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

作者：Zhou, Yanjie; Luo, Zhendong^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018, 2018(1): 137.

DOI：10.1186/s13660-018-1728-5

• Crank-Nicolson collocation spectral method
• Telegraph equation
• Existence, stability, and convergence
• Numerical experiment

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.

• 出版日期2018-6-19
• 单位华北电力大学（保定）; 华北电力大学; 北京工商大学