Numerical features of the fifth-order nonlinear Kawahara equation for modeling shallow water waves

Abstract

In the present study, numerical solutions of the important type of the fifth-order Korteweg-de Vries (KdV) equation for modeling shallow water waves, namely, Kawahara equation, are investigated. With the solutions of the higher order Kawahara equation used in the modeling of shallow water waves, the behavior change of the wave with parameter changes is revealed. Unlike the classical numerical methods, two effective numerical methods are combined and used together. One of the components of the scheme is differential quadrature method (DQM) that approaches the derivative of the mesh points in the solution domain. In other words, space discretization is completed by using DQM. The other component is the Crank-Nicolson scheme, which is the effective type of the finite difference method. By using the advantages of the DQM and Crank-Nicolson scheme with effective linearization technique together, high accurate solutions are obtained. Four different test problems and their various forms are solved numerically. Error norms, central processing unit times, rate of convergence, and three invariants are calculated and reported. Published under an exclusive license by AIP Publishing.https://doi.org/10.1063/5.0276849I