IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v325y2018icp146-158.html
   My bibliography  Save this article

Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation

Author

Listed:
  • Hajipour, Mojtaba
  • Jajarmi, Amin
  • Malek, Alaeddin
  • Baleanu, Dumitru

Abstract

This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscillations close to non-smooth points. In order to admit large time steps, a class of implicit Runge–Kutta methods is used for the temporal discretization. The implicit parts of these methods are linearized in time by using the local Taylor expansion of the flux. The stability analysis of the semi-implicit WENO scheme with 3-stages form is provided. Finally, some comparative results for one-, two- and three-dimensional PDEs are included to illustrate the effectiveness of the proposed approach.

Suggested Citation

  • Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:146-158
    DOI: 10.1016/j.amc.2017.12.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317308858
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.12.026?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. Feng, Hui & Huang, Cong & Wang, Rong, 2014. "An improved mapped weighted essentially non-oscillatory scheme," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 453-468.
    2. Huang, Cong, 2016. "WENO scheme with new smoothness indicator for Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 21-32.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D.G. & Gao, Wei & Yel, Gulnur, 2020. "Regarding new numerical solution of fractional Schistosomiasis disease arising in biological phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    3. Mustapha, Umar Tasiu & Qureshi, Sania & Yusuf, Abdullahi & Hincal, Evren, 2020. "Fractional modeling for the spread of Hookworm infection under Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Ahmed, Nauman & Rafiq, Muhammad & Adel, Waleed & Rezazadeh, Hadi & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2020. "Structure Preserving Numerical Analysis of HIV and CD4+T-Cells Reaction Diffusion Model in Two Space Dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    6. Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Lu, Dianchen, 2020. "Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    7. Khan, Aziz & Abdeljawad, Thabet & Gómez-Aguilar, J.F. & Khan, Hasib, 2020. "Dynamical study of fractional order mutualism parasitism food web module," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Sadat, R. & Saleh, R. & Kassem, M. & Mousa, Mohamed M., 2020. "Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Nehad Ali Shah & Ioannis Dassios & Essam R. El-Zahar & Jae Dong Chung, 2022. "An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform," Mathematics, MDPI, vol. 10(5), pages 1-16, March.

    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. Tang, Shujiang & Feng, Yujie & Li, Mingjun, 2022. "Novel weighted essentially non-oscillatory schemes with adaptive weights," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Huang, Cong, 2016. "WENO scheme with new smoothness indicator for Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 21-32.
    3. Ruo Li & Wei Zhong, 2022. "An Improved Component-Wise WENO-NIP Scheme for Euler System," Mathematics, MDPI, vol. 10(20), pages 1-21, October.
    4. Huang, Cong & Chen, Li Li, 2021. "A simple WENO-AO method for solving hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    5. Zhang, Xin & Huang, Lintao & Qin, Xueyu & Qu, Feng & Yan, Chao, 2023. "An efficient finite difference IFWENO-THINC hybrid scheme for capturing discontinuities," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    6. Katta, Kiran K. & Nair, Ramachandran D. & Kumar, Vinod, 2015. "High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 316-327.
    7. Omer Musa & Guoping Huang & Mingsheng Wang, 2020. "A New Smoothness Indicator of Adaptive Order Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws," Mathematics, MDPI, vol. 9(1), pages 1-31, December.
    8. Li, Ruo & Zhong, Wei, 2023. "A robust and efficient component-wise WENO scheme for Euler equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).

    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:325:y:2018:i:c:p:146-158. 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.