Open Access
Translator Disclaimer
December, 2018 Numerical Methods for Solving the Time-fractional Telegraph Equation
Leilei Wei, Lijie Liu, Huixia Sun
Taiwanese J. Math. 22(6): 1509-1528 (December, 2018). DOI: 10.11650/tjm/180503

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.

Citation

Download Citation

Leilei Wei. Lijie Liu. Huixia Sun. "Numerical Methods for Solving the Time-fractional Telegraph Equation." Taiwanese J. Math. 22 (6) 1509 - 1528, December, 2018. https://doi.org/10.11650/tjm/180503

Information

Received: 17 September 2017; Revised: 25 February 2018; Accepted: 10 April 2018; Published: December, 2018
First available in Project Euclid: 24 May 2018

zbMATH: 07021702
MathSciNet: MR3880238
Digital Object Identifier: 10.11650/tjm/180503

Subjects:
Primary: 35S10 , 65M06 , 65M12

Keywords: convergence , discontinuous Galerkin method , fractional telegraph equation , stability

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.22 • No. 6 • December, 2018
Back to Top