Numerical Solution for Kawahara Equation by Using Spectral Methods

Some nonlinear wave equations are more difficult to investigate mathematically, as no general analytical method for their solutions exists. The Exponential Time Differencing (ETD) technique requires minimum stages to obtain the requiredaccurateness, which suggests an efficient technique relatingto computational duration thatensures remarkable stability characteristicsupon resolving nonlinear wave equations. This article solves the diagonal example of Kawahara equation via the ETD Runge-Kutta 4 technique. Implementation of this technique is proposed by short Matlab programs.