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Mathematical Biosciences and Engineering

2022, Volume 19, Issue 5: 4672-4689. doi: 10.3934/mbe.2022217
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An efficient numerical method for a time-fractional telegraph equation

  • Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China

  • Academic Editor: Yang Kuang
  • Received: 20 December 2021 Revised: 10 February 2022 Accepted: 28 February 2022 Published: 09 March 2022

  • In this paper a time-fractional telegraph equation is considered. First the time-fractional telegraph equation is transformed into an integral-differential equation with a weakly singular kernel. Then an integral-difference discretization scheme on a graded mesh is developed to approximate the integral-differential equation. The possible singularity of the exact solution is taken into account in the convergence analysis. It is proved that the scheme is second-order convergent for both the spatial discretization and the time discretization. Numerical experiments confirm the validity of the theoretical results.

    Citation: Jian Huang, Zhongdi Cen, Aimin Xu. An efficient numerical method for a time-fractional telegraph equation[J]. Mathematical Biosciences and Engineering, 2022, 19(5): 4672-4689. doi: 10.3934/mbe.2022217

    Related Papers:

  • In this paper a time-fractional telegraph equation is considered. First the time-fractional telegraph equation is transformed into an integral-differential equation with a weakly singular kernel. Then an integral-difference discretization scheme on a graded mesh is developed to approximate the integral-differential equation. The possible singularity of the exact solution is taken into account in the convergence analysis. It is proved that the scheme is second-order convergent for both the spatial discretization and the time discretization. Numerical experiments confirm the validity of the theoretical results.


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