Open Access
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


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.


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Leilei Wei. Lijie Liu. Huixia Sun. "Numerical Methods for Solving the Time-fractional Telegraph Equation." Taiwanese J. Math. 22 (6) 1509 - 1528, December, 2018.


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

Primary: 35S10 , 65M06 , 65M12

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

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

Vol.22 • No. 6 • December, 2018
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