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A decoupled, linearly implicit and high-order structure-preserving scheme for Euler–Poincaré equations

Author

Listed:
  • Gao, Ruimin
  • Li, Dongfang
  • Mei, Ming
  • Zhao, Dan

Abstract

It is challenging to develop high-order structure-preserving finite difference schemes for the modified two-component Euler–Poincaré equations due to the nonlinear terms and high-order derivative terms. To overcome the difficulties, we introduce a bi-variate function and carefully choose the intermediate average variable in the temporal discretization. Then, we obtain a decoupled and linearly implicit scheme. It is shown that the fully-discrete scheme can keep both the discrete mass and energy conserved. And the fully-discrete scheme has fourth-order accuracy in the spatial direction and second-order accuracy in the temporal direction. Several numerical examples are given to confirm the theoretical results.

Suggested Citation

  • Gao, Ruimin & Li, Dongfang & Mei, Ming & Zhao, Dan, 2024. "A decoupled, linearly implicit and high-order structure-preserving scheme for Euler–Poincaré equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 679-703.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:679-703
    DOI: 10.1016/j.matcom.2023.12.009
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