The integration of unmanned aerial vehicles (UAVs) with wireless power transfer (WPT) technology is promising for overcoming energy constraints in wireless rechargeable sensor networks (WRSNs). Earlier studies focused on UAV trajectory optimization, assuming full sensor charging at each visit, impractical in real-world scenarios. However, optimizing trajectory and hovering time considering constraints like limited UAV battery capacity and varying energy consumption rates among sensor nodes poses a significant challenge in developing efficient charging scheduling algorithms for WRSNs. This paper addresses the aforementioned challenges and introduces a periodic multi-node partial charging model for UAV-assisted WRSNs. It proposes an efficient charging schedule optimizing trajectory and hovering time to maximize harvested energy by sensor nodes. The charging scheduling problem is initially formulated as a mixed integer nonlinear programming problem, proven NP-hard. It is then reformulated as a monotone sub-modular maximization problem with partitioned matroid constraints, allowing a greedy solution approach to achieving a ([Formula presented]) approximation. For large-scale networks, the differential evolution algorithm is employed. Simulation analysis demonstrates the proposed approach’s performance improvement by maximizing harvested energy, reducing dead nodes, and optimizing UAV tour time.