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Analysis of L1-difference methods for time-fractional nonlinear parabolic problems with delay

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Abstract
This work is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-difference methods. The analysis of L1 methods for timefractional nonlinear problems with delay is limited mainly due to the lack of a fundamental Gronwall type inequality. We establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative. In terms of the Gronwall type inequality, we will provide error estimates of a fully discrete linearized difference scheme for this kind of problems.
Keywords
time-fractional, parabolic problem, delay, L1-difference scheme, error estimates, Gronwall inequality, linearized schemes

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Chicago
De Staelen, Rob, and Ahmed S. Hendy. 2017. “Analysis of L1-difference Methods for Time-fractional Nonlinear Parabolic Problems with Delay.” In Book of Abstracts of the 7th International Conference on Advanced Computationale Methods in Engineering, ACOMEN 2017.
APA
De Staelen, Rob, & Hendy, A. S. (2017). Analysis of L1-difference methods for time-fractional nonlinear parabolic problems with delay. Book of Abstracts of the 7th International Conference on Advanced Computationale Methods in Engineering, ACOMEN 2017. Presented at the ACOMEN2017.
Vancouver
1.
De Staelen R, Hendy AS. Analysis of L1-difference methods for time-fractional nonlinear parabolic problems with delay. Book of Abstracts of the 7th International Conference on Advanced Computationale Methods in Engineering, ACOMEN 2017. 2017.
MLA
De Staelen, Rob, and Ahmed S. Hendy. “Analysis of L1-difference Methods for Time-fractional Nonlinear Parabolic Problems with Delay.” Book of Abstracts of the 7th International Conference on Advanced Computationale Methods in Engineering, ACOMEN 2017. 2017. Print.
@inproceedings{8534231,
  abstract     = {This work is concerned with numerical solutions of time-fractional nonlinear parabolic
problems by a class of L1-difference methods. The analysis of L1 methods for timefractional
nonlinear problems with delay is limited mainly due to the lack of a fundamental
Gronwall type inequality. We establish such a fundamental inequality for the
L1 approximation to the Caputo fractional derivative. In terms of the Gronwall type inequality,
we will provide error estimates of a fully discrete linearized difference scheme
for this kind of problems.},
  author       = {De Staelen, Rob and Hendy, Ahmed S.},
  booktitle    = {Book of Abstracts of the 7th International Conference on Advanced Computationale Methods in Engineering, ACOMEN 2017},
  keyword      = {time-fractional,parabolic problem,delay,L1-difference scheme,error estimates,Gronwall inequality,linearized schemes},
  language     = {eng},
  location     = {Gent},
  title        = {Analysis of L1-difference methods for time-fractional nonlinear parabolic problems with delay},
  year         = {2017},
}