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Numerical solution of the Degasperis–Procesi equation by the cubic B-spline quasi-interpolation method

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Listed:
  • Zhang, JiHong
  • Zheng, JunSheng
  • Gao, QinJiao

Abstract

In this paper, a numerical scheme is presented to solve the non-dissipative Degasperis–Procesi equation based on the u-p formulation. The cubic B-spline quasi-interpolation coupled with the finite difference method is applied to approximate the spatial derivatives and an optimal third order TVD Runge–Kutta method to estimate the time derivative of the dependent variable. The accuracy and effectiveness of the proposed method are validated by six classical problems. Numerical results indicate that the proposed scheme is simple, easy to implement with high accuracy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:324:y:2018:i:c:p:218-227
    DOI: 10.1016/j.amc.2017.11.058
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    References listed on IDEAS

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    1. 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.
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