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.
H. Wang, B.J. Zhang, X.Z. Liu, D.Z. Luo, S.B. Zhong
T. G. Zhao et al., "Chebyshev-Legendre Pseudo-Spectral Method for the Modified Kawahara Equation", Advanced Materials Research, Vols. 143-144, pp. 191-195, 2011