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Peer-reviewedCC BY 4.0Axioms

Corrected L1 Scheme for the Fractional Subdiffusion Equation

  • Marian Milev1
  • Radka Koleva2
  • Yuri Dimitrov3,4
  • Mehran Paziresh5
5 affiliations
  1. 1Faculty of Economics and Business Administration, Sofia University, 1504 Sofia, Bulgaria
  2. 2Department of Mathematics, Physics and Chemistry, Faculty of Mechanical Engineering, Plovdiv Branch of Technical University of Sofia, 4000 Plovdiv, Bulgaria
  3. 3Department of Mathematics, Physics and Informatics, University of Forestry, 1756 Sofia, Bulgaria
  4. 4Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
  5. 5Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51656-98513, Iran
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Abstract

In this paper, a second-order implicit difference scheme for the time-fractional subdiffusion equation is constructed using a corrected L1 approximation of the fractional derivative. Estimates for the generating functions and resolvent coefficients are derived and used to establish the stability and convergence of the scheme. Numerical results are consistent with the theoretical error estimates and confirm the second-order accuracy of the scheme.

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Cite

BibTeXRIS
BibTeX
@article{milev2026corrected,
  title = {{Corrected L1 Scheme for the Fractional Subdiffusion Equation}},
  author = {Marian Milev and Radka Koleva and Yuri Dimitrov and Mehran Paziresh},
  journal = {Axioms},
  year = {2026},
  month = nov,
  doi = {10.3390/axioms15110813},
  url = {https://www.mdpi.com/2075-1680/15/11/813},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Corrected L1 Scheme for the Fractional Subdiffusion Equation
AU  - Marian Milev
AU  - Radka Koleva
AU  - Yuri Dimitrov
AU  - Mehran Paziresh
PY  - 2026
DA  - 2026/11/02
JO  - Axioms
DO  - 10.3390/axioms15110813
UR  - https://www.mdpi.com/2075-1680/15/11/813
AB  - In this paper, a second-order implicit difference scheme for the time-fractional subdiffusion equation is constructed using a corrected L1 approximation of the fractional derivative. Estimates for the generating functions and resolvent coefficients are derived and used to establish the stability and convergence of the scheme. Numerical results are consistent with the theoretical error estimates and confirm the second-order accuracy of the scheme.
SN  - 2075-1680
ER  -