Numerical analysis of 3D space-fractional neutral-type delayed reaction–diffusion equations using a high-order difference technique

In this study, a high-order scheme is developed to solve 3D space-fractional delay reaction–diffusion equations of neutral type. The method is specifically formulated to address the complexities arising from neutral delays, the 3D configuration, and the challenges associated with space-fractional derivatives. A high-order compact approximation is implemented for the discretization of spatial variables, while a second-order accurate scheme is implemented for temporal discretization, resulting in a fully discrete system formulated in matrix form, which provides efficient implementation. The stability of the method is analyzed under mild conditions, and the results demonstrate its robustness throughout the simulation. Theoretical analysis also confirms the fourth-order convergence in space and second-order convergence in time of the scheme. The novelty of this work relies on the combination of high-order spatial discretization with stable and accurate treatment of neutral delays within a fully discrete framework for 3D space-fractional neutral-type delayed reaction–diffusion equations. Numerical experiments further validate the accuracy, and computational performance of the developed approach.