The boundary layer transition is a crucial focus in aerospace engineering. This study conducts a thorough analysis of the transition from laminar to turbulent flow on a low-pressure turbine blade, utilizing two different approaches: Linear Stability Theory (LST) and Linear Parabolized Stability Equations (LPSE). By conducting simulations and comparing them with experimental data, this research investigates the differences and similarities between the two theories, with the goal of understanding the transition in the low-pressure turbine. The focus is on the dynamic characteristics of the boundary layer flow, the instability patterns, and the envelope of Tollmien-Schlichting (TS) waves on the turbine blade.