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Volume 34, Issue 1
An Exponential Wave Integrator Pseudospectral Method for the Symmetric Regularized-Long-Wave Equation

Xiaofei Zhao

DOI: 10.4208/jcm.1510-m4467

J. Comp. Math., 34 (2016), pp. 49-69.

Published online: 2016-02

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  • Abstract

An efficient and accurate exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed and analyzed for solving the symmetric regularized-long-wave (SRLW) equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.

  • Keywords

Symmetric regularized-long-wave equation, Exponential wave integrator, Pseudospecral method, Error estimate, Explicit scheme, Large step size.

  • AMS Subject Headings

65M12, 65M15, 65M70.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhxfnus@gmail.com (Xiaofei Zhao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-49, author = {Zhao , Xiaofei}, title = {An Exponential Wave Integrator Pseudospectral Method for the Symmetric Regularized-Long-Wave Equation}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {1}, pages = {49--69}, abstract = {

An efficient and accurate exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed and analyzed for solving the symmetric regularized-long-wave (SRLW) equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1510-m4467}, url = {http://global-sci.org/intro/article_detail/jcm/9782.html} }
TY - JOUR T1 - An Exponential Wave Integrator Pseudospectral Method for the Symmetric Regularized-Long-Wave Equation AU - Zhao , Xiaofei JO - Journal of Computational Mathematics VL - 1 SP - 49 EP - 69 PY - 2016 DA - 2016/02 SN - 34 DO - http://doi.org/10.4208/jcm.1510-m4467 UR - https://global-sci.org/intro/article_detail/jcm/9782.html KW - Symmetric regularized-long-wave equation, Exponential wave integrator, Pseudospecral method, Error estimate, Explicit scheme, Large step size. AB -

An efficient and accurate exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed and analyzed for solving the symmetric regularized-long-wave (SRLW) equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.

Xiaofei Zhao. (2020). An Exponential Wave Integrator Pseudospectral Method for the Symmetric Regularized-Long-Wave Equation. Journal of Computational Mathematics. 34 (1). 49-69. doi:10.4208/jcm.1510-m4467
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