Abstract and Applied Analysis

A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes

Ibrahim Karatay and Serife R. Bayramoglu

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 548292, 11 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168347

Digital Object Identifier
doi:10.1155/2012/548292

Mathematical Reviews number (MathSciNet)
MR2991024

Zentralblatt MATH identifier
1253.80024

Citation

Karatay, Ibrahim; Bayramoglu, Serife R. A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 548292, 11 pages. doi:10.1155/2012/548292. https://projecteuclid.org/euclid.aaa/1365168347


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