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A Crank-Nicolson collocation spectral method for the two-dimensional telegraph equations
11School of Science, Beijing Technology and Business University, Beijing, China.
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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