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A meshless symplectic algorithm for nonlinear wave equation using highly accurate RBFs quasi-interpolation

Author

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  • Zhang, Shengliang
  • Yang, Yu
  • Yang, Hongqiang

Abstract

This study suggests a high-order meshless symplecitc algorithm for Hamiltonian wave equation by using highly accurate radial basis functions (RBFs) quasi-interpolation operator. The method does not require solving a resultant full matrix and possesses a high order accuracy compared with existing numerical methods. We also present a theoretical framework to show the conservativeness and convergence of the proposed symplectic method. As the numerical experiments shown, it not only offers a high order accuracy but also has a good property of long-time tracking capability.

Suggested Citation

  • Zhang, Shengliang & Yang, Yu & Yang, Hongqiang, 2017. "A meshless symplectic algorithm for nonlinear wave equation using highly accurate RBFs quasi-interpolation," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 110-120.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:110-120
    DOI: 10.1016/j.amc.2017.07.010
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