Using the Multi-Domain Spectral Relaxation Method through a Numerical Simulation for the Brusselator System

Abstract

We introduce the numerical solutions to examine the behavior of the Brusselator system by applying the multi-domain spectral relaxation method (MSRM). The proposed method is a combination of the Chebyshev pseudo-spectral method and the Gauss-Seidel relaxation approach. This method breaks down the main interval into several small subintervals, finding solutions within each interval. This approach also transforms the model into a set of algebraic equations. Some mathematical analyses, like error attitude and its order degree, were also included. We validate the effectiveness and precision of the given procedure by utilizing two computational algorithms: the fourth-order Runge-Kutta method (RK4M) and the variational iteration method. The considered results are tabularly and graphically demonstrated with different values of the model's parameters. From a numerical viewpoint, the given simulations and results indicate that the proposed algorithm is a straightforward and appropriate tool with computational efficiency for such models.