A Novel Numerical Method for Solving Two‐Dimensional Fractional Mobile/Immobile Equation in Subsurface Pollutant Transport and Groundwater Flow

This study presents a new numerical approach specifically developed to solve the two‐dimensional fractional mobile/immobile equation (FMIE). These equations have various applications in areas such as subsurface pollutant transport, groundwater flow, and heat transfer in porous media. The suggested method utilizes the compact higher order finite difference scheme (CHFDS) and incorporates the Crank–Nicolson (C–N) method. This combination results in a unique combination of unconditional stability and a high convergence order of . The method achieves accuracy and efficiency by utilizing the C–N fourth‐order finite difference scheme for spatial variables and the Caputo derivative for temporal fractional derivatives. The proposed approach effectively manages complex FMIEs in real‐world scenarios, optimizing computational efficiency, minimizing simulation time, and enhancing robustness. The results confirm the enhanced precision and efficiency compared to conventional methods, hence reinforcing the practical significance of the CHFDS methodology.