A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

作者：Karatay Ibrahim^*; Kale Nurdane; Bayramoglu Serife R

来源：Journal of Fractional Calculus and Applied Analysis, 2013, 16(4): 892-910.

DOI：10.2478/s13540-013-0055-2

• Crank-Nicholson difference schemes
• initial value problems for time-fractional heat equations
• Caputo derivative
• stability
• convergence
• method of Fourier analysis

In this paper, 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 the Caputo derivative of order alpha, where 0 < alpha < 1. The main purpose of this work is to extend the idea on the Crank-Nicholson method to the time-fractional heat equations. By the method of the Fourier analysis, we prove that the proposed method is stable and the numerical solution converges to the exact one with the order O(tau (2-alpha) + h (2)), conditionally. Numerical experiments are carried out to support the theoretical claims.

• 出版日期2013-12