An efficient numerical method for a time-fractional telegraph equation | Zendy

Jian Huang | Zendy; Zhongdi Cen | Zendy; Aimin Xu | Zendy

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An efficient numerical method for a time-fractional telegraph equation

Author(s) -

Jian Huang,

Zhongdi Cen,

Aimin 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 , mathematical analysis , telegrapher's equations , singularity , convergence (economics) , differential equation , integral equation , partial differential equation , kernel (algebra) , 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.

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