High‐Precision Numerical Simulation for Fractional Convection–Diffusion–Reaction Equations

ABSTRACT This work develops a stable high‐accuracy numerical approach for the numerical solution of time‐fractional convection–diffusion–reaction equations (TFCDREs). The time fractional derivative is defined in the Caputo sense. The method employs finite difference schemes for spatial discretization and a high‐order discretization technique for Caputo fractional derivative. The stability analysis, conducted via the Fourier method, establishes the conditional stability, while error estimates confirm high‐order convergence speed of the constructed discretization with ), where denotes the temporal step and represents the spatial step. Comparison of numerical results with analytical and other approximate solutions indicates the viability and efficiency of the proposed algorithm. This study contributes a robust method to the field of numerical analysis, with potential applications in various scientific and engineering disciplines.