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

Lu Zhang; Lei Chen; Xiao Song

Simulation Tools and Techniques. 12th EAI International Conference, SIMUtools 2020, Guiyang, China, August 28-29, 2020, Proceedings, Part II

Research Article

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

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@INPROCEEDINGS{10.1007/978-3-030-72795-6_29,
    author={Lu Zhang and Lei Chen and Xiao Song},
    title={Preconditioned Iteration Method for the Nonlinear Space Fractional Complex Ginzburg-Landau Equation},
    proceedings={Simulation Tools and Techniques. 12th EAI International Conference, SIMUtools 2020, Guiyang, China, August 28-29, 2020, Proceedings, Part II},
    proceedings_a={SIMUTOOLS PART 2},
    year={2021},
    month={4},
    keywords={Nonlinear fractional ginzburg-landau equation Toeplitz matrix Circulant preconditioner Fast fourier transform},
    doi={10.1007/978-3-030-72795-6_29}
}

Lu Zhang
Lei Chen
Xiao Song
Year: 2021
Preconditioned Iteration Method for the Nonlinear Space Fractional Complex Ginzburg-Landau Equation
SIMUTOOLS PART 2
Springer
DOI: 10.1007/978-3-030-72795-6_29

Lu Zhang¹, Lei Chen², Xiao Song¹

1: School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou
2: School of Information Engineering, Xuzhou University of Technology, Xuzhou

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.

Keywords: Nonlinear fractional ginzburg-landau equation Toeplitz matrix Circulant preconditioner Fast fourier transform

Published: 2021-04-26
Appears in: SpringerLink

: http://dx.doi.org/10.1007/978-3-030-72795-6_29

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

Abstract

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