<![CDATA[Accurate crop phenology prediction is essential for modern agricultural management, irrigation scheduling, and climate change adaptation. This study develops a numerical-analysis-based framework to predict maize (Zea mays L.) growth stages using daily meteorological data. The proposed workflow integrates: (i) the non-linear Wang–Engel formulation to compute daily thermal units, (ii) cubic spline interpolation for data reconstruction under a missing-data validation scenario, (iii) Simpson’s 3/8 rule for numerical integration of cumulative thermal units, (iv) the central difference method to analyze the accumulation-rate dynamics, and (v) Taylor series expansion for local approximation of the Wang–Engel function around the optimum temperature. Daily meteorological data were obtained from the Open-Meteo Historical API for Jakarta, Indonesia in 2025, comprising 348 observation days. Numerical integration yields a cumulative thermal unit of 112.37 over the first 120 days. Derivative analysis identifies the maximum accumulation rate of 0.9784 per day at day 44. Using the adopted thermal thresholds, the model predicts the V3 stage at day 127 and the V6 stage at day 342. Furthermore, the second-order Taylor approximation attains a maximum error of approximately 8.4 × 10⁻³ within a ±7°C range around the optimum, while the third-order approximation reduces the error to the order of 10⁻⁴ over the tested range. This numerically robust framework can be extended for future integration with machine learning approaches.]]>
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