IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923006410.html
   My bibliography  Save this article

Analysis of the absorbing boundary conditions for anomalous diffusion in comb model with Cattaneo model in an unbounded region

Author

Listed:
  • Liu, Lin
  • Chen, Siyu
  • Bao, Chunxu
  • Feng, Libo
  • Zheng, Liancun
  • Zhu, Jing
  • Zhang, Jiangshan

Abstract

A fractional governing equation is derived from the two-dimensional anomalous diffusion in the comb model with the Cattaneo model by using rigorous derivation. One strategy to deal with the unbounded region is to create acceptable truncation. We abandon the traditional method of approximating infinite boundaries by enormous value and use the artificial boundary method to construct absorbing boundary conditions using the Laplace transform. The absorbing boundary conditions with the Mittag-Leffler function are obtained, and the stability is demonstrated. We discretise the governing equation by using the finite difference method, and the accuracy of the numerical method is confirmed by comparing with the exact solution, which is generated by introducing a source term. The particle distributions and the mean square displacement under the absorbing boundary conditions are in good agreement with the exact expressions which are superior to the conventional direct truncation boundary conditions. Additionally, the particle distributions under different parameters are examined and explained graphically.

Suggested Citation

  • Liu, Lin & Chen, Siyu & Bao, Chunxu & Feng, Libo & Zheng, Liancun & Zhu, Jing & Zhang, Jiangshan, 2023. "Analysis of the absorbing boundary conditions for anomalous diffusion in comb model with Cattaneo model in an unbounded region," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923006410
    DOI: 10.1016/j.chaos.2023.113740
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923006410
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113740?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Méndez, Vicenç & Iomin, Alexander, 2013. "Comb-like models for transport along spiny dendrites," Chaos, Solitons & Fractals, Elsevier, vol. 53(C), pages 46-51.
    2. Sandev, Trifce & Schulz, Alexander & Kantz, Holger & Iomin, Alexander, 2018. "Heterogeneous diffusion in comb and fractal grid structures," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 551-555.
    3. Iomin, A., 2020. "Quantum dynamics and relaxation in comb turbulent diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Iomin, A., 2021. "Anomalous diffusion in umbrella comb," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Iomin, A. & Zaburdaev, V. & Pfohl, T., 2016. "Reaction front propagation of actin polymerization in a comb-reaction system," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 115-122.
    6. Suleiman, Kheder & Song, Qixuan & Zhang, Xuelan & Liu, Shengna & Zheng, Liancun, 2022. "Anomalous diffusion in a circular comb with external velocity field," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    7. Qi, Haitao & Jiang, Xiaoyun, 2011. "Solutions of the space-time fractional Cattaneo diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1876-1883.
    8. Wang, Zhaoyang & Lin, Ping & Wang, Erhui, 2021. "Modeling multiple anomalous diffusion behaviors on comb-like structures," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    9. Dzhanoev, A.R. & Sokolov, I.M., 2018. "The effect of the junction model on the anomalous diffusion in the 3D comb structure," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 330-336.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Khalili Golmankhaneh, Alireza & Ontiveros, Lilián Aurora Ochoa, 2023. "Fractal calculus approach to diffusion on fractal combs," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Trifce Sandev & Viktor Domazetoski & Alexander Iomin & Ljupco Kocarev, 2021. "Diffusion–Advection Equations on a Comb: Resetting and Random Search," Mathematics, MDPI, vol. 9(3), pages 1-24, January.
    3. Wang, Zhaoyang & Zheng, Liancun, 2020. "Anomalous diffusion in inclined comb-branch structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    4. Wang, Zhaoyang & Lin, Ping & Wang, Erhui, 2021. "Modeling multiple anomalous diffusion behaviors on comb-like structures," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    5. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    6. Dzhanoev, A.R. & Sokolov, I.M., 2018. "The effect of the junction model on the anomalous diffusion in the 3D comb structure," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 330-336.
    7. Awad, Emad, 2019. "On the time-fractional Cattaneo equation of distributed order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 210-233.
    8. Guo, Wei & Liu, Ying-Zhou & Huang, Fei-Jie & Shi, Hong-Da & Du, Lu-Chun, 2023. "Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. Suleiman, Kheder & Song, Qixuan & Zhang, Xuelan & Liu, Shengna & Zheng, Liancun, 2022. "Anomalous diffusion in a circular comb with external velocity field," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    11. Iomin, Alexander, 2023. "Fractional Floquet theory," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Wang, Feifei & Chen, Diyi & Xu, Beibei & Zhang, Hao, 2016. "Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 329-338.
    13. Tawfik, Ashraf M. & Elkamash, I.S., 2022. "On the correlation between Kappa and Lévy stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    14. Alexander Iomin, 2023. "Floquet Theory of Classical Relaxation in Time-Dependent Field," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    15. Liu, Zhengguang & Cheng, Aijie & Li, Xiaoli, 2017. "A second order Crank–Nicolson scheme for fractional Cattaneo equation based on new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 361-374.
    16. Mishra, T.N. & Rai, K.N., 2016. "Numerical solution of FSPL heat conduction equation for analysis of thermal propagation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1006-1017.
    17. Tawfik, Ashraf M. & Fichtner, Horst & Elhanbaly, A. & Schlickeiser, Reinhard, 2018. "Analytical solution of the space–time fractional hyperdiffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 178-187.
    18. Kostrobij, P.P. & Markovych, B.M. & Viznovych, O.V. & Tokarchuk, M.V., 2019. "Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 63-70.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923006410. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.