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

作者：Karatay Ibrahim^*; Bayramoglu Serife R

来源：Abstract and Applied Analysis, 2012, 2012: 548292.

DOI：10.1155/2012/548292

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 alpha, 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.

• 出版日期2012