Optimal error estimate of two linear and momentum-preserving Fourier pseudo-spectral schemes for the RLW equation

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Hong, Qi; Wang, Yushun; Gong, Yuezheng;
  • Subject: Mathematics - Numerical Analysis

In this paper, two novel linear-implicit and momentum-preserving Fourier pseudo-spectral schemes are proposed and analyzed for the regularized long-wave equation. The numerical methods are based on the blend of the Fourier pseudo-spectral method in space and the linear-... View more
  • References (41)
    41 references, page 1 of 5

    1. Akbari, R., Mokhtari, R.: A new compact finite difference method for solving the generalized long wave equation. Numer. Funct. Anal. Optim. 35, 133-152 (2014)

    2. Avrin, J., Goldstein, J.: Global existence for the Benjamin-Bona-Mahony equation in arbitrary dimensions. Nonlinear Anal. 9, 861-865 (1985)

    3. 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)

    4. Bridges, T., Reich, S.: Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Phys. Lett. A. 284, 184-193 (2001)

    5. Bubb, C., Piggot, M.: Geometric Integration and Its Application, Handbook of Numerical Analysis, vol. XI. NorthHolland, Amsterdam (2003)

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

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

    8. Cai, J., Gong, Y., Liang, H.: Novel implicit/explicit local conservative scheme for the regularized long-wave equation and convergence analysis. J. Math. Anal. Appl. 447, 17-31 (2017)

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

    10. Canuto, C., Quarteroni, A.: Approximation results for orthogonal polynomials in sobolev spaces,. Math. Comput. 38, 67-86 (1982)

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