Volume 50, Issue 3
Optimal Error Estimate of Fourier Spectral Method for the Kawahara Equation

Zhenguo Deng

J. Math. Study, 50 (2017), pp. 291-306.

Published online: 2017-09

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  • Abstract

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.

  • Keywords

Fourier spectral method, Kawahara equation, error estimate.

  • AMS Subject Headings

65M70, 76B15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

deng@gxu.edu.cn (Zhenguo Deng)

  • BibTex
  • RIS
  • TXT
@Article{JMS-50-291, author = {Zhenguo and Deng and deng@gxu.edu.cn and 12653 and School of Mathematics and Information Science, Guangxi University, Nanning 530004, Guangxi, P.R. China and Zhenguo Deng}, title = {Optimal Error Estimate of Fourier Spectral Method for the Kawahara Equation}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {3}, pages = {291--306}, abstract = {

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} }
TY - JOUR T1 - Optimal Error Estimate of Fourier Spectral Method for the Kawahara Equation AU - Deng , Zhenguo JO - Journal of Mathematical Study VL - 3 SP - 291 EP - 306 PY - 2017 DA - 2017/09 SN - 50 DO - http://doi.org/10.4208/jms.v50n3.17.06 UR - https://global-sci.org/intro/article_detail/jms/10622.html KW - Fourier spectral method, Kawahara equation, error estimate. AB -

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.

Zhenguo Deng. (2019). Optimal Error Estimate of Fourier Spectral Method for the Kawahara Equation. Journal of Mathematical Study. 50 (3). 291-306. doi:10.4208/jms.v50n3.17.06
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