IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v197y2022icp396-412.html
   My bibliography  Save this article

Singular over-determined systems of linear differential equations

Author

Listed:
  • Dassios, Ioannis
  • Tzounas, Georgios
  • Liu, Muyang
  • Milano, Federico

Abstract

We study a class of singular over-determined systems of differential equations and firstly prove that there exist solutions under certain conditions. For the case of existence we provide closed formulas of solutions and based on the spectrum of the pencil of the system we study uniqueness of solutions. Then, we extend these results to higher order singular overdetermined systems. Finally, we use this type of systems to model electrical power systems and provide numerical examples.

Suggested Citation

  • Dassios, Ioannis & Tzounas, Georgios & Liu, Muyang & Milano, Federico, 2022. "Singular over-determined systems of linear differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 396-412.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:396-412
    DOI: 10.1016/j.matcom.2022.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422000568
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.02.003?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. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    2. Dassios, Ioannis & Tzounas, Georgios & Milano, Federico, 2019. "The Möbius transform effect in singular systems of differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 338-353.
    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. Fernando Ortega & Maria Filomena Barros, 2020. "The Samuelson macroeconomic model as a singular linear matrix difference equation," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 9(1), pages 1-10, December.
    2. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Alijani, Zahra & Baleanu, Dumitru & Shiri, Babak & Wu, Guo-Cheng, 2020. "Spline collocation methods for systems of fuzzy fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Liao, Xiaozhong & Wang, Yong & Yu, Donghui & Lin, Da & Ran, Manjie & Ruan, Pengbo, 2023. "Modeling and analysis of Buck-Boost converter with non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Fabio Tramontana & Laura Gardini, 2021. "Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 10(1), pages 1-15, December.
    6. Dassios, Ioannis & Tzounas, Georgios & Milano, Federico, 2019. "The Möbius transform effect in singular systems of differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 338-353.
    7. Su, Guangwang & Lu, Liang & Tang, Bo & Liu, Zhenhai, 2020. "Quasilinearization technique for solving nonlinear Riemann-Liouville fractional-order problems," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    8. Maria Filomena Barros & Fernando Ortega, 2019. "An optimal equilibrium for a reformulated Samuelson economic discrete time system," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.

    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:396-412. 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.