IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v258y2015icp49-59.html
   My bibliography  Save this article

Numerical oscillation of neutral logistic delay differential equation

Author

Listed:
  • Wang, Qi

Abstract

This paper mainly deals with the oscillation of numerical solution for the neutral logistic delay differential equation. Applying the θ-methods to the simplified type of the original equation which is got through an invariant oscillation transformation. It is proven that every non-oscillatory numerical solution tends to the steady state of the model. Moreover, some conditions under which the numerical solution oscillates are obtained. Finally, to demonstrate our theoretical results, some numerical examples are adopted.

Suggested Citation

  • Wang, Qi, 2015. "Numerical oscillation of neutral logistic delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 49-59.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:49-59
    DOI: 10.1016/j.amc.2015.01.113
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315001459
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.01.113?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. Vijayakumar, V. & Selvakumar, A. & Murugesu, R., 2014. "Controllability for a class of fractional neutral integro-differential equations with unbounded delay," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 303-312.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    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. Tan, Zengqiang & Zhang, Chengjian, 2022. "Numerical approximation to semi-linear stiff neutral equations via implicit–explicit general linear methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 68-87.
    2. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Qin, Hongyu & Zhang, Qifeng & Wan, Shaohua, 2019. "The continuous Galerkin finite element methods for linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 76-85.
    4. Hamdy M. Ahmed & Mahmoud M. El-Borai & Hassan M. El-Owaidy & Ahmed S. Ghanem, 2019. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    5. Qin, Tingting & Zhang, Chengjian, 2015. "Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 47-57.
    6. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    7. Xu, Y. & Zhao, J.J., 2008. "Stability of Runge–Kutta methods for neutral delay-integro-differential-algebraic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 571-583.
    8. Amat, Sergio & José Legaz, M. & Pedregal, Pablo, 2015. "A variable step-size implementation of a variational method for stiff differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 49-57.
    9. Cheng, Xue & Chen, Zhong & Zhang, Qingpu, 2015. "An approximate solution for a neutral functional–differential equation with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 27-34.
    10. Zhang, Chengjian & Chen, Hao, 2010. "Asymptotic stability of block boundary value methods for delay differential-algebraic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 100-108.
    11. 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.
    12. M. Motawi Khashan & Rohul Amin & Muhammed I. Syam, 2019. "A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    13. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    14. Tan, Zengqiang & Zhang, Chengjian, 2018. "Implicit-explicit one-leg methods for nonlinear stiff neutral equations," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 196-210.
    15. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    16. Zhao, Jingjun & Zhan, Rui & Xu, Yang, 2018. "D-convergence and conditional GDN-stability of exponential Runge–Kutta methods for semilinear delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 45-58.
    17. Bürger, Raimund & Ruiz-Baier, Ricardo & Tian, Canrong, 2017. "Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 28-52.
    18. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
    19. V. Subburayan & N. Ramanujam, 2013. "An Initial Value Technique for Singularly Perturbed Convection–Diffusion Problems with a Negative Shift," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 234-250, July.
    20. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(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:258:y:2015:i:c:p:49-59. 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.