Journal of Inequalities and Applications (Jun 2018)

A Crank–Nicolson collocation spectral method for the two-dimensional telegraph equations

  • Yanjie Zhou,
  • Zhendong Luo

DOI
https://doi.org/10.1186/s13660-018-1728-5
Journal volume & issue
Vol. 2018, no. 1
pp. 1 – 17

Abstract

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Abstract In this paper, we mainly focus to study the Crank–Nicolson collocation spectral method for two-dimensional (2D) telegraph equations. For this purpose, we first establish a Crank–Nicolson collocation spectral model based on the Chebyshev polynomials for the 2D telegraph equations. We then discuss the existence, uniqueness, stability, and convergence of the Crank–Nicolson collocation spectral numerical solutions. Finally, we use two sets of numerical examples to verify the validity of theoretical analysis. This implies that the Crank–Nicolson collocation spectral model is very effective for solving the 2D telegraph equations.

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