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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 11
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Articles

Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay

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Pages 1867-1884 | Received 25 Apr 2016, Accepted 01 Jun 2016, Published online: 17 Jun 2016
 

Abstract

In the paper, a linearized compact finite difference scheme is presented for the semilinear fractional delay convection-reaction–diffusion equation. Firstly, the equation is transformed into an equivalent semilinear fractional delay reaction–diffusion equation by using a special transformation. Then, the temporal Caputo derivative is discreted by using approximation and the second-order spatial derivative is approximated by the compact finite difference scheme. The solvability, unconditional stability, and convergence in the sense of - and - norms are proved rigorously. Finally, numerical examples are carried out extensively to support our theoretical analysis.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by Natural Science Foundation of China [grant number 11501514], [grant number 11471287]; Natural Sciences Foundation of Zhejiang Province [grant number LQ16A010007]; Zhejiang Province Ministry of Education [grant number Y201533134]; Start-up Fund of ZSTU [grant number 11432932611470] and PhD Thesis Innovation Fund of HUST.

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