IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v484y2025ics0096300324004533.html

Redefined fourth order uniform hyperbolic polynomial B-splines based collocation method for solving advection-diffusion equation

Author

Listed:
  • Palav, Mansi S.
  • Pradhan, Vikas H.

Abstract

In the present paper, uniform hyperbolic polynomial (UHP) B-spline based collocation method is proposed for solving advection-diffusion equation (ADE) numerically. The Von-Neumann's criterion is used to perform stability analysis. It reveals that the proposed scheme is unconditionally stable. The proposed method is implemented on various examples and numerical outcomes which are reported in table. The numerical outcomes are compared with the other methods available in standard literature. The rate of convergence is also calculated numerically which is found to be closed to 2. The numerical investigation reveals that the developed scheme is efficient, accurate and easy to implement. The proposed method is also applied to solve two-dimensional and three-dimensional ADE to demonstrate the efficiency of proposed scheme.

Suggested Citation

  • Palav, Mansi S. & Pradhan, Vikas H., 2025. "Redefined fourth order uniform hyperbolic polynomial B-splines based collocation method for solving advection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 484(C).
    • Handle: RePEc:eee:apmaco:v:484:y:2025:i:c:s0096300324004533
    DOI: 10.1016/j.amc.2024.128992
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324004533
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128992?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

    for a different version of it.

    References listed on IDEAS

    as
    1. van Genuchten, M. Th. & Alves, W. J., 1982. "Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation," Technical Bulletins 157268, United States Department of Agriculture, Economic Research Service.
    2. Korkmaz, Alper & Dağ, Idris, 2016. "Quartic and quintic B-spline methods for advection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 208-219.
    3. Tamsir, Mohammad & Srivastava, Vineet K. & Jiwari, Ram, 2016. "An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 111-124.
    4. Dhawan, S. & Bhowmik, Samir Kumar & Kumar, Sheo, 2015. "Galerkin-least square B-spline approach toward advection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 128-140.
    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. Lin, Ji & Reutskiy, Sergiy, 2020. "A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    2. Gurhan Gurarslan, 2021. "Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters," Mathematics, MDPI, vol. 9(9), pages 1-14, May.
    3. Moisés A. C. Lemos & Camilla T. Baran & André L. B. Cavalcante & Ennio M. Palmeira, 2023. "A Semi-Analytical Model of Contaminant Transport in Barrier Systems with Arbitrary Numbers of Layers," Sustainability, MDPI, vol. 15(23), pages 1-18, November.
    4. Chen, Changkai & Zhang, Xiaohua & Liu, Zhang, 2020. "A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of n-dimensional Burgers’ system," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    5. Salah A. Faroughi & Ramin Soltanmohammadi & Pingki Datta & Seyed Kourosh Mahjour & Shirko Faroughi, 2023. "Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media," Mathematics, MDPI, vol. 12(1), pages 1-23, December.
    6. Ricardo Mendonça de Moraes & Luan Carlos de Sena Monteiro Ozelim & André Luís Brasil Cavalcante, 2022. "Generalized Skewed Model for Spatial-Fractional Advective–Dispersive Phenomena," Sustainability, MDPI, vol. 14(7), pages 1-19, March.
    7. Jui-Sheng Chen & Ching-Ping Liang & Cheng-Hung Chang & Ming-Hsien Wan, 2019. "Simulating Three-Dimensional Plume Migration of a Radionuclide Decay Chain through Groundwater," Energies, MDPI, vol. 12(19), pages 1-22, September.
    8. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    9. Tinesh Pathania & T. I. Eldho, 2020. "A Moving Least Squares Based Meshless Element-Free Galerkin Method for the Coupled Simulation of Groundwater Flow and Contaminant Transport in an Aquifer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(15), pages 4773-4794, December.
    10. Kaur, Navneet & Joshi, Varun, 2024. "Kuramoto-Sivashinsky equation: Numerical solution using two quintic B-splines and differential quadrature method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 105-127.
    11. Unknown, 1994. "Proceedings of an international workshop held in Kota Bharu, Kelantan, Malaysia, 24-27 October 1994: Agricultural Impacts on Groundwater Quality," ACIAR Proceedings Series 134721, Australian Centre for International Agricultural Research.
    12. Changbing Yang & Ramón H. Treviño & Susan D. Hovorka & Jesus Delgado‐Alonso, 2015. "Semi‐analytical approach to reactive transport of CO 2 leakage into aquifers at carbon sequestration sites," Greenhouse Gases: Science and Technology, Blackwell Publishing, vol. 5(6), pages 786-801, December.
    13. Richa Rani & Geeta Arora, 2024. "A Comparative Study of PSO and LOOCV for the Numerical Approximation of Sine–Gordon Equation with Exponential Modified Cubic B-Spline DQM," SN Operations Research Forum, Springer, vol. 5(4), pages 1-31, December.
    14. Mohammad Hossein Golestan & Carl Fredrik Berg, 2024. "Simulations of CO 2 Dissolution in Porous Media Using the Volume-of-Fluid Method," Energies, MDPI, vol. 17(3), pages 1-21, January.
    15. Grifka, Jasmin & Nehler, Mathias & Licha, Tobias & Heinze, Thomas, 2023. "Fines migration poses challenge for reservoir-wide chemical stimulation of geothermal carbonate reservoirs," Renewable Energy, Elsevier, vol. 219(P1).
    16. Abhishek Sanskrityayn & Heejun Suk & Jui-Sheng Chen & Eungyu Park, 2021. "Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients," Sustainability, MDPI, vol. 13(14), pages 1-23, July.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:apmaco:v:484:y:2025:i:c:s0096300324004533. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.