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Fast iteration method for nonlinear fractional complex Ginzburg-Landau equations

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Abstract

In this paper, we solve the nonlinear space fractional complex Ginzburg-Landau equations. The motivation of this work is to give a fast numerical method to solve the linear system, which is obtained from the nonlinear space fractional complex Ginzburg-Landau equations. The coefficient matrix of the linear system is the sum of a complex diagonal matrix and a real Toeplitz matrix. The significance of this work is that the new method has a superiority in computation because we can use the circulant preconditioner and the fast Fourier transform to solve the linear system. Numerical examples are tested to illustrate the advantage of the numerical method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, 221018, Jiangsu, China

    Lu Zhang & Xiao Song

  2. Jiangsu Province Key Laboratory of Intelligent Industry Control Technology, Xuzhou University of Technology, Xuzhou, 221018, Jiangsu, China

    Lei Chen

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  1. Lu Zhang
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  2. Lei Chen
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  3. Xiao Song
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Correspondence to Lei Chen.

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Supported by Training Program from Xuzhou University of Technology (Grant Number XKY2019104).

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Zhang, L., Chen, L. & Song, X. Fast iteration method for nonlinear fractional complex Ginzburg-Landau equations. Wireless Netw (2021). https://doi.org/10.1007/s11276-021-02669-0

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