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Linearly Implicit Conservative Schemes with a High Order for Solving a Class of Nonlocal Wave Equations

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  • Shaojun Chen

    (The Public Course Teaching Department, Henan Vocational University of Science and Technology, Zhoukou 466000, China)

  • Yayun Fu

    (School of Science, Xuchang University, Xuchang 461000, China)

Abstract

This paper introduces a class of novel high-accuracy energy-preserving numerical schemes tailored specifically for solving the nonlocal wave equation with Gaussian kernel, which plays a fundamental role in various scientific and engineering applications where traditional local wave equations are inadequate. Comprehensive numerical experiments, including comparisons with analytical solutions and benchmark tests, demonstrate the superior accuracy and energy-preserving capabilities of the proposed schemes. These high-accuracy energy-preserving schemes represent a valuable tool for researchers and practitioners in fields reliant on nonlocal wave equation modeling, offering enhanced predictive capabilities and robustness in capturing complex wave dynamics while ensuring long-term numerical stability.

Suggested Citation

  • Shaojun Chen & Yayun Fu, 2024. "Linearly Implicit Conservative Schemes with a High Order for Solving a Class of Nonlocal Wave Equations," Mathematics, MDPI, vol. 12(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2408-:d:1448638
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    References listed on IDEAS

    as
    1. Wang, Dongling & Xiao, Aiguo & Yang, Wei, 2015. "Maximum-norm error analysis of a difference scheme for the space fractional CNLS," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 241-251.
    2. Macías-Díaz, J.E. & Hendy, A.S. & De Staelen, R.H., 2018. "A compact fourth-order in space energy-preserving method for Riesz space-fractional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 1-14.
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