IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v361y2019icp583-598.html
   My bibliography  Save this article

Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay

Author

Listed:
  • Sahihi, Hussein
  • Abbasbandy, Saeid
  • Allahviranloo, Tofigh

Abstract

In this paper, Reproducing Kernel Hilbert Space Method (RKHSM) based on collocation scheme is used to solve singularly perturbed second order differential-difference equations. We implement RKHSM without Gram–Schmidt orthogonalization process for singularly perturbed differential-difference equation with boundary layer behavior and also oscillatory behavior with small delay. RKHSM in this study, is based on the division of the problem domain into two subintervals, one with boundary layer and the other one without such a boundary layer. Several numerical examples are studied to demonstrate the accuracy of the present method. Results of the present scheme indicate that new algorithm has the following advantages: small computational work, fast convergence, and high precision.

Suggested Citation

  • Sahihi, Hussein & Abbasbandy, Saeid & Allahviranloo, Tofigh, 2019. "Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 583-598.
  • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:583-598
    DOI: 10.1016/j.amc.2019.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319304758
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2019.06.010?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. Geng, F.Z. & Qian, S.P. & Cui, M.G., 2015. "Improved reproducing kernel method for singularly perturbed differential-difference equations with boundary layer behavior," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 58-63.
    2. Li, Zhi-Yuan & Wang, Yu-Lan & Tan, Fu-Gui & Wan, Xiao-Hui & Yu, Hao & Duan, Jun-Sheng, 2015. "Solving a class of linear nonlocal boundary value problems using the reproducing kernel," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1098-1105.
    3. V. Y. Glizer, 2000. "Asymptotic Solution of a Boundary-Value Problem for Linear Singularly-Perturbed Functional Differential Equations Arising in Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 309-335, August.
    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. Li, X.Y. & Wu, B.Y., 2020. "A new kernel functions based approach for solving 1-D interface problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).

    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. V.Y. Glizer, 2003. "Asymptotic Analysis and Solution of a Finite-Horizon H ∞ Control Problem for Singularly-Perturbed Linear Systems with Small State Delay," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 295-325, May.
    2. Brdar, Mirjana & Franz, Sebastian & Ludwig, Lars & Roos, Hans-Görg, 2023. "A balanced norm error estimation for the time-dependent reaction-diffusion problem with shift in space," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    3. Allahviranloo, Tofigh & Sahihi, Hussein, 2021. "Reproducing kernel method to solve fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    4. Gemechis File Duressa & Imiru Takele Daba & Chernet Tuge Deressa, 2023. "A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    5. Al-Smadi, Mohammed & Arqub, Omar Abu & Shawagfeh, Nabil & Momani, Shaher, 2016. "Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 137-148.
    6. Kumar, Sunil & Kumar, B. V. Rathish, 2017. "A domain decomposition Taylor Galerkin finite element approximation of a parabolic singularly perturbed differential equation," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 508-522.
    7. Chen, Shu-Bo & Soradi-Zeid, Samaneh & Dutta, Hemen & Mesrizadeh, Mehdi & Jahanshahi, Hadi & Chu, Yu-Ming, 2021. "Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(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:361:y:2019:i:c:p:583-598. 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.