Nonlinear differential equations are essential in modelling complex systems such as power grids, which exhibit nonlinearity due to interactions between various components like generators and loads. Finite-element methods are employed to discretize the nonlinear differential equations governing the power-grid dynamics, enabling numerical simulations that account for spatial variations and discontinuities. Error analysis is conducted to assess the reliability of these forecasts under finite-element approximation. Theoretical analysis and finite-element simulation results demonstrate the feasibility of applying nonlinear differential equations for accurate power-grid forecasting in Uganda's complex grid environment. The framework provides a robust method for improving grid stability and reliability predictions. Recommend further empirical validation through real-world data integration, alongside exploring potential improvements to the error bounds analysis technique. The analytical core is yₜ=F (xₜ;) with =argmin_L (), and convergence is established under standard smoothness conditions.
Kizza Mukasa (2005) studied this question.