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Preconditioned Iteration Method for the Nonlinear Space Fractional Complex Ginzburg-Landau Equation

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Simulation Tools and Techniques (SIMUtools 2020)

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Abstract

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

Supported by the “Peiyu” Project from Xuzhou University of Technology (Grant Number XKY2019104).

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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. School of Information Engineering, Xuzhou University of Technology, Xuzhou, 221018, Jiangsu, China

    Lei Chen

Authors
  1. Lu Zhang
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  2. Lei Chen
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  3. Xiao Song
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Editor information

Editors and Affiliations

  1. Embry-Riddle Aeronautical University, Daytona Beach, FL, USA

    Houbing Song

  2. School of Astronautics and Aeronautic, UESTC, Chengdu, China

    Dingde Jiang

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Zhang, L., Chen, L., Song, X. (2021). Preconditioned Iteration Method for the Nonlinear Space Fractional Complex Ginzburg-Landau Equation. In: Song, H., Jiang, D. (eds) Simulation Tools and Techniques. SIMUtools 2020. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 370. Springer, Cham. https://doi.org/10.1007/978-3-030-72795-6_29

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  • DOI: https://doi.org/10.1007/978-3-030-72795-6_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72794-9

  • Online ISBN: 978-3-030-72795-6

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