This letter proposes three novel resource and user scheduling algorithms with contiguous frequency-domain resource allocation (FDRA) for wireless communications systems. The first proposed algorithm jointly schedules users and resources selected adaptively from both ends of the bandwidth part (BWP), while the second and third ones apply disjoint user and resource selection with either single-end or dual-end BWP strategies. Distinct from existing contiguous FDRA approaches, the proposed schemes comply with standards specifications for fifth-generation (5G) and beyond 5G communications, and have lower computational complexity hence are more practical. Simulation results show that all of the proposed algorithms can achieve near-optimal performance in terms of throughput and packet loss rate for low to moderate traffic load, and the first one can still perform relatively well even with a large number of users.