Research on State of Charge Modeling and Multi-Scenario Endurance Prediction of Lithium-Ion Batteries in Smartphones Based on Continuous-Time Dynamics

Battery-life uncertainty remains one of the most significant factors affecting smartphone user experience. This study develops a continuous-time dynamic model for the state of charge (SOC) of lithium-ion batteries in smartphones and applies it to multi-scenario endurance prediction. The model is established using ordinary differential equations grounded in the Coulomb counting principle, while incorporating component-level current consumption, including screen brightness, processor load, wireless communication, GPS, Bluetooth, and standby power. Temperature correction and battery aging effects are also introduced to improve physical realism and practical applicability. Numerical integration is then used to simulate SOC evolution under different usage scenarios, and endurance time is defined as the moment when SOC drops to the cut-off threshold. The results show substantial differences in battery life across scenarios, with heavy-use conditions leading to rapid depletion and standby conditions providing the longest endurance. Furthermore, Monte Carlo simulation is employed to quantify uncertainty in endurance prediction, while sensitivity analysis identifies CPU load, screen brightness, and battery capacity as the most influential factors. The study not only provides a mathematically interpretable framework for smartphone battery modeling, but also offers a theoretical basis for power optimization strategies and intelligent battery management.