High-Order Numerical Methods of the Fractional Order Stokes’ First Problem for a Heated Generalized Second Grade Fluid

YE Chao; LUO Xian-nan; WEN Li-ping

doi:10.3879/j.issn.1000-0887.2012.01.006

Volume 33 Issue 1

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YE Chao, LUO Xian-nan, WEN Li-ping. High-Order Numerical Methods of the Fractional Order Stokes’ First Problem for a Heated Generalized Second Grade Fluid[J]. Applied Mathematics and Mechanics, 2012, 33(1): 61-75. doi: 10.3879/j.issn.1000-0887.2012.01.006

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High-Order Numerical Methods of the Fractional Order Stokes’ First Problem for a Heated Generalized Second Grade Fluid

doi: 10.3879/j.issn.1000-0887.2012.01.006

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

Received Date: 2011-08-03
Rev Recd Date: 2011-11-07
Publish Date: 2012-01-15

Abstract

Abstract

High-order implicit finite difference methods for solving the Stokes’ first problem for a heated generalized second grade fluid with fractional derivative were studied. The stability, solvability and convergence of the numerical scheme were discussed via fourier analysis and matrix analysis method. An improved implicit scheme was also obtained. Finally, two numerical examples were presented to demonstrate the effectiveness of the mentioned schemes.
- fractional order Stokes’ first problem,
- implicit difference scheme,
- solvability stability,
- convergence,

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References

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