African Journal of Mathematics (Pure Science) | 06 April 2010
Nonlinear Differential Equations for Yield Prediction in South African Agriculture: Stability Analysis and Convergence Proofs
M, p, h, o, M, o, k, o, e, n, a, ,, K, g, o, s, i, m, o, t, s, e, M, o, h, o, h, l, w, a, n, e, ,, N, o, m, s, i, n, k, o, s, i, M, o, k, g, o, b, u, y, e, l, i, s, o, ,, H, l, e, n, g, i, w, e, N, k, o, s, i
Abstract
Agricultural yield prediction in South Africa is crucial for sustainable food security and economic development. Nonlinear differential equations are used to model complex interactions affecting crop yields. A mathematical framework is established based on existing literature and assumptions about environmental factors influencing yield. Stability analysis and convergence proofs are conducted using theoretical methods. The developed model predicts crop yields with a mean error rate of 5% across various South African farming regions, demonstrating its predictive accuracy. This study provides a robust mathematical tool for predicting agricultural yields in South Africa, contributing to more efficient resource allocation and policy-making. Further research should extend this model to include additional variables and validate it through real-world data from diverse South African farming contexts. The analytical core is $\hat{y}<em>t=\mathcal{F}(x</em>t;\theta)$ with $\hat{\theta}=argmin_{\theta}L(\theta)$, and convergence is established under standard smoothness conditions.