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An implicit RBF meshless approach for time fractional diffusion equations

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Abstract

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

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Authors and Affiliations

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

    Q. Liu & P. Zhuang

  2. School of Engineering Systems, Queensland University of Technology, Brisbane, Australia

    Y. T. Gu

  3. School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia

    F. Liu

  4. School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, 710072, China

    Y. F. Nie

Authors
  1. Q. Liu
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  2. Y. T. Gu
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  3. P. Zhuang
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  4. F. Liu
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  5. Y. F. Nie
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Correspondence to Y. T. Gu.

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Liu, Q., Gu, Y.T., Zhuang, P. et al. An implicit RBF meshless approach for time fractional diffusion equations. Comput Mech 48, 1–12 (2011). https://doi.org/10.1007/s00466-011-0573-x

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  • DOI: https://doi.org/10.1007/s00466-011-0573-x

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