Optimal Error Estimate of Fourier Spectral Method for the Kawahara Equation (Journal of Mathematical Study, 2017)
An optimal error estimate in $L^2$-norm for Fourier spectral method is presentedfor the Kawahara equation with periodic boundary conditions. A numericalexample is provided to confirm the theoretical analysis. The method and proving skillsare also applicable to the periodic boundary problems for some nonlinear dispersivewave equations provided that the dispersive operator is bounded and antisymmetricand commutes with differentiation.