## Abstract and Applied Analysis

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

#### 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 $0<\alpha <1$. 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 $O({\tau }^{2}+{h}^{2})$. 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

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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