard-Myers condition. The Galerkin method also enables robust mode tracking even at mode merging

whereas the collocation method struggles to resolve mode trajectories under such conditions. Comparative results across parabolic shear flow profiles establish the weak-form Galerkin method as a superior

stable

and accurate computational framework for duct acoustics.