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An analysis of implicit conservative difference solver for fractional Klein–Gordon–Zakharov system

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  • Xie, Jianqiang
  • Zhang, Zhiyue

Abstract

In this paper, we propose an efficient linearly implicit conservative difference solver for the fractional Klein–Gordon–Zakharov system. First of all, we present a detailed derivation of the energy conservation property of the system in the discrete setting. Then, by using the mathematical induction, it is proved that the proposed scheme is uniquely solvable. Subsequently, by virtue of the discrete energy method and a ‘cut-off’ function technique, it is shown that the proposed solver possesses the convergence rates of O(Δt2+h2) in the sense of L∞- and L2- norms, respectively, and is unconditionally stable. Finally, numerical results testify the effectiveness of the proposed scheme and exhibit the correctness of theoretical results.

Suggested Citation

  • Xie, Jianqiang & Zhang, Zhiyue, 2019. "An analysis of implicit conservative difference solver for fractional Klein–Gordon–Zakharov system," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 153-166.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:153-166
    DOI: 10.1016/j.amc.2018.10.031
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    References listed on IDEAS

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    1. Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2015. "Energy conservation issues in the numerical solution of the semilinear wave equation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 842-870.
    2. Deng, Dingwen & Liang, Dong, 2018. "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 188-209.
    3. Li, Dongfang & Zhang, Chengjian, 2016. "Construction of high-order Runge–Kutta methods which preserve delay-dependent stability of DDEs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 168-179.
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