fourier spectral approximation for the time-fractional reaction-diffusion brusselator system

This paper introduces a robust numerical method for analyzing the time- fractional reaction-diffusion brusselator system. the problem is discretized in the spa- tial direction using the fourier spectral method and in the temporal direction using a high-order approximation for the caputo derivative. by leveraging the fourier spectral method’s properties, we can eliminate the second spatial derivatives from the system. the convergence of this method has been proven, and its efficiency and accuracy are demonstrated through various numerical examples. the findings reveal a consistent rate of convergence of two for multiple values of α, affirming the method’s efficacy in tackling the established system.