Approximation Theory and Related Applications II

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 2098

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Department of Theory of Functions and Methods of Teaching Mathematics, Lesya Ukrainka Volyn National University, 13 Voli Ave., 43025 Lutsk, Ukraine
Interests: function theory; approximation theory
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Special Issue Information

Dear Colleagues,

This issue is a continuation of the previous successful Special Issue “Approximation Theory and Related Applications”.  Thank you for all authors and reviewers. We are glad to announce this Special Issue to collect more works in various aspects of approximation theory.

In this Special Issue, we will cover the field of approximations in special function classes, fractional approximations, approximation operators, approximations of functions of infinitely many variables, numerical analysis, harmonic analysis, spline approximation, stochastic approximation, asymptotic analysis, and applications of approximation theory. Our goal is to gather articles reflecting new trends approximation theory and related topics.

Prof. Dr. Yurii Kharkevych
Guest Editor

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Keywords

  • approximation operators
  • special functions
  • fractional approximation
  • numerical analysis
  • harmonic analysis
  • functional spaces
  • asymptotic analysis
  • extremal problems
  • approximation of solutions of differential and integral equations
  • approximation in the complex plane
  • interpolation
  • spline approximation
  • stochastic approximation

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Published Papers (1 paper)

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Research

11 pages, 312 KiB  
Article
Approximating Multiple Roots of Applied Mathematical Problems Using Iterative Techniques
by Ramandeep Behl, Himani Arora, Eulalia Martínez and Tajinder Singh
Axioms 2023, 12(3), 270; https://doi.org/10.3390/axioms12030270 - 6 Mar 2023
Viewed by 1401
Abstract
In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the nonlinear operator be non-differentiable. So, we present, [...] Read more.
In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the nonlinear operator be non-differentiable. So, we present, in this paper, iterative methods that do not use the derivative of the non-linear operator in their iterative expression. With our new iterative technique, we find better numerical results of Planck’s radiation, Van Der Waals, Beam designing, and Isothermal continuous stirred tank reactor problems. Divided difference and weight function approaches are adopted for the construction of our schemes. The convergence order is studied thoroughly in the Theorems 1 and 2, for the case when multiplicity p2. The obtained numerical results illustrate the preferable outcomes as compared to the existing ones in terms of absolute residual errors, number of iterations, computational order of convergence (COC), and absolute error difference between two consecutive iterations. Full article
(This article belongs to the Special Issue Approximation Theory and Related Applications II)
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