Open AccessAn efficient numerical method for a time-fractional telegraph equation
Author(s) -
Jian Huang,
Zhongdi Cen,
Aiqiang Xu
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022217
Subject(s) - discretization , mathematics , singularity , telegrapher's equations , convergence (economics) , mathematical analysis , differential equation , integral equation , kernel (algebra) , partial differential equation , summation equation , integro differential equation , first order partial differential equation , computer science , telecommunications , transmission line , combinatorics , economics , economic growth
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.