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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
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    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.
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