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Multi-quadric quasi-interpolation method coupled with FDM for the Degasperis–Procesi equation

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  • Wu, Hui-Yuan
  • Duan, Yong

Abstract

In this paper, the Degasperis–Procesi (DP) equation which contains nonlinear high order derivatives and discontinuous solutions is recast to its equivalent form: u−P. Based on the equivalent formulation of DP equation, a new numerical method is presented. The multi-quadric (MQ) quasi-interpolation method coupled with finite difference method is applied to approximate the spatial derivatives and the third order TVD method is used to approximate the time derivative. Several examples are presented to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Wu, Hui-Yuan & Duan, Yong, 2016. "Multi-quadric quasi-interpolation method coupled with FDM for the Degasperis–Procesi equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 83-92.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:83-92
    DOI: 10.1016/j.amc.2015.10.044
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    References listed on IDEAS

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    1. Gao, Wenwu & Wu, Zongmin, 2015. "Solving time-dependent differential equations by multiquadric trigonometric quasi-interpolation," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 377-386.
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    Cited by:

    1. Zhu, Xiaomin & Dou, Fangfang & Karageorghis, Andreas & Chen, C.S., 2020. "A fictitious points one–step MPS–MFS technique," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Zhang, JiHong & Zheng, JunSheng & Gao, QinJiao, 2018. "Numerical solution of the Degasperis–Procesi equation by the cubic B-spline quasi-interpolation method," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 218-227.
    3. Lin, Ji & Zhao, Yuxiang & Watson, Daniel & Chen, C.S., 2020. "The radial basis function differential quadrature method with ghost points," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 173(C), pages 105-114.
    4. Dou, Fangfang & Li, Zi-Cai & Chen, C.S. & Tian, Zhaolu, 2018. "Analysis on the method of fundamental solutions for biharmonic equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 346-366.
    5. Chang, Wanru & Chen, C.S. & Liu, Xiao-Yan & Li, J., 2020. "Localized meshless methods based on polynomial basis functions for solving axisymmetric equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 487-499.
    6. Hui Zheng & Xiaoling Lai & Anyu Hong & Xing Wei, 2022. "A Novel RBF Collocation Method Using Fictitious Centre Nodes for Elasticity Problems," Mathematics, MDPI, vol. 10(19), pages 1-15, October.

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