High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations. (13th February 2014)

• Record Type: Journal Article
• Authors: Karatay, Ibrahim; Bayramoglu, Serife R.
• Other Names: Atangana A. Academic Editor.; Kılıçman A. Academic Editor.; Ray S. S. Academic Editor.; Secer A. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-02-13
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/642989
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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.