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The Scientific World Journal
Volume 2014, Article ID 642989, 8 pages
Research Article

High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations

Department of Mathematics, Fatih University, 34500 Istanbul, Turkey

Received 31 August 2013; Accepted 16 December 2013; Published 13 February 2014

Academic Editors: A. Atangana, A. Kılıçman, S. S. Ray, and A. Secer

Copyright © 2014 Ibrahim Karatay and Serife R. Bayramoglu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space derivative. The spectral stability and the Fourier stability analysis of the difference scheme are shown. Finally a detailed numerical analysis, including tables, figures, and error comparison, is given to demonstrate the theoretical results and high accuracy of the proposed scheme.