Abstract
In this paper, we construct a stable finite difference scheme for the generalized non-Fickian time-fractional reaction-diffusion equations with time delay. The proposed difference scheme has second-order accuracy in both space and time directions. The stability and convergence of the difference solutions are proved rigorously in the maximum norm. Three representative models with delay are carried out to verify the effectiveness of our method.
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Funding
This work described in this paper was supported by the Sichuan Science and Technology Program (Grant No. 2020YJ0110), the National Natural Science Foundation of China (Grant No. 11801389), the Sichuan Science and Technology Program (Grants No. 2022JDTD0019), and the National-Local Joint Engineering Laboratory of System Credibility Automatic Verification.
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Ran, M., Feng, Z. A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations. Numer Algor 93, 993–1012 (2023). https://doi.org/10.1007/s11075-022-01450-4
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DOI: https://doi.org/10.1007/s11075-022-01450-4
Keywords
- Time-fractional delay differential equations
- Maximum norm error estimate
- Stability
- Convergence
- Numerical simulation