IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v545y2020ics0378437119321077.html

An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions

Author

Listed:
  • Singh, Somveer
  • Devi, Vinita
  • Tohidi, Emran
  • Singh, Vineet Kumar

Abstract

This article provides an efficient matrix approach by using Euler approximation for solving numerically the two-dimensional diffusion and telegraph equations subject to the Dirichlet boundary conditions. First, the main equation is reduced into partial integro-differential equations (PIDEs) and then operational matrices of differentiation and integration of Euler polynomials transform those PIDEs into algebraic generalized Sylvester equations. The inclusion of several test examples confirms the predicted accuracy and effectiveness of the method. Comparison of obtained numerical results is made with some earlier works (Zogheib and Tohidi, 2016, Singh et al., 2018).

Suggested Citation

  • Singh, Somveer & Devi, Vinita & Tohidi, Emran & Singh, Vineet Kumar, 2020. "An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321077
    DOI: 10.1016/j.physa.2019.123784
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119321077
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123784?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. Zogheib, Bashar & Tohidi, Emran, 2016. "A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 1-13.
    2. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
    3. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2016. "Operational matrix approach for the solution of partial integro-differential equation," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 195-207.
    4. Dehghan, Maziar & Rahmani, Yousef & Domiri Ganji, Davood & Saedodin, Seyfollah & Valipour, Mohammad Sadegh & Rashidi, Saman, 2015. "Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: Homotopy perturbation method versus numerical analysis," Renewable Energy, Elsevier, vol. 74(C), pages 448-455.
    5. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar & Tohidi, Emran, 2017. "Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 310-321.
    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. Mohammed M. Al-Shomrani & Mohamed A. Abdelkawy & António M. Lopes, 2023. "Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model," Mathematics, MDPI, vol. 11(9), pages 1-14, April.

    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. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    2. Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2019. "A novel Legendre operational matrix for distributed order fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 215-231.
    4. repec:plo:pone00:0135004 is not listed on IDEAS
    5. Srivastava, Raj Shekhar & Kumar, Anuruddh & Thakur, Harishchandra & Vaish, Rahul, 2022. "Solar assisted thermoelectric cooling/heating system for vehicle cabin during parking: A numerical study," Renewable Energy, Elsevier, vol. 181(C), pages 384-403.
    6. Huu-Quan, Do & Memarian, Amir & Izadi, Mohsen & Shehzad, Sabir Ali, 2020. "Thermal performance and effectiveness of a dual-porous domestic heat exchanger for building heating application," Renewable Energy, Elsevier, vol. 162(C), pages 1874-1889.
    7. M. Momenzadeh & I. Y. Kakangi, 2017. "Approximation Properties of q‐Bernoulli Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2017(1).
    8. Rashidi, Saman & Esfahani, Javad Abolfazli & Rashidi, Abbas, 2017. "A review on the applications of porous materials in solar energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 73(C), pages 1198-1210.
    9. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Siavashi, Majid & Hosseini, Farzad & Talesh Bahrami, Hamid Reza, 2021. "A new design with preheating and layered porous ceramic for hydrogen production through methane steam reforming process," Energy, Elsevier, vol. 231(C).
    11. Neslihan Ozdemir & Aydin Secer & Mustafa Bayram, 2019. "The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative," Mathematics, MDPI, vol. 7(6), pages 1-15, May.
    12. Bashar Zogheib & Emran Tohidi & Stanford Shateyi, 2017. "Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    13. Rahimkhani, Parisa & Abdeljawad, Thabet, 2026. "Application of χ-fractional Genocchi wavelets for solving χ-fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 790-804.
    14. Devi, Vinita & Maurya, Rahul Kumar & Singh, Somveer & Singh, Vineet Kumar, 2020. "Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    15. Azmat Ullah & Suheel Abdullah Malik & Khurram Saleem Alimgeer, 2018. "Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-18, January.
    16. Haifa Bin Jebreen & Fairouz Tchier, 2020. "On the Numerical Simulation of HPDEs Using θ -Weighted Scheme and the Galerkin Method," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    17. Xinyu Xu, 2021. "Application of Image Recognition Algorithm Based on Partial Differential Equation and Wavelet Transform in the Intelligent Linkage System of Government Urban Public Management," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    18. Rashidi, Saman & Kashefi, Mohammad Hossein & Kim, Kyung Chun & Samimi-Abianeh, Omid, 2019. "Potentials of porous materials for energy management in heat exchangers – A comprehensive review," Applied Energy, Elsevier, vol. 243(C), pages 206-232.
    19. Behera, S. & Ray, S. Saha, 2020. "An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    20. Vida Afosaa & Anthony Y. Aidoo & Nicholas Kwasi-Do Ohene Opoku & Joseph Ackora-Prah, 2025. "A Comparative Analysis of Wavelet‐Based Collocation Algorithms for Solving Systems of Fractional Order Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    21. Norouzi, Amir Mohammad & Siavashi, Majid & Ahmadi, Rouhollah & Tahmasbi, Milad, 2021. "Experimental study of a parabolic trough solar collector with rotating absorber tube," Renewable Energy, Elsevier, vol. 168(C), pages 734-749.

    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:phsmap:v:545:y:2020:i:c:s0378437119321077. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.