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An optimal error estimate in $L^2$-norm for Fourier spectral method is presented for the Kawahara equation with periodic boundary conditions. A numerical example is provided to confirm the theoretical analysis. The method and proving skills are also applicable to the periodic boundary problems for some nonlinear dispersive wave equations provided that the dispersive operator is bounded and antisymmetric and commutes with differentiation.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n3.17.06}, url = {http://global-sci.org/intro/article_detail/jms/10622.html} }An optimal error estimate in $L^2$-norm for Fourier spectral method is presented for the Kawahara equation with periodic boundary conditions. A numerical example is provided to confirm the theoretical analysis. The method and proving skills are also applicable to the periodic boundary problems for some nonlinear dispersive wave equations provided that the dispersive operator is bounded and antisymmetric and commutes with differentiation.