Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 219, Issue 6, Pages 2975-2988Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2012.09.022
Keywords
Time-space fractional telegraph equation; Riemann-Liouville derivative; Caputo derivative; Fractional difference method; Fractional finite element method
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Funding
- Scientific Research Project of Shanghai Customs College [2312006]
- Key Program of Shanghai Municipal Education Commission [12ZZ084]
- Shanghai Leading Academic Discipline Project [S30104]
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In this paper, we study the numerical solution of the time-space fractional order (fractional for simplicity) telegraph equation, which can be used in signal analysis for transmission and propagation of electrical signals, also the modeling of the reaction diffusion and the random walk of suspension flows and so on. The semi-discrete and fully discrete numerical approximations are both analyzed, where the Galerkin finite element method for the spatial Riemann-Liouville fractional derivative with order 1 + beta is an element of (1, 2) and the finite difference schemes for the temporal Caputo derivatives with orders alpha is an element of (1/2, 1) and 2 alpha are analyzed respectively. Results on the existence and uniqueness of the solution, the numerical stability, and the error estimates are displayed in details. Numerical examples are included to confirm the theoretical analysis. (C) 2012 Elsevier Inc. All rights reserved.
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