Open Access
Translator Disclaimer
2012 A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes
Ibrahim Karatay, Serife R. Bayramoglu
Abstr. Appl. Anal. 2012(SI01): 1-11 (2012). DOI: 10.1155/2012/548292

Abstract

We consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with Riemann-Liouville fractional derivative of order α, where 0 < α < 1 . The main purpose of this work is to extend the idea on Crank-Nicholson method to the time-fractional heat equations. We prove that the proposed method is unconditionally stable, and the numerical solution converges to the exact one with the order O ( τ 2 + h 2 ) . Numerical experiments are carried out to support the theoretical claims.

Citation

Download Citation

Ibrahim Karatay. Serife R. Bayramoglu. "A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes." Abstr. Appl. Anal. 2012 (SI01) 1 - 11, 2012. https://doi.org/10.1155/2012/548292

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1253.80024
MathSciNet: MR2991024
Digital Object Identifier: 10.1155/2012/548292

Rights: Copyright © 2012 Hindawi

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.2012 • No. SI01 • 2012
Back to Top