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Mathematics
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Numerical Analysis and Scientific Computing for Applied Mathematics
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Numerical Analysis and Scientific Computing for Applied Mathematics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 July 2025 | Viewed by 1683

Special Issue Editor

Prof. Dr. Miodrag Spalević

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, 11 000 Belgrade, Serbia
Interests: numerical analysis; approximation theory; scientific computing

Special Issue Information

Dear Colleagues,

Numerical analysis is a natural link between pure mathematics and computer science. The array of problems faced in science and engineering can be tackled via the development of mathematical models that can then be via methods of numerical analysis. Numerical methods used to solve the mentioned models, as well as their applications in mathematics and generally in sciences and technologies, are often the subject of scientific computing. Numerical analysis most commonly finds uses in mathematics and applied mathematics, while scientific computing is an interdisciplinary field with applications in computer science and mathematics, but also in the various engineering and science disciplines.

This Special Issue of Mathematics, entitled “Numerical Analysis and Scientific Computing for Applied Mathematics”, invites the submission of both original research and review papers that bring together new methods of numerical analysis and scientific computing for use in applied mathematics.

Articles can involve theory, algorithms, programming, coding, numerical simulation and/or novel applications of computational techniques to problems in science and engineering. Potential topics of interest include, but are not limited to: approximation theory, methods of numerical linear algebra, numerical methods for solving non-linear equations and systems, methods of numerical differentiation and integration (quadrature and cubature),  optimization methods, finite element methods, finite difference methods, finite volume methods, meshless and particle methods, numerical methods for ordinary and partial differential equations, numerical methods for integral equations, etc., and their applications for solving real problems in areas of science and engineering.

Prof. Dr. Miodrag Spalević
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 analysis
  • scientific computing
  • optimization
  • interpolation
  • approximation
  • orthogonal polynomials
  • rational approximation
  • splines
  • error bound
  • error estimation
  • numerical differentiation
  • quadrature rules
  • cubature rules
  • convergence analysis
  • numerical methods for ordinary differential equations
  • numerical methods for partial differential equations
  • numerical solving of integral equations

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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21 pages, 8636 KiB  
Article
Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks
by Chih-Yu Liu, Cheng-Yu Ku, Wei-Da Chen, Ying-Fan Lin and Jun-Hong Lin
Mathematics 2025, 13(5), 725; https://doi.org/10.3390/math13050725 - 24 Feb 2025
Viewed by 363
Abstract
Conventional methods for solving inverse wave problems struggle with ill-posedness, significant computational demands, and discretization errors. In this study, we propose an innovative framework for solving inverse problems in wave equations by using deep learning techniques with spacetime radial basis functions (RBFs). The [...] Read more.
Conventional methods for solving inverse wave problems struggle with ill-posedness, significant computational demands, and discretization errors. In this study, we propose an innovative framework for solving inverse problems in wave equations by using deep learning techniques with spacetime radial basis functions (RBFs). The proposed method capitalizes on the pattern recognition strength of deep neural networks (DNNs) and the precision of spacetime RBFs in capturing spatiotemporal dynamics. By utilizing initial conditions, boundary data, and radial distances to construct spacetime RBFs, this approach circumvents the need for wave equation discretization. Notably, the model maintains accuracy even with incomplete or noisy boundary data, illustrating its robustness and offering significant advancements over traditional techniques in solving wave equations. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing for Applied Mathematics)
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19 pages, 348 KiB  
Article
Internality of Two-Measure-Based Generalized Gauss Quadrature Rules for Modified Chebyshev Measures II
by Dušan Lj. Djukić, Rada M. Mutavdžić Djukić, Aleksandar V. Pejčev, Lothar Reichel, Miodrag M. Spalević and Stefan M. Spalević
Mathematics 2025, 13(3), 513; https://doi.org/10.3390/math13030513 - 4 Feb 2025
Viewed by 480
Abstract
Gaussian quadrature rules are commonly used to approximate integrals with respect to a non-negative measure dσ^. It is important to be able to estimate the quadrature error in the Gaussian rule used. A common approach to estimating this error is [...] Read more.
Gaussian quadrature rules are commonly used to approximate integrals with respect to a non-negative measure dσ^. It is important to be able to estimate the quadrature error in the Gaussian rule used. A common approach to estimating this error is to evaluate another quadrature rule that has more nodes and higher algebraic degree of precision than the Gaussian rule, and use the difference between this rule and the Gaussian rule as an estimate for the error in the latter. This paper considers the situation when dσ^ is a Chebyshev measure that is modified by a linear factor and a linear divisor, and investigates whether the rules in a recently proposed new class of quadrature rules for estimating the error in Gaussian rules are internal, i.e., if all nodes of the new quadrature rules are in the interval (−1,1). These new rules are defined by two measures, one of which is a modified Chebyshev measure dσ^. The other measure is auxiliary. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing for Applied Mathematics)
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