A fourth order energy dissipative scheme for a traffic flow model

Abstract

We propose, analyze and numerically validate a new energy dissipative scheme for the Ginzburg-Landau equation by using the invariant energy quadratization approach. First, the Ginzburg-Landau equation is transformed into an equivalent formulation which possesses the quadratic energy dissipation law. After the space-discretization of the Fourier pseudo-spectral method, the semi-discrete system is proved to be energy dissipative. Using diagonally implicit Runge-Kutta scheme, the semi-discrete system is integrated in the time direction. Then the presented full-discrete scheme preserves the energy dissipation, which is beneficial to the numerical stability in long-time simulations. Several numerical experiments are provided to illustrate the effectiveness of the proposed scheme and verify the theoretical analysis.