IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v409y2021ics0096300321005105.html
   My bibliography  Save this article

Exact solution to a multidimensional wave equation with delay

Author

Listed:
  • Jornet, Marc

Abstract

This paper deals with a mixed problem for the wave equation with discrete delay τ>0,utt(t,x)=a12Δxu(t,x)+a22Δxu(t−τ,x)+b1u(t,x)+b2u(t−τ,x),t>τ,0≤x≤l,with Dirichlet boundary conditions. The exact infinite series solution is constructed by the method of separation of variables, where the time-dependent functions of the decomposition satisfy second-order delay differential equations. Our approach is based on and extends the work by Rodríguez, Roales and Martín (Applied Mathematics and Computation, 2012).

Suggested Citation

  • Jornet, Marc, 2021. "Exact solution to a multidimensional wave equation with delay," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321005105
    DOI: 10.1016/j.amc.2021.126421
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321005105
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126421?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. M. A. Castro & F. Rodríguez & J. Escolano & J. A. Martín, 2013. "Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, December.
    2. Joseph Wiener & Lokenath Debnath, 1992. "A wave equation with discontinuous time delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-8, January.
    3. Joseph Wiener & Lokenath Debnath, 1997. "Boundary value problems for the diffusion equation with piecewise continuous time delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-9, January.
    4. Josef Diblík & Denis Khusainov & Oleksandra Kukharenko & Zdeněk Svoboda, 2012. "Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-27, July.
    5. García, M.A. & Castro, M.A. & Martín, J.A. & Rodríguez, F., 2018. "Exact and nonstandard numerical schemes for linear delay differential models," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 337-345.
    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. Kerr, Gilbert & González-Parra, Gilberto, 2022. "Accuracy of the Laplace transform method for linear neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 308-326.

    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. Kerr, Gilbert & González-Parra, Gilberto & Sherman, Michele, 2022. "A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Sharmin Sultana & Gilberto González-Parra & Abraham J. Arenas, 2023. "Mathematical Modeling of Toxoplasmosis in Cats with Two Time Delays under Environmental Effects," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    3. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    4. Julia Calatayud & Juan Carlos Cortés & Marc Jornet & Francisco Rodríguez, 2020. "Mean Square Convergent Non-Standard Numerical Schemes for Linear Random Differential Equations with Delay," Mathematics, MDPI, vol. 8(9), pages 1-17, August.
    5. María Ángeles Castro & Miguel Antonio García & José Antonio Martín & Francisco Rodríguez, 2019. "Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems," Mathematics, MDPI, vol. 7(11), pages 1-14, November.
    6. Carlos Julio Mayorga & María Ángeles Castro & Antonio Sirvent & Francisco Rodríguez, 2023. "On the Construction of Exact Numerical Schemes for Linear Delay Models," Mathematics, MDPI, vol. 11(8), pages 1-9, April.

    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:409:y:2021:i:c:s0096300321005105. 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.