A robust time-split linearized explicit/implicit technique for solving a two-dimensional hydrodynamic model: Case of floods in the far north region of Cameroon.

This article focuses on the development and analysis of a time-split linearized explicit/implicit numerical method for solving a two-dimensional shallow water hydrodynamic flow model with given initial and boundary conditions. The proposed approach employs a symmetric fractional step scheme combining explicit and implicit one-dimensional difference operators to achieve spatial fourth-order accuracy and temporal second-order convergence, while controlling numerical oscillations and stability. A rigorous stability analysis establishes a specific time step restriction based on the \(L^\infty(0,T;L^2)\)-norm, which is confirmed through numerical experiments including Thacker's analytical solutions and a practical flood forecasting case in the far north region of Cameroon during July–October 2024. Results demonstrate that, under appropriate initial conditions and time step constraints, the method reliably predicts water depth and velocity fields, aiding flood extent estimation and risk management in the studied region.