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A boundary value problem for the KdV equation: Comparison of finite-difference and Chebyshev methods

Author

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  • Skogestad, Jan Ole
  • Kalisch, Henrik

Abstract

Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at the boundaries. The Chebyshev method is found to be more efficient.

Suggested Citation

  • Skogestad, Jan Ole & Kalisch, Henrik, 2009. "A boundary value problem for the KdV equation: Comparison of finite-difference and Chebyshev methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 151-163.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:1:p:151-163
    DOI: 10.1016/j.matcom.2009.06.009
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    Cited by:

    1. Zhang, Xiaohua & Zhang, Ping, 2018. "A reduced high-order compact finite difference scheme based on proper orthogonal decomposition technique for KdV equation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 535-545.
    2. Kohnesara, Sima Molaei & Firoozjaee, Ali Rahmani, 2023. "Numerical solution of Korteweg–de Vries equation using discrete least squares meshless method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 65-76.

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