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Axioms
Special Issues
Applied Mathematics and Numerical Analysis: Theory and Applications, 2nd Edition
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Applied Mathematics and Numerical Analysis: Theory and Applications, 2nd Edition

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 3014

Special Issue Editor

Dr. Avrilia Konguetsof

E-Mail Website
Guest Editor
Department of Civil Engineering, Polytechnic School, Democritus University of Thrace, Kimmeria Campus, 671 00 Xanthi, Greece
Interests: applied mathematics; numerical analysis; numerical solution of differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Numerical analysis is a major branch of mathematics and consists of mathematical approximation techniques and computational methods.

Numerical methods are applied in all fields of engineering, physical sciences, life sciences, social sciences, medicine, business, etc. The main interests of numerical schemes include approximation, simulation, and estimation, and they are used in virtually every scientific field.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following: numerical approaches and solutions to ordinary differential equations (ODEs), partial differential equations (PDEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), numerical stability, interpolation, approximation, quadrature methods, numerical linear algebra, initial and boundary conditions, numerical fractional analyses, optimization, integral equations, iterative methods for solving nonlinear equations and systems, etc., and their applications for solving real problems in the sciences and engineering.

I look forward to receiving your contributions.

Dr. Avrilia Konguetsof
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 250 words) can be sent to the Editorial Office for assessment.

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

  • ordinary differential equations (ODEs)
  • partial differential equations (PDEs)
  • stochastic differential equations (SDEs)
  • delay differential equations (DDEs)
  • differential-algebraic equations (DAEs)
  • integral equations
  • iterative methods
  • fluid dynamics
  • thermodynamics
  • quantum dynamics
  • control theory

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Published Papers (2 papers)

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Research

67 pages, 53787 KB  
Article
A Novel Generalized Time-Stepping Scheme for Time-Fractional Reaction–Diffusion Models Using a New Rational Function Approximation of Mittag-Leffler Functions
by Madushi U. Wickramasinghe and Olaniyi S. Iyiola
Axioms 2026, 15(4), 288; https://doi.org/10.3390/axioms15040288 - 14 Apr 2026
Viewed by 126
Abstract
The Mittag-Leffler function holds significant importance in fractional calculus due to its extensive applications in addressing challenges across science, engineering, biology, hydrology, and earth sciences. Notably, the closed-form solution of a time-fractional model naturally emerges as the Mittag-Leffler function (MLF), necessitating precise and [...] Read more.
The Mittag-Leffler function holds significant importance in fractional calculus due to its extensive applications in addressing challenges across science, engineering, biology, hydrology, and earth sciences. Notably, the closed-form solution of a time-fractional model naturally emerges as the Mittag-Leffler function (MLF), necessitating precise and efficient computations. Consequently, numerical approximations are essential for accurately calculating the Mittag-Leffler function. In this study, we develop a straightforward yet precise real pole rational approximation for the Mittag-Leffler function. We demonstrate first-order convergence and L-acceptability, which aid in mitigating unwanted oscillations. Additionally, we create an effective and precise first-order generalized exponential time differencing scheme to solve the time-fractional reaction–diffusion equations. We obtain and prove the convergence result using Grönwall-type inequality. Several numerical experiments are conducted to confirm the efficiency and accuracy of the proposed numerical scheme compared with exact solutions. The computational efficiency of the proposed method is compared with another existing first-order numerical technique. Furthermore, our proposed scheme is crucial for developing higher-order predictor–corrector schemes for solving time-fractional models. Full article
(This article belongs to the Special Issue Applied Mathematics and Numerical Analysis: Theory and Applications, 2nd Edition)
24 pages, 1811 KB  
Article
Third-Order Nonlinear Neutral Delay Differential Equations with Several Deviating Arguments: Improved Oscillation Criteria
by Asma Al-Jaser, Stefano Serra-Capizzano, Eman Alluqmani and Belgees Qaraad
Axioms 2025, 14(11), 850; https://doi.org/10.3390/axioms14110850 - 18 Nov 2025
Viewed by 569
Abstract
In this paper, we initiate the study of the asymptotic and oscillatory properties of solutions to third-order functional differential equations. Using the Riccati transformation to eliminate the existence of non-oscillatory solutions, we derive various oscillation criteria that address different models of the studied [...] Read more.
In this paper, we initiate the study of the asymptotic and oscillatory properties of solutions to third-order functional differential equations. Using the Riccati transformation to eliminate the existence of non-oscillatory solutions, we derive various oscillation criteria that address different models of the studied equation. Our primary focus is on reducing the constraints imposed on oscillation criteria, thereby broadening their applicability. Our results improve, refine, and extend some of the known findings in previous studies. Several examples are presented to illustrate the significance of the main results. Full article
(This article belongs to the Special Issue Applied Mathematics and Numerical Analysis: Theory and Applications, 2nd Edition)
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