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Energy-preserving exponential wave integrator method and the long-time dynamics for the two-dimensional space fractional coupled Klein–Gordon–Dirac equation

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  • Zhang, Pingrui
  • Jiang, Xiaoyun
  • Jia, Junqing

Abstract

In this article, uniform error bounds of an exponential wave integrator Fourier pseudo-spectral (EWIFP) method are established for the long-time dynamics of two-dimensional nonlinear space fractional Klein–Gordon–Dirac equation (NSFKGDE) with a small coupling parameter ɛ∈(0,1] and small potentials. By using the Fourier spectral discretization in space, followed with a second-order exponential wave integrator based on certain efficient quadrature rule in phase field, we construct a time-symmetric and energy-preserving numerical scheme. Rigorous analysis of uniform error bounds at Ohm0+ɛ1−γτ2 for γ∈[0,1] is carried out with the tool of cut-off technique as well as the energy method. Extensive numerical experiments demonstrate that the proposed discretization performs identically with our theoretical results. For applications, we profile the dynamical evolution of NSFKGDE in two dimensions (2D) with a honeycomb lattice potential, which correlates greatly with coupling, amplitude of potentials and fractional orders.

Suggested Citation

  • Zhang, Pingrui & Jiang, Xiaoyun & Jia, Junqing, 2025. "Energy-preserving exponential wave integrator method and the long-time dynamics for the two-dimensional space fractional coupled Klein–Gordon–Dirac equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 448-474.
    • Handle: RePEc:eee:matcom:v:233:y:2025:i:c:p:448-474
    DOI: 10.1016/j.matcom.2025.02.008
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    References listed on IDEAS

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    1. Chen, W., 2006. "Time–space fabric underlying anomalous diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 923-929.
    2. Hu, Dongdong & Cai, Wenjun & Xu, Zhuangzhi & Bo, Yonghui & Wang, Yushun, 2021. "Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 35-59.
    3. Wang, Junjie & Xiao, Aiguo, 2019. "Conservative Fourier spectral method and numerical investigation of space fractional Klein–Gordon–Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 348-365.
    4. Li, Jiyong, 2023. "Optimal error estimates of a time-splitting Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 398-423.
    5. Wang, Xianfen & Li, Jiyong, 2023. "Convergence analysis of two conservative finite difference fourier pseudo-spectral schemes for klein-Gordon-Dirac system," Applied Mathematics and Computation, Elsevier, vol. 439(C).
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