Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations

HU Jiahui; WANG Jungang; NIE Yufeng

doi:10.21656/1000-0887.390358

Volume 40 Issue 7

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HU Jiahui, WANG Jungang, NIE Yufeng. Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations[J]. Applied Mathematics and Mechanics, 2019, 40(7): 791-800. doi: 10.21656/1000-0887.390358

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Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations

doi: 10.21656/1000-0887.390358

¹Department of Applied Mathematics, Northwestern Polytechnical University,Xi’an 710129, P.R.China;²School of Sciences, Henan University of Technology, Zhengzhou 450001, P.R.China

Funds: The National Natural Science Foundation of China(11471262)

Received Date: 2018-12-25
Rev Recd Date: 2019-03-09
Publish Date: 2019-07-01

Abstract

Abstract

Based on the composite Simpson’s quadrature rule and the composite 2-point Gauss-Legendre quadrature rule, 2 high-order finite difference schemes were proposed for solving time distributed-order diffusion equations. Other than the existing methods whose convergence rates are only 1st-order or 2nd-order in the temporal domain, the proposed 2 schemes both have 3rd-order convergence rates in the temporal domain, and 4th-order rates in the spatial domain and the distributed order, respectively. Such high-order convergence rates were further verified with numerical examples. The results show that, both of the proposed 2 schemes are stable, and have higher accuracy and efficiency compared with existing algorithms.
- time distributed-order diffusion equation,
- fractional derivative,
- high-order difference scheme,
- convergence rate

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References(18)

References

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