An Exponential Wave Integrator Pseudospectral Method for the Symmetric Regularized-Long-Wave Equation
Year: 2016
Author: Xiaofei Zhao
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1510-m4467
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 1 : pp. 49–69
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Symmetric regularized-long-wave equation Exponential wave integrator Pseudospecral method Error estimate Explicit scheme Large step size.