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Axioms
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Numerical Analysis and Applied Mathematics, 2nd Edition
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Numerical Analysis and Applied Mathematics, 2nd Edition

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

Deadline for manuscript submissions: 30 July 2026 | Viewed by 1535

Special Issue Editor

Dr. Stoil I. Ivanov

E-Mail Website
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
Special Issues, Collections and Topics in MDPI journals

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 especially welcome.

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 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

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

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Related Special Issue

Published Papers (3 papers)

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Research

63 pages, 788 KB  
Article
From Biased to Unbiased: Theory and Benchmarks for a New Monte Carlo Solver of Fredholm Integral Equations
by Venelin Todorov and Ivan Dimov
Axioms 2026, 15(5), 338; https://doi.org/10.3390/axioms15050338 - 4 May 2026
Viewed by 255
Abstract
We investigate biased and unbiased Monte Carlo algorithms for solving Fredholm integral equations of the second kind and for estimating linear functionals of their solutions. Fredholm integral equations provide a common mathematical framework in uncertainty quantification, Bayesian inference, physics, finance, engineering modeling, telecommunication [...] Read more.
We investigate biased and unbiased Monte Carlo algorithms for solving Fredholm integral equations of the second kind and for estimating linear functionals of their solutions. Fredholm integral equations provide a common mathematical framework in uncertainty quantification, Bayesian inference, physics, finance, engineering modeling, telecommunication systems, signal processing, and other applied problems where system responses depend on distributed, uncertain, or noise-affected inputs. The comparison covers Crude Monte Carlo and Markov Chain Monte Carlo baselines, modified Sobol quasi–Monte Carlo schemes (MSS variants), the classical Unbiased Stochastic Algorithm (USA), and a new variance-controlled unbiased estimator, the Novel Unbiased Stochastic Algorithm (NUSA). NUSA preserves unbiasedness via a randomized-trajectory representation while improving stability through two mechanisms: adaptive absorption control, governed by a parameter Pd that regulates the effective trajectory length, and kernel-weight normalization based on an auxiliary proposal density to curb heavy-tailed weight products. Extensive experiments in one- and multi-dimensional settings (including regular and discontinuous kernels and weak/strong coupling regimes) show that NUSA consistently reduces dispersion and achieves smaller errors than USA under identical sampling budgets. In representative tests, NUSA attains relative errors below 10−3 and improves average accuracy by approximately 30–50% compared with USA, while maintaining near-linear runtime scaling in N and competitive scaling with dimension. Although NUSA is moderately more expensive per run than USA, the variance reduction yields a superior accuracy–cost trade-off, especially near strong-coupling regimes and in higher dimensions where standard unbiased estimators become variance-limited. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics, 2nd Edition)
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10 pages, 245 KB  
Article
A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces
by Takuto Kajimura and Yasunori Kimura
Axioms 2026, 15(4), 276; https://doi.org/10.3390/axioms15040276 - 10 Apr 2026
Viewed by 315
Abstract
In 2024, Kimura proposed the modified shrinking method without assuming the existence of a common fixed point for a family of nonexpansive mappings defined on a complete geodesic space with a nonpositive upper curvature bound. In this paper, we discuss this method for [...] Read more.
In 2024, Kimura proposed the modified shrinking method without assuming the existence of a common fixed point for a family of nonexpansive mappings defined on a complete geodesic space with a nonpositive upper curvature bound. In this paper, we discuss this method for vicinal mappings in an admissible complete geodesic space whose upper curvature bound is an arbitrary real number. Moreover, we investigate the convex minimization problem by using the main result and a resolvent for convex functions. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics, 2nd Edition)
17 pages, 327 KB  
Article
Fixed Point Approximation of Generalized α-Non-Expansive Multi-Valued Mapping in Convex Metric Space
by Tanveer Hussain, Vasile Berinde and Abdul Rahim Khan
Axioms 2026, 15(3), 188; https://doi.org/10.3390/axioms15030188 - 4 Mar 2026
Viewed by 368
Abstract
In this paper, we present approximation results for a generalized α-non-expansive multi-valued mapping using a four-step iteration scheme introduced in the context of a convex metric space. We extend some recent results about generalized α-non-expansive multi-valued mappings from the Banach space [...] Read more.
In this paper, we present approximation results for a generalized α-non-expansive multi-valued mapping using a four-step iteration scheme introduced in the context of a convex metric space. We extend some recent results about generalized α-non-expansive multi-valued mappings from the Banach space setting to a convex metric space. Two examples of generalized α-non-expansive multi-valued mappings are presented, and it is numerically shown that our iteration scheme enables faster convergence than other well-known schemes in the literature. To demonstrate the application of one of our results, we provide the solution of a non-linear integral equation. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics, 2nd Edition)
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