Accurate and efficient time integration is a central challenge in computational structural dynamics of rotor systems characterized by stiff ODEs, high-frequency response content, and resonance-driven behavior. This contribution presents an investigation of implicit and explicit time integration schemes for linear and nonlinear rotor dynamics, with a focus on the generalized-α method and backward differentiation formula (BDF) methods. The study is conducted on a typical benchmark problem (Jeffcott rotor) and on a geometrically detailed large-scale low pressure (LP) rotor used in jet engines. The rotor is discretized using isogeometric Kirchhoff–Love shell elements, enabling an exact geometric representation and high accuracy with a moderate number of degrees of freedom. Within this framework, both linear and nonlinear transient analyses are performed under unbalance excitation, targeting the accurate prediction of resonance crossings, amplitude envelopes, and phase behavior. For the generalized-α method, particular emphasis is placed on the role of numerical dissipation controlled through the spectral radius and on time-step selection, which is treated as an accuracy and numerical dispersion aspect. For BDF methods, fixed-step and adaptive formulations are examined, including Newton–Raphson solution strategies for nonlinear problems. The performance of these approaches is assessed in terms of accuracy, stability, numerical dissipation, and computational efficiency. The results demonstrate that, for rotor dynamic problems dominated by resonance phenomena and broadband excitation, fixed-step generalized-α and fixed-step BDF2 methods provide robust and computationally efficient alternatives to adaptive solvers especially for nonlinear problems. Validation against frequency-response analyses confirms accurate prediction of resonance locations, amplitude levels, and phase relationships. The findings highlight practical guidelines for time-step selection and solver configuration and show that carefully designed fixed-step implicit schemes can outperform adaptive approaches for large-scale rotor dynamics. The presented results support the use of advanced discretization IGA-frameworks and time integration strategies for high-fidelity transient simulations in computational structural dynamics.