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Implicit difference approximation for the time fractional diffusion equation

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Abstract

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order 0 < α < 1 ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent withO(Τ +h 2), where Τ andh are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

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Authors and Affiliations

  1. School of Mathematical Science, Xiamen University, 361005, Xiamen, China

    P. Zhuang

  2. Department of Mathematics, Xiamen University, 361005, Xiamen, China

    F. Liu

  3. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, 4001, Brisbane, Qld., Australia

    F. Liu

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  1. P. Zhuang
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  2. F. Liu
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Correspondence to F. Liu.

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Zhuang, P., Liu, F. Implicit difference approximation for the time fractional diffusion equation. J. Appl. Math. Comput. 22, 87–99 (2006). https://doi.org/10.1007/BF02832039

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  • DOI: https://doi.org/10.1007/BF02832039

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