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Preconditioned method for the nonlinear complex Ginzburg–Landau equations

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Abstract

In this work, we give an effective preconditioned numerical method to solve the discretized linear system, which is obtained from the space fractional complex Ginzburg–Landau equations. The coefficient matrix of the linear system is the sum of a symmetric tridiagonal matrix and a complex Toeplitz matrix. The preconditioned iteration method has computational superiority since we can use the fast Fourier transform and the circulant preconditioner to solve the discretized linear system. Numerical examples are tested to illustrate the advantage of the proposed preconditioned numerical method.

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Funding

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

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Authors and Affiliations

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

    Lei Chen

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

    Lu Zhang & Wenyu Zhou

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  1. Lei Chen
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  2. Lu Zhang
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  3. Wenyu Zhou
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Correspondence to Lu Zhang.

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Chen, L., Zhang, L. & Zhou, W. Preconditioned method for the nonlinear complex Ginzburg–Landau equations. Wireless Netw 27, 3701–3708 (2021). https://doi.org/10.1007/s11276-021-02657-4

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  • DOI: https://doi.org/10.1007/s11276-021-02657-4

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