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Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Author

Listed:
  • Archna Kumari

    (Department of Mathematics, SLIET, Longowal 148106, Punjab, India)

  • Vijay K. Kukreja

    (Department of Mathematics, SLIET, Longowal 148106, Punjab, India)

Abstract

With progress on both the theoretical and the computational fronts, the use of Hermite interpolation for mathematical modeling has become an established tool in applied science. This article aims to provide an overview of the most widely used Hermite interpolating polynomials and their implementation in various algorithms to solve different types of differential equations, which have important applications in different areas of science and engineering. The Hermite interpolating polynomials, their generalization, properties, and applications are provided in this article.

Suggested Citation

  • Archna Kumari & Vijay K. Kukreja, 2023. "Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations," Mathematics, MDPI, vol. 11(14), pages 1-28, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3157-:d:1196895
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    References listed on IDEAS

    as
    1. Ishfaq Ahmad Ganaie & Shelly Arora & V. K. Kukreja, 2013. "Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method," International Journal of Differential Equations, Hindawi, vol. 2013, pages 1-7, September.
    2. G. Min, 1996. "On approximation of functions and their derivatives by quasi-Hermite interpolation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-8, January.
    3. Arora, Shelly & Kaur, Inderpreet, 2018. "Applications of Quintic Hermite collocation with time discretization to singularly perturbed problems," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 409-421.
    4. Haifa Bin Jebreen & Ioannis Dassios, 2022. "A Biorthogonal Hermite Cubic Spline Galerkin Method for Solving Fractional Riccati Equation," Mathematics, MDPI, vol. 10(9), pages 1-14, April.
    5. Aatika Yousaf & Thabet Abdeljawad & Muhammad Yaseen & Muhammad Abbas, 2020. "Novel Cubic Trigonometric B-Spline Approach Based on the Hermite Formula for Solving the Convection-Diffusion Equation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-17, October.
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