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Axioms
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The Numerical Analysis and Its Application
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The Numerical Analysis and Its Application

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

Deadline for manuscript submissions: 29 August 2024 | Viewed by 1981

Special Issue Editor

Dr. Janis Bajars

E-Mail Website
Guest Editor
Faculty of Physics, Mathematics and Optometry, University of Latvia, Rīga, Latvia
Interests: numerical methods for differential and integral equations; dynamical systems; crystal lattice models; wave phenomena; data-driven algorithms

Special Issue Information

Dear Colleagues,

The value of applied numerical analysis and the power of computational modelling of real-life phenomena cannot be understated. The applications range from the computer, physical, life, and social sciences to engineering and emerging technologies. Further research in advancing applied and computational mathematics is indispensable for resolving real-life, engineering, technological, and scientific problems.

This Special Issue is dedicated to illustrating the numerical analysis and development of novel computational techniques and algorithms advancing diverse applications of mathematical modelling, theoretical physics, dynamical systems, differential and integral equations, optimization methods, structure-preserving methods, learning algorithms, and data-driven methods, but is not limited to these research fields only. With this Special Issue, we aim to appraise either the improvements of existing computational methods or demonstrate new algorithmic and computational methodologies, including learning and data-driven methods. For this Special Issue, theoretical and applied contributions with extensive numerical studies for different applications are welcome. Contributions demonstrating improved analytical results and computational efficiency of already existing or new algorithms as well as the discovery of new phenomena driven by the development of numerical algorithms are of particular interest.

Dr. Janis Bajars
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

  • applied numerical analysis
  • computational mathematics
  • numerical methods for differential and integral equations
  • geometric numerical integration
  • data-driven dynamical systems
  • physics-informed learning
  • optimization techniques in mathematical modelling

Published Papers (3 papers)

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Research

19 pages, 1790 KiB  
Article
Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems
by Bo Yu, Ning Dong and Baiquan Hu
Axioms 2024, 13(4), 249; https://doi.org/10.3390/axioms13040249 - 10 Apr 2024
Viewed by 356
Abstract
Consider a class of coupled Stein equations arising from jump control systems. An operator Smith algorithm is proposed for calculating the solution of the system. Convergence of the algorithm is established under certain conditions. For large-scale systems, the operator Smith algorithm is extended [...] Read more.
Consider a class of coupled Stein equations arising from jump control systems. An operator Smith algorithm is proposed for calculating the solution of the system. Convergence of the algorithm is established under certain conditions. For large-scale systems, the operator Smith algorithm is extended to a low-rank structured format, and the error of the algorithm is analyzed. Numerical experiments demonstrate that the operator Smith iteration outperforms existing linearly convergent iterative methods in terms of computation time and accuracy. The low-rank structured iterative format is highly effective in approximating the solutions of large-scale structured problems. Full article
(This article belongs to the Special Issue The Numerical Analysis and Its Application)
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14 pages, 1500 KiB  
Article
Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method
by K. A. Alzahrani, N. A. Alzaid, H. O. Bakodah and M. H. Almazmumy
Axioms 2024, 13(4), 248; https://doi.org/10.3390/axioms13040248 - 09 Apr 2024
Viewed by 384
Abstract
The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian [...] Read more.
The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian decomposition method. The approach starts by transforming the governing BVP into two appropriate initial-value problems, and thereafter, solves the resulting IVPs recurrently. In addition, the application of this method to varied test models remains feasible—of course, this is supported by the competing Runge–Kutta method, among others, and reported through comparison plots and tables. Full article
(This article belongs to the Special Issue The Numerical Analysis and Its Application)
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16 pages, 437 KiB  
Article
A Reliable Combination of Double Laplace Transform and Homotopy Analysis Method for Solving a Singular Nonlocal Problem with Bessel Operator
by Said Mesloub, Hassan Eltayeb Gadain and Imed Bachar
Axioms 2023, 12(10), 933; https://doi.org/10.3390/axioms12100933 - 29 Sep 2023
Viewed by 573
Abstract
In this article, we present a numerical iterative scheme for solving a non-local singular initial-boundary value problem by combining two well known efficient methods. Namely, the homotopy analysis method and the double Laplace transform method. The resulting scheme is tested on a set [...] Read more.
In this article, we present a numerical iterative scheme for solving a non-local singular initial-boundary value problem by combining two well known efficient methods. Namely, the homotopy analysis method and the double Laplace transform method. The resulting scheme is tested on a set of test examples to illustrate its efficiency, it generates the exact analytical solution for each one of these examples. The convergence of the resulting numerical solutions of these examples is tested both graphically and numerically. Full article
(This article belongs to the Special Issue The Numerical Analysis and Its Application)
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