Chebyshev-Legendre Pseudo-Spectral Method for the Modified Kawahara Equation

Chebyshev-Legendre pseudo-spectral method was applied to resolve the modified Kawahara equation. The proposed approach is based on Legendre-Petrov Galerkin formulation but only the Chebyshev-Gauss-Lobatto nodes are used in the computation. The Petrov method is considered for the unsymmetry of the fifth-order derivative term appeared in the modified Kawahara equation and Chebyshev-Legendre method is used for reducing the computational complexity. Numerical tests are presented to verify the efficiency of the proposed approach.