A new compact finite difference scheme for solving the complex Ginzburg–Landau equation

Yun Yan, Frederick Ira Moxley and Weizhong Dai

Applied Mathematics and Computation, 2015, vol. 260, issue C, 269-287

Abstract: The complex Ginzburg–Landau equation is often encountered in physics and engineering applications, such as nonlinear transmission lines, solitons, and superconductivity. However, it remains a challenge to develop simple, stable and accurate finite difference schemes for solving the equation because of the nonlinear term. Most of the existing schemes are obtained based on the Crank–Nicolson method, which is fully implicit and must be solved iteratively for each time step. In this article, we present a fourth-order accurate iterative scheme, which leads to a tri-diagonal linear system in 1D cases. We prove that the present scheme is unconditionally stable. The scheme is then extended to 2D cases. Numerical errors and convergence rates of the solutions are tested by several examples.

Keywords: Compact finite difference scheme; Complex Ginzburg–Landau equation; Stability (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:260:y:2015:i:c:p:269-287

DOI: 10.1016/j.amc.2015.03.053

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