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Asian Simulation Conference

AsiaSim 2012: AsiaSim 2012 pp 273–284Cite as

A Compact Difference Scheme for Time Fractional Diffusion Equation with Neumann Boundary Conditions

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 323))

Abstract

This paper is devoted to the numerical treatment of time fractional diffusion equation with Neumann boundary conditions. A compact difference scheme is derived for solving this problem, by combining the classic finite difference method for Caputo derivative in time, the second order central difference method in space and the compact difference treatment for Neumann boundary conditions. The solvability, stability and convergence of this scheme are rigorously discussed. We prove that the convergence order of this proposed scheme is O(τ2 − α + h2), where τ, α and h are the time step size, the index of fractional derivative and space step size respectively. Numerical experiments are carried out to demonstrate the theoretical analysis.

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Author information

Authors and Affiliations

  1. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Jianfei Huang, Yifa Tang & Jiye Yang

  2. Yuanpei College, Peking University, Beijing, 100871, China

    Wenjia Wang

Authors
  1. Jianfei Huang
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  2. Yifa Tang
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  3. Wenjia Wang
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  4. Jiye Yang
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Editor information

Editors and Affiliations

  1. National CIMS Engineering Research Center, Department of Automation, Tsinghua University, 100084, Beijing, China

    Tianyuan Xiao

  2. School of Automation Science and Electrical Engineering, Beihang University, 100191, Beijing, China

    Lin Zhang

  3. School of Mechatronics Engineering and Automation, Shanghai University, 200072, Shanghai, China

    Minrui Fei

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© 2012 Springer-Verlag Berlin Heidelberg

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Huang, J., Tang, Y., Wang, W., Yang, J. (2012). A Compact Difference Scheme for Time Fractional Diffusion Equation with Neumann Boundary Conditions. In: Xiao, T., Zhang, L., Fei, M. (eds) AsiaSim 2012. AsiaSim 2012. Communications in Computer and Information Science, vol 323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34384-1_33

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  • DOI: https://doi.org/10.1007/978-3-642-34384-1_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34383-4

  • Online ISBN: 978-3-642-34384-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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