A COMPACT DIFFERENCE SCHEME FOR FOURTH-ORDER FRACTIONAL SUB-DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

Zhongsheng Yao; Zhibo Wang

doi:10.11948/2018.1159

2018 Volume 8 Issue 4

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Zhongsheng Yao, Zhibo Wang. A COMPACT DIFFERENCE SCHEME FOR FOURTH-ORDER FRACTIONAL SUB-DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(4): 1159-1169. doi: 10.11948/2018.1159

Citation:

Zhongsheng Yao, Zhibo Wang. A COMPACT DIFFERENCE SCHEME FOR FOURTH-ORDER FRACTIONAL SUB-DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(4): 1159-1169. doi: 10.11948/2018.1159

A COMPACT DIFFERENCE SCHEME FOR FOURTH-ORDER FRACTIONAL SUB-DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China

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Abstract

Abstract

In this paper, a compact finite difference scheme with global convergence order O(τ² + h⁴) is derived for fourth-order fractional sub-diffusion equations subject to Neumann boundary conditions. The difficulty caused by the fourth-order derivative and Neumann boundary conditions is carefully handled. The stability and convergence of the proposed scheme are studied by the energy method. Theoretical results are supported by numerical experiments.
- Fourth-order fractional sub-diffusion equation /
- compact difference scheme /
- energy method
MSC: 65M06;65M12;65M15;35R11

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References

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