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Axioms
Special Issues
Approximation Theory and Its Applications
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Approximation Theory and Its Applications

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

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 1946

Special Issue Editor

Dr. Filomena Di Tommaso

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Calabria, via P. Bucci cubo 30 A, 87036 Rende (CS), Italy
Interests: theory of approximation; scattered data interpolation

Special Issue Information

Dear Colleagues,

Approximation theory is concerned with the reconstruction of a function from sampled given data. Such kinds of situations occur when dealing with real world problems, such as reconstruction of geological surfaces, image restoration, demographic data fittings and in all the fields that need to treat big data. Many methods have already been proven as effective numerical tools in this area, such as multivariate splines, RBF and finite element methods (FEM). In this Special Issue, we would like to cover the field of scattered data interpolation/approximation, which includes previously mentioned applications and it is a very recent and fast growing research area.

Dr. Filomena Di Tommaso
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

  • Scattered data interpolation and approximation
  • Multivariate interpolation
  • Special functions and orthogonal polynomials
  • Barycentric interpolation
  • Rational approximation
  • Radial Basis Functions
  • Splines

Published Papers (1 paper)

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Research

22 pages, 1505 KiB  
Article
An Efficient Localized Meshless Method Based on the Space–Time Gaussian RBF for High-Dimensional Space Fractional Wave and Damped Equations
by Marzieh Raei and Salvatore Cuomo
Axioms 2021, 10(4), 259; https://doi.org/10.3390/axioms10040259 - 19 Oct 2021
Cited by 2 | Viewed by 1228
Abstract
In this paper, an efficient localized meshless method based on the space–time Gaussian radial basis functions is discussed. We aim to deal with the left Riemann–Liouville space fractional derivative wave and damped wave equation in high-dimensional space. These significant problems as anomalous models [...] Read more.
In this paper, an efficient localized meshless method based on the space–time Gaussian radial basis functions is discussed. We aim to deal with the left Riemann–Liouville space fractional derivative wave and damped wave equation in high-dimensional space. These significant problems as anomalous models could arise in several research fields of science, engineering, and technology. Since an explicit solution to such equations often does not exist, the numerical approach to solve this problem is fascinating. We propose a novel scheme using the space–time radial basis function with advantages in time discretization. Moreover this approach produces the (n + 1)-dimensional spatial-temporal computational domain for n-dimensional problems. Therefore the local feature, as a remarkable and efficient property, leads to a sparse coefficient matrix, which could reduce the computational costs in high-dimensional problems. Some benchmark problems for wave models, both wave and damped, have been considered, highlighting the proposed method performances in terms of accuracy, efficiency, and speed-up. The obtained experimental results show the computational capabilities and advantages of the presented algorithm. Full article
(This article belongs to the Special Issue Approximation Theory and Its Applications)
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