IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v197y2022icp308-326.html
   My bibliography  Save this article

Accuracy of the Laplace transform method for linear neutral delay differential equations

Author

Listed:
  • Kerr, Gilbert
  • González-Parra, Gilberto

Abstract

In this paper, we study and solve linear neutral delay differential equations. We investigate the reliability and accuracy of applying the Laplace transform to obtain the solutions of linear neutral delay differential equations. These types of equations are more difficult to solve because the time delay appears in the derivative of the state variable. We rely on computer algebra and numerical methods to determine the poles which are required for computing the inverse Laplace transform. The form of the resulting solution is a non-harmonic Fourier series. A sufficient degree of accuracy can often be achieved by using a relatively small number of terms in the associated truncated series. We compare these solutions with the solutions obtained by the classical method of steps and numerical solutions obtained by the discretization of the linear delay differential equations. It is shown that the Laplace transform method provides very reliable and accurate solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:308-326
    DOI: 10.1016/j.matcom.2022.02.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422000702
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.02.017?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. Higinio Ramos & Osama Moaaz & Ali Muhib & Jan Awrejcewicz, 2021. "More Effective Results for Testing Oscillation of Non-Canonical Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(10), pages 1-10, May.
    2. 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.
    3. Li, Jing & Sun, Gui-Quan & Jin, Zhen, 2014. "Pattern formation of an epidemic model with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 100-109.
    4. Jornet, Marc, 2021. "Exact solution to a multidimensional wave equation with delay," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    5. Xu, Rui, 2012. "Global dynamics of an SEIS epidemiological model with time delay describing a latent period," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 90-102.
    6. Juan Carlos Cortés & Marc Jornet, 2020. "L p -Solution to the Random Linear Delay Differential Equation with a Stochastic Forcing Term," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    7. Fabiano, R.H. & Payne, Catherine, 2018. "Spline approximation for systems of linear neutral delay-differential equations," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 789-808.
    8. Jamilla, Cristeta & Mendoza, Renier & Mező, István, 2020. "Solutions of neutral delay differential equations using a generalized Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    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. Khalili Golmankhaneh, Alireza & Tejado, Inés & Sevli, Hamdullah & Valdés, Juan E. Nápoles, 2023. "On initial value problems of fractal delay equations," Applied Mathematics and Computation, Elsevier, vol. 449(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. 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. Huang, He & Chen, Yahong & Ma, Yefeng, 2021. "Modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    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. Wang, Xiuping & Gao, Fuzheng & Liu, Yang & Sun, Zhengjia, 2020. "A Weak Galerkin Finite Element Method for High Dimensional Time-fractional Diffusion Equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.
    6. Nian, Fuzhong & Hu, Chasheng & Yao, Shuanglong & Wang, Longjing & Wang, Xingyuan, 2018. "An immunization based on node activity," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 228-233.
    7. Wang, Yi & Cao, Jinde & Sun, Gui-Quan & Li, Jing, 2014. "Effect of time delay on pattern dynamics in a spatial epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 137-148.
    8. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.
    9. Vsevolod G. Sorokin & Andrei V. Vyazmin, 2022. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration," Mathematics, MDPI, vol. 10(11), pages 1-39, May.
    10. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    11. Zheng, Qianqian & Shen, Jianwei & Pandey, Vikas & Guan, Linan & Guo, Yantao, 2023. "Turing instability in a network-organized epidemic model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Sabermahani, Sedigheh & Ordokhani, Yadollah, 2021. "General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    13. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    14. Li, Hong-Li & Zhang, Long & Teng, Zhidong & Jiang, Yao-Lin & Muhammadhaji, Ahmadjan, 2018. "Global stability of an SI epidemic model with feedback controls in a patchy environment," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 372-384.
    15. Jamilla, Cristeta & Mendoza, Renier & Mező, István, 2020. "Solutions of neutral delay differential equations using a generalized Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    16. Liu, Pan-Ping, 2015. "Periodic solutions in an epidemic model with diffusion and delay," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 275-291.
    17. Julio C. Miranda & Abraham J. Arenas & Gilberto González-Parra & Luis Miguel Villada, 2024. "Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay," Mathematics, MDPI, vol. 12(5), pages 1-36, February.
    18. Jian, Huan-Yan & Huang, Ting-Zhu & Ostermann, Alexander & Gu, Xian-Ming & Zhao, Yong-Liang, 2021. "Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods," Applied Mathematics and Computation, Elsevier, vol. 408(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:matcom:v:197:y:2022:i:c:p:308-326. 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/mathematics-and-computers-in-simulation/ .

    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.