Some notes on numerical waves of fifth-order Korteweg-de Vries equations

This paper addresses the Fourier spectral method being applied on two types of fifth-order Korteweg-de Vries (fKdV) equations, which are partial differential equations containing various types of nonlinear terms and are often applied to the modeling of different wave phenomena. The Fourier spectral scheme is established and implemented to compute the solitary wave solutions for fKdV equations. We compute the numerical solution based on solitary waves with different velocities and amplitudes and show that the global accuracy is quite satisfactory for a fast convergence rate in producing numerical solutions. In addition, we analyze the numerical stability for the numerical schemes on the third-order KdV and fKdV equations based on von Neumann method of Fourier modes. (C) 2019 Physics Essays Publication.