Numerical Simulation of Space Fractional Order Schnakenberg Model

A numerical solution of a fractional-order reaction-diffusion model is discussed. With the development of fractional-order differential equations, Schnakenberg model becomes more and more important. However, there are few researches on numerical simulation of Schnakenberg model with spatial fractional order. It is also important to find a simple and effective numerical method. In this paper, the Schnakenberg model is numerically simulated by Fourier spectral method. The Fourier transform is applied to transforming the partial differential equation into ordinary differential equation in space, and the fourth order Runge-Kutta method is used to solve the ordinary differential equation to obtain the numerical solution from the perspective of time. Simulation results show the effectiveness of the proposed method.