IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1864-d827189.html
   My bibliography  Save this article

Full Hermite Interpolation and Approximation in Topological Fields

Author

Listed:
  • Leonard Dăuş

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 020396 Bucharest, Romania)

  • Ghiocel Groza

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 020396 Bucharest, Romania)

  • Marilena Jianu

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 020396 Bucharest, Romania)

Abstract

By using generalized divided differences, we study the simultaneous interpolation of an m times continuously differentiable function and its derivatives up to a fixed order in a topological field K . If K is a valued field, then simultaneous Hermite interpolation and approximation are considered. Newton interpolating series are used in the case of an infinite number of conditions of interpolation. Applications to the numerical approximation of variational problems, the solution of a functional equation and, in the case of p -adic fields, the representation of solutions of a boundary value problem for an equation of the Fuchsian type illustrate the efficiency of the theoretical results.

Suggested Citation

  • Leonard Dăuş & Ghiocel Groza & Marilena Jianu, 2022. "Full Hermite Interpolation and Approximation in Topological Fields," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1864-:d:827189
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1864/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/11/1864/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mehdi Dehghan & Mehdi Tatari, 2006. "The use of Adomian decomposition method for solving problems in calculus of variations," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-12, June.
    2. Pshtiwan Othman Mohammed & José António Tenreiro Machado & Juan L. G. Guirao & Ravi P. Agarwal, 2021. "Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-18, May.
    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. Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.
    2. Sabermahani, Sedigheh & Ordokhani, Yadollah & Rahimkhani, Parisa, 2023. "Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    4. Kamsing Nonlaopon & Awais Gul Khan & Farah Ameen & Muhammad Uzair Awan & Clemente Cesarano, 2022. "Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    5. Moghadam, Amin Abrishami & Soheili, Ali R. & Bagherzadeh, Amir Saboor, 2022. "Numerical solution of fourth-order BVPs by using Lidstone-collocation method," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    6. Kenzu Abdella & Jeet Trivedi, 2020. "Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation," Mathematics, MDPI, vol. 8(12), pages 1-14, November.

    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:gam:jmathe:v:10:y:2022:i:11:p:1864-:d:827189. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.