MODELING THE EVOLUTIONARY DYNAMICS OF SMARTPHONE BATTERY TIMING

Addressing the complexity of smartphone battery life prediction, this study constructs a continuous-time dynamic model based on the law of energy conservation. The model defines the rate of change in battery state of charge as the ratio of total power consumption to effective capacity, which is influenced by temperature and aging. A first-order ordinary differential equation describes its evolution over time. Through physical modular modeling of core components—including the display, processor, network communication, and background applications—the study achieves a refined decomposition of total transient power. Parameters are calibrated using high-precision datasets, and numerical solutions are obtained via the fourth-order Runge-Kutta method. The resulting state-of-charge evolution curves exhibit smoothness and stable convergence, with locally truncated errors controlled at extremely low levels. Empirical analysis demonstrates the model's ability to accurately capture instantaneous power fluctuations triggered by user behavior transitions, revealing the dominant role of processor power consumption across different usage phases. This research establishes a robust physical foundation for achieving high-precision remaining power prediction and energy efficiency attribution analysis.