Li, Jichun; Visbal, Miguel R. High-order compact schemes for nonlinear dispersive waves. (English) Zbl 1089.76043 J. Sci. Comput. 26, No. 1, 1-23 (2006). Summary: 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. Cited in 25 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:KdV equation; KdV-Burgers equation; third derivative term Software:FDL3DI PDF BibTeX XML Cite \textit{J. Li} and \textit{M. R. Visbal}, J. Sci. Comput. 26, No. 1, 1--23 (2006; Zbl 1089.76043) Full Text: DOI 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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.