A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model

Xiaowei Chen, Mingzhan Song and Songhe Song
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Xiaowei Chen: College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
Mingzhan Song: College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
Songhe Song: College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China

Mathematics, 2020, vol. 8, issue 8, 1-10

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.

Keywords: Ginzburg–Landau equation; invariant energy quadratization approach; Fourier pseudo-spectral method; diagonally implicit Runge–Kutta scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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