Second-order linear structure-preserving modified finite volume schemes for the regularized long-wave equation

Preprint English OPEN
Hong, Qi; Wang, Jialing; Gong, Yuezheng;
  • Subject: Mathematics - Numerical Analysis

In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three linear-implicit energy conservation nu... View more
  • References (32)
    32 references, page 1 of 4

    [1] Benjamin, T., Bona, J., Mahony, J.: Model equations for long waves in nonlinear dispersive systems. Philos. Trans. R Soc. Lond. A 227, 47-78 (1972)

    [2] Bubb, C., Piggot, M.: Geometric Integration and Its Application, Handbook of Numerical Analysis. vol. XI., North-Holland, Amsterdam (2003)

    [3] Cai, J.: Multi-symplectic numerical method for the regularized long-wave equation. Comput. Phys. Commun. 180, 1821-1831 (2009)

    [4] Cai, J.: A new explicit multi-symplectic scheme for the regularized long-wave equation. J. Math. Phys. 50, 013535 (2009)

    [5] Cai, J.: A multi-symplectic explicit scheme for the modified regularized long-wave equation. J Comput. Appl. Math. 234, 899-905 (2010)

    [6] Cai, J.: Some linearly and nonlinearly implicit schemes for the numerical solutions of the regularized long-wave equation. Appl. Math. Comput. 217, 9948-9955 (2011)

    [7] Cai J.X. Hong, Q.: Efficient local structure-preserving schemes for the RLW-Type equation. Numer. Methods Partial Differential Equations 33, 1678-1691 (2017)

    [8] Dag, I., Saka, B., Irk, D.: Application of cubic B-splines for numerical solution of the RLW equation. Appl. Math. Comput. 159, 373-389 (2004)

    [9] Dahlby, M., Owren, B.: A general framework for deriving integral preserving numerical methods for PDEs. SIAM J. Sci. Comput. 33, 2318-2340 (2011)

    [10] Dehghan, M., Salehi, R.: The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas. Comput. Phys. Commun. 182, 2540-2549 (2011)

  • Related Organizations (1)
  • Metrics
Share - Bookmark