An efficient numerical method for a time-fractional telegraph equation

Mathematical Biosciences and Engineering

Aimin Xu¹  Jian Huang¹  Zhongdi Cen¹ 

[1] Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China;

关键词: telegraph equation;    caputo derivative;    integro-differential equation;    finite difference;    singularity;   

DOI  :  10.3934/mbe.2022217

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown