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<p>This paper proposes a high-order energy-preserving numerical scheme for the space-fractional Klein-Gordon-Zakharov system which models nonlinear wave phenomena in plasma physics by combining the weighted and shifted Lubich difference operator for spatial discretization with the exponential Fourier collocation method for temporal integration. The weighted and shifted Lubich difference operator ensures fourth-order accuracy in space while preserving the energy conservation, boundedness, and stability of the semi-discrete system. The exponential Fourier collocation method, leveraging matrix exponential and local Fourier expansions, achieves arbitrary high-order accuracy in time and efficiently handles the system’s oscillatory dynamics. Theoretical analysis demonstrates that the fully discrete scheme conserves energy with high precision and exhibits fourth order spatial convergence and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation>-th order temporal convergence, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation> depends on the quadrature precision. Several numerical experiments validate the method’s accuracy, energy preservation and computational efficiency of the present method for both integer and fractional-order Klein-Gordon-Zakharov systems.</p>

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High-order structure-preserving scheme for the space-fractional Klein-Gordon-Zakharov system via exponential Fourier collocation approach

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Yu Li,
  • Jiayu Li,
  • Yanming Zhang

摘要

This paper proposes a high-order energy-preserving numerical scheme for the space-fractional Klein-Gordon-Zakharov system which models nonlinear wave phenomena in plasma physics by combining the weighted and shifted Lubich difference operator for spatial discretization with the exponential Fourier collocation method for temporal integration. The weighted and shifted Lubich difference operator ensures fourth-order accuracy in space while preserving the energy conservation, boundedness, and stability of the semi-discrete system. The exponential Fourier collocation method, leveraging matrix exponential and local Fourier expansions, achieves arbitrary high-order accuracy in time and efficiently handles the system’s oscillatory dynamics. Theoretical analysis demonstrates that the fully discrete scheme conserves energy with high precision and exhibits fourth order spatial convergence and \(r\) -th order temporal convergence, where \(r\) depends on the quadrature precision. Several numerical experiments validate the method’s accuracy, energy preservation and computational efficiency of the present method for both integer and fractional-order Klein-Gordon-Zakharov systems.