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

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  • Ibrahim Karatay
  • Serife R. Bayramoglu

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 . 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 . Numerical experiments are carried out to support the theoretical claims.

Suggested Citation

  • Ibrahim Karatay & Serife R. Bayramoglu, 2012. "A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, October.
    • Handle: RePEc:hin:jnlaaa:548292
    DOI: 10.1155/2012/548292
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