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
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
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