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Symmetry
Special Issues
Advance in Partial Differential Equations of Applied Mathematics
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Advance in Partial Differential Equations of Applied Mathematics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (15 July 2022) | Viewed by 7103

Special Issue Editors

Prof. Dr. Mustafa Bayram

E-Mail Website
Guest Editor
Department of Computer Engineering, Biruni University, Istanbul, Turkey
Interests: differential equations; applied mathematics; computer engineering; computer algebra
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Aydin Secer

E-Mail Website
Guest Editor
Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34010, Turkey
Interests: soliton solutions of Schrödinger equation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

For many years, partial differential equations have been considered an efficient modeling tool in many scientific areas such as space technologies, biology, fluid dynamics, physics, computer sciences, control theory, materials science, thermal science, optics, ocean sciences, and many other engineering branches.

To enhance mathematical models and stimulate new findings in the above areas, many Special Issues have been organized in different journals.

This Special Issue’s aim is to construct and produce some recent applications of partial differential equations in applied mathematics. The scope of this Special Issue covers areas such as analytical methods, numerical methods, and Lie symmetry analysis methods for both partial and ordinary differential equations, including fractional order derivatives.

The manuscripts in this issue will focus on partial differential equations and their applications to solve the problems arising in engineering as well as natural sciences. The papers will address new theoretical improvements and applied results with the help of topics such as operational calculus, differential operators, lie symmetries analysis and lie point symmetries, related methods of wave equations to find soliton solutions, different methods for numerical solutions, recent progress on nonlinear Schrödinger systems, modeling, novel iterative schemes, the iterative methods of linearization, and identifying and using the underlying symmetries of the given nonlinear differential equations.

The guest editors of this issue hope that this collection of papers will be a useful and powerful tool for a large community of researchers and readers.

Please note that all submissions must be within the general scope of the Symmetry journal.

Prof. Dr. Mustafa Bayram
Prof. Dr. Aydin Secer
Guest Editors

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. Symmetry 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

  • nonlinear Schrödinger systems
  • Lie symmetries
  • soliton solutions
  • operational calculus
  • iterative methods
  • novel analytical methods
  • novel numerical methods

Benefits of Publishing in a Special Issue

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
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Further information on MDPI's Special Issue polices can be found here.

Published Papers (2 papers)

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Research

17 pages, 1253 KiB  
Article
An Efficient Red–Black Skewed Modified Accelerated Arithmetic Mean Iterative Method for Solving Two-Dimensional Poisson Equation
by Azali Saudi and A’qilah Ahmad Dahalan
Symmetry 2022, 14(5), 993; https://doi.org/10.3390/sym14050993 - 12 May 2022
Cited by 2 | Viewed by 3399
Abstract
This paper presents the extended variants to the established two-stage Arithmetic Mean (AM) method known as the Modified Accelerated Arithmetic Mean (MAAM) and Skewed Modified Accelerated Arithmetic Mean (SkMAAM) methods to solve the two-dimensional elliptic problem. The existing two-stage AM and its skewed [...] Read more.
This paper presents the extended variants to the established two-stage Arithmetic Mean (AM) method known as the Modified Accelerated Arithmetic Mean (MAAM) and Skewed Modified Accelerated Arithmetic Mean (SkMAAM) methods to solve the two-dimensional elliptic problem. The existing two-stage AM and its skewed variants apply one weighted parameter for the computation of nodes in Levels 1 and 2. The suggested MAAM and SkMAAM methods employ red–black ordering with two different weighted parameters and an additional two distinct accelerated parameters for red and black nodes, respectively. By carefully choosing optimum parameter values, the proposed MAAM and SkMAAM improve the computational execution of the algorithm. With red–black ordering, the computational molecules of red and black nodes are symmetrical, in which the computation of red nodes applies the updated values of their four neighbouring black nodes and vice versa. These symmetrical computational molecules of red and black nodes can be seen for the modified variants MAM and MAAM, and their corresponding skewed variants SkMAM and SkMAAM. The proposed MAAM and SkMAAM methods are compared to the existing AM and Modified AM (MAM) and their corresponding skewed variants, namely the Skewed AM (SkAM) and Skewed MAM (SkMAM) methods. The performance of the newly proposed MAAM and SkMAAM methods is compared against the existing methods in terms of computational complexity and actual execution time. It is shown in the simulation results that the skewed variants are superior to their corresponding regular variants, in which the SkMAAM method gives the best performance. Full article
(This article belongs to the Special Issue Advance in Partial Differential Equations of Applied Mathematics)
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17 pages, 2680 KiB  
Article
Analytical Investigation of Fractional-Order Korteweg–De-Vries-Type Equations under Atangana–Baleanu–Caputo Operator: Modeling Nonlinear Waves in a Plasma and Fluid
by Nehad Ali Shah, Haifa A. Alyousef, Samir A. El-Tantawy, Rasool Shah and Jae Dong Chung
Symmetry 2022, 14(4), 739; https://doi.org/10.3390/sym14040739 - 4 Apr 2022
Cited by 56 | Viewed by 2667
Abstract
This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. This method combines the Zain Ul Abadin Zafar-transform (ZZ-T) and the homotopy perturbation technique (HPT) to show the validation and efficiency of this technique to investigate three [...] Read more.
This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. This method combines the Zain Ul Abadin Zafar-transform (ZZ-T) and the homotopy perturbation technique (HPT) to show the validation and efficiency of this technique to investigate three examples. It is also shown that the fractional and integer-order solutions have closed contact with the exact result. The suggested technique is found to be reliable, efficient, and straightforward to use for many related models of engineering and several branches of science, such as modeling nonlinear waves in different plasma models. Full article
(This article belongs to the Special Issue Advance in Partial Differential Equations of Applied Mathematics)
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