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Transient sensitivity information is useful in circuit design community and the scales of modern circuits are big. This paper investigates transient sensitivity computations of large-scale MOSFET circuits using relaxation-based algorithms, including Waveform Relaxation (WR) and Iterative Timing Analysis (ITA). These algorithms have been strengthened for efficiency and robustness. This paper also proposes a novel method for sensitivity subcircuit computation, which is derived from the traditional Direct Approach and is called Adaptive Direct Approach. Some related time-saving techniques are proposed, too. All mentioned methods have been implemented and tested to justify their performances.