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High-order numerical methods of fractional-order Stokes’ first problem for heated generalized second grade fluid

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Abstract

The high-order implicit finite difference schemes for solving the fractional-order Stokes’ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition are given. The stability, solvability, and convergence of the numerical scheme are discussed via the Fourier analysis and the matrix analysis methods. An improved implicit scheme is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness of the mentioned schemes.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan Province, P. R. China

    Chao Ye  (叶 超), Xian-nan Luo  (骆先南) & Li-ping Wen  (文立平)

Authors
  1. Chao Ye  (叶 超)
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  2. Xian-nan Luo  (骆先南)
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  3. Li-ping Wen  (文立平)
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Corresponding author

Correspondence to Chao Ye  (叶 超).

Additional information

Project supported by the National Natural Science Foundation of China (No. 10971175) and the Scientific Research Fund of Hunan Provincial Education Department (No. 09A093)

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Ye, C., Luo, Xn. & Wen, Lp. High-order numerical methods of fractional-order Stokes’ first problem for heated generalized second grade fluid. Appl. Math. Mech.-Engl. Ed. 33, 65–80 (2012). https://doi.org/10.1007/s10483-012-1534-8

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  • DOI: https://doi.org/10.1007/s10483-012-1534-8

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Chinese Library Classification

2010 Mathematics Subject Classification

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