High-order Compact Schemes for Nonlinear Dispersive Waves

Authors:
Jichun Li;Miguel R. Visbal
Affiliations:
Department of Mathematical Sciences, University of Nevada, Las Vegas, USA 89154;Computational Sciences Branch, Air Vehicles Directorate, Air Force Research Laboratory, Wright-Patterson AFB, USA 45433
Venue:
Journal of Scientific Computing
Year:
2006

Citing 7
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Abstract

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.