The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls

Abstract

This paper suggests hyperbolic relaxation system as a new efficient way in finding various types of numerical solutions of forced Korteweg-de Vries (fKdV) equations. When non-periodic numerical solutions such as hydraulic falls of fKdV equations with bumps are considered, the application of the spectral method or the finite difference methods may not work properly. As an alternative, the relaxation method has been applied to obtain the hyperbolic system for fKdV equations. The computational results show that the derived relaxation systems capture both hydraulic falls and solitary-type solutions accurately without numerical oscillations and require much less computational costs than other methods. (C) 2016 Elsevier Masson SAS. All rights reserved.