Advances in Difference Equations (Mar 2019)

Legendre spectral element method for solving sine-Gordon equation

  • Mahmoud Lotfi,
  • Amjad Alipanah

DOI
https://doi.org/10.1186/s13662-019-2059-7
Journal volume & issue
Vol. 2019, no. 1
pp. 1 – 15

Abstract

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Abstract In this paper, we study the Legendre spectral element method for solving the sine-Gordon equation in one dimension. Firstly, we discretize the equation by Legendre spectral element in space and then discretize the time by the second-order leap-frog method. We study the stability and convergence of the method and show the convergence of our method. Finally, we show the results with numerical examples.

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