High-order compact schemes for nonlinear dispersive waves.

*(English)*Zbl 1089.76043Summary: High-order compact finite difference schemes coupled with high-order low-pass filter and the classical fourth-order Runge-Kutta scheme are applied to simulate nonlinear dispersive wave propagation problems described the Korteweg-de Vries (KdV)-like equations, which involve a third derivative term. Several examples such as KdV equation, and KdV-Burgers equation are presented, and the solutions obtained are compared with some other numerical methods. Computational results demonstrate that high-order compact schemes work very well for problems involving a third derivative term.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

##### Software:

FDL3DI
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\textit{J. Li} and \textit{M. R. Visbal}, J. Sci. Comput. 26, No. 1, 1--23 (2006; Zbl 1089.76043)

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##### References:

[2] | Gaitonde, D. V., and Visbal, M. R., (1998). High-order schemes for Navier–Stokes equations: algorithms and implementation into FDL3DI. Technical Report AFRL-VA-WP-TR-1998-3060, Air Force Research Laboratory, Wright-Patterson AFB, Ohio. |

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