Numerical Analysis and Applied Mathematics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 4154

Special Issue Editor


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Guest Editor
Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Interests: iterative methods; numerical algorithms; convergence analysis; polynomial zeros; phase transitions
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Special Issue Information

Dear Colleagues,

Numerical analysis and applied mathematics are essential in many areas of modern life. The current growth of computer technologies further impels the fast development of numerical analysis, which, in turn, finds increasing application in applied mathematics, with a strong influence on numerous branches of natural sciences, engineering, finance and industry.

The aim of this Special Issue is to provide an advanced forum for high-value scientific studies in numerical analysis and applied mathematics. In particular, works dedicated to the construction, analysis, real-world application and computer implementation of original numerical algorithms are greatly appreciated.

A limited number of expository and survey articles on the topic will also be considered for publication.

Dr. Stoil I. Ivanov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • numerical algorithms
  • iterative methods
  • convergence analysis
  • numerical stability
  • computational efficiency
  • error analysis
  • operator equations
  • dynamical systems
  • real-world applications

Published Papers (3 papers)

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Research

15 pages, 295 KiB  
Article
High-Order, Accurate Finite Difference Schemes for Fourth-Order Differential Equations
by Allaberen Ashyralyev and Ibrahim Mohammed Ibrahım
Axioms 2024, 13(2), 90; https://doi.org/10.3390/axioms13020090 - 30 Jan 2024
Viewed by 1108
Abstract
This article is devoted to the study of high-order, accurate difference schemes’ numerical solutions of local and non-local problems for ordinary differential equations of the fourth order. Local and non-local problems for ordinary differential equations with constant coefficients can be solved by classical [...] Read more.
This article is devoted to the study of high-order, accurate difference schemes’ numerical solutions of local and non-local problems for ordinary differential equations of the fourth order. Local and non-local problems for ordinary differential equations with constant coefficients can be solved by classical integral transform methods. However, these classical methods can be used simply in the case when the differential equation has constant coefficients. We study fourth-order differential equations with dependent coefficients and their corresponding boundary value problems. Novel compact numerical solutions of high-order, accurate finite difference schemes generated by Taylor’s decomposition on five points have been studied in these problems. Numerical experiments support the theoretical statements for the solution of these difference schemes. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)
25 pages, 2582 KiB  
Article
Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations
by Alicia Cordero, José A. Reyes, Juan R. Torregrosa and María P. Vassileva
Axioms 2024, 13(1), 34; https://doi.org/10.3390/axioms13010034 - 31 Dec 2023
Viewed by 1250
Abstract
In this paper, a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations is presented. After the convergence analysis, a study of the stability of this class is made using the tools of complex discrete dynamics, allowing [...] Read more.
In this paper, a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations is presented. After the convergence analysis, a study of the stability of this class is made using the tools of complex discrete dynamics, allowing those elements of the class with lower dependence on initial estimations to be selected in order to find a very stable subfamily. Numerical tests indicate that the stable members perform better on quadratic polynomials than the unstable ones when applied to other non-polynomial functions. Moreover, the performance of the best elements of the family are compared with known methods, showing robust and stable behaviour. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)
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16 pages, 3260 KiB  
Article
Two Dynamic Remarks on the Chebyshev–Halley Family of Iterative Methods for Solving Nonlinear Equations
by José M. Gutiérrez and Víctor Galilea
Axioms 2023, 12(12), 1114; https://doi.org/10.3390/axioms12121114 - 12 Dec 2023
Viewed by 1062
Abstract
The aim of this paper is to delve into the dynamic study of the well-known Chebyshev–Halley family of iterative methods for solving nonlinear equations. Our objectives are twofold: On the one hand, we are interested in characterizing the existence of extraneous attracting fixed [...] Read more.
The aim of this paper is to delve into the dynamic study of the well-known Chebyshev–Halley family of iterative methods for solving nonlinear equations. Our objectives are twofold: On the one hand, we are interested in characterizing the existence of extraneous attracting fixed points when the methods in the family are applied to polynomial equations. On the other hand, we are also interested in studying the free critical points of the methods in the family, as a previous step to determine the existence of attracting cycles. In both cases, we want to identify situations where the methods in the family have bad behavior from the root-finding point of view. Finally, and joining these two studies, we look for polynomials for which there are methods in the family where these two situations happen simultaneously. The rational map obtained by applying a method in the Chebyshev–Halley family to a polynomial has both super-attracting extraneous fixed points and super-attracting cycles different from the roots of the polynomial. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)
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