## Taiwanese Journal of Mathematics

### Numerical Methods for Solving the Time-fractional Telegraph Equation

#### Abstract

A flexible numerical method for the time-fractional telegraph equation is proposed and analyzed in this paper. The solution is discretized with a new finite difference scheme in time, and a local discontinuous Galerkin (LDG) method in space. We prove that the method is unconditionally stable and convergent with order $O(h^{k+1} + (\Delta t)^{3-\alpha})$, where $h$, $\Delta t$, $k$ are the space step size, time step size and degree of piecewise polynomial, respectively. Numerical experiments are carried out to illustrate the robustness, reliability, and accuracy of the method.

#### Article information

Source
Taiwanese J. Math., Volume 22, Number 6 (2018), 1509-1528.

Dates
Revised: 25 February 2018
Accepted: 10 April 2018
First available in Project Euclid: 24 May 2018

https://projecteuclid.org/euclid.twjm/1527127364

Digital Object Identifier
doi:10.11650/tjm/180503

Mathematical Reviews number (MathSciNet)
MR3880238

Zentralblatt MATH identifier
07021702

#### Citation

Wei, Leilei; Liu, Lijie; Sun, Huixia. Numerical Methods for Solving the Time-fractional Telegraph Equation. Taiwanese J. Math. 22 (2018), no. 6, 1509--1528. doi:10.11650/tjm/180503. https://projecteuclid.org/euclid.twjm/1527127364

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