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EDITORIAL article

Front. Appl. Math. Stat., 09 August 2021
Sec. Statistical and Computational Physics
This article is part of the Research Topic Analytical and Numerical Methods for Differential Equations and Applications View all 11 articles

Editorial: Analytical and Numerical Methods for Differential Equations and Applications

  • 1University of Salamanca, Salamanca, Spain
  • 2University of Louisiana at Lafayette, Lafayette, LA, United States
  • 3Universidad Politécnica de Cartagena, Cartagena, Spain
  • 4University of Evora, Évora, Portugal

In the last few decades, new mathematical problems and models, described by differential equations, have brought to light applications in many areas including Physics, Chemistry, Engineering, Biomedicine, and Economics, among others.

This research topic shows the large amount of different types of differential equations, thus it contains a selection of papers with recent advances in subjects as different as delay differential equations, nonlinear partial differential equations (PDEs), studied analytically or numerically, or because of their applications, fractional PDEs, and q-differential equations, etc. We would like to thank all the contributors of this issue, and also the referees. They all worked hard to shed some light on these topics for young researchers who would like to investigate some of these areas. Thus, in this research topic, readers can find papers on varying numerical methods and applications.

Delay differential equations (DDEs): During the last few years, there have been many studies on DDEs. A very special type of retarded delay differential equations called fuzzy hybrid retarded equations are studied in [1]. For these equations, numerical schemes based on Runge-Kutta schemes are a good option to obtain accurate solutions.

Recent advances in stochastic or fractional ODEs and PDEs have been published in the last few years. In this special issue, researchers can find two papers on a fractional PDEs model by [2] and [3], solved numerically with different procedures.

Many scientific papers study PDEs, their applications, and also analytical procedures to study their properties. Thus, an analytical solution of the Biswas-Arshed equation is obtained in [4]. This is a non-linear PDE with important applications in physics. In a similar topic, the variable-coefficient Heisenberg ferromagnetic spin chain (vcHFSC) equation is considered in [5]. This equation is also a nonlinear PDEs method, and it can be solved with Lie-algebra groups.

However, many other nonlinear PDEs are transformed into large systems of nonlinear ordinary differential equations (ODEs), where efficient solvers are necessary. In some cases, these PDEs need to be solved in complex geometries, a recent approach is described in [6], where a new procedure to solve nonlinear parabolic PDEs in triangles is explained. But, in other cases, research groups focus their works on the applications of these PDEs such as in [7]. For example, many physical (such as the magneto-hydrodynamics [MHD] problem analyzed in [8]), industrial, or complex economical situations can be modeled by nonlinear PDEs. Chemistry is another very important area; in Awais-Kuman, the authors modelized the peristaltic flow dynamics of (Cu-H2O) nanofluid in a homogeneous porous medium. They solved their model numerically in order to be able to physically interpret how the different parameters that appear in their equation affect the outcome. Another important area of interest is mechanics, thus two papers in this research topic are related with this field: In a study by Alanazi et al. [9], a q-differential problem is solved with applications in Newtonian mechanics and Mushtaq et al. [10] describes a Python solver to solve some important quantum mechanical eigenvalue PDE problems (such as the Schroedinger) in one or more dimensions.

Author Contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

References

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Keywords: ordinary diffeential equations, partial differential equations, delay differential equations, fractional PDEs, applied mathematics

Citation: Martin-Vaquero J, Wade B, García Guirao JL and Minhós F (2021) Editorial: Analytical and Numerical Methods for Differential Equations and Applications. Front. Appl. Math. Stat. 7:712813. doi: 10.3389/fams.2021.712813

Received: 21 May 2021; Accepted: 17 June 2021;
Published: 09 August 2021.

Edited and reviewed by:

José S. Andrade, Federal University of Ceara, Brazil

Copyright © 2021 Martin-Vaquero, Wade, García Guirao and Minhós. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Jesus Martin-Vaquero, amVzbWFydmFAdXNhbC5lcw==

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.