Best Paper Award

Güldem Yıldız
Nigde Omer Halisdemir University

Güldem Yıldız
Affiliation	Nigde Omer Halisdemir University
Country	Turkey
Article Title	Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model
Scopus ID	55735455100
Article Type	Research Article
Article Views	192
Reference Count	40
Award Category	Best Paper Award
Event	Global Best Achievements Awards
ORCID	0000-0002-8120-3525

Güldem Yıldız of Nigde Omer Halisdemir University, Turkey, is associated with the 2026 research article Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model, published by MDPI. The study concerns the Mathematics subject area and combines an analytical sub-equation technique with a hybrid artificial neural network framework. The supplied publication record reports 192 article views and 40 references. The research is presented in connection with the Best Paper Award category of the Global Best Achievements Awards.

Contents

Abstract
Keywords
Introduction to the Research Topic
Research Profile
Scientific Background
Methodology
Key Findings
Scientific Contributions
Conclusion
External Links
References

Abstract

This article presents the academic recognition of Güldem Yıldız for research on solving the Gardner equation through the Sardar Sub-Equation Method and a hybrid artificial neural network model. The work addresses an analytical and computational treatment of a nonlinear mathematical equation, combining a sub-equation approach with neural-network-based modeling. Such a hybrid framework connects symbolic solution techniques with data-driven approximation, offering a structured basis for examining nonlinear wave equations and related mathematical behavior. The research was published by MDPI in 2026 and is associated with the Mathematics subject area. This page summarizes the researcher, scientific context, methodology, contributions, and recognition academically.

Keywords

Keywords: Gardner equation; Sardar Sub-Equation Method; artificial neural networks; hybrid computational model; nonlinear equations; mathematical physics; analytical solutions; Mathematics.

Introduction to the Research Topic

The Gardner equation is a nonlinear partial differential equation studied in mathematical physics. Analytical methods can provide explicit solution forms, while computational learning approaches can approximate relationships. The reported study combines the Sardar Sub-Equation Method with a hybrid artificial neural network model, linking analytical and computational perspectives in nonlinear research. [1]

Research Profile

Güldem Yıldız is affiliated with Nigde Omer Halisdemir University, Turkey, and is represented in Scopus by Author ID 55735455100 and in ORCID by 0000-0002-8120-3525. The supplied research record identifies Mathematics as the subject area, with six documents, seventeen citations, and an h-index of one at the time of this profile. [2] [3]

Scientific Background

The Gardner equation extends nonlinear wave models by incorporating nonlinear effects, making its solution structure relevant to applied mathematics and mathematical physics. Sub-equation methods seek tractable analytical forms, whereas artificial neural networks provide computational approximation. Combining these perspectives can support comparison between explicit solutions and learned representations for nonlinear research. [1]

Methodology

The approach uses the Sardar Sub-Equation Method to construct analytical solutions of the Gardner equation, followed by a hybrid artificial neural network model computationally. The methodology connects symbolic derivation with numerical or learning-based approximation. The article title establishes this methodological combination, while implementation should be verified in the published article. [1]

Key Findings

The study addresses the Gardner equation through a sub-equation solution method and a hybrid artificial neural network model. This combination indicates an emphasis on complementary analytical and computational treatment rather than one technique. Solution families, numerical results, training procedures, and error measures should be taken directly from the article carefully. [1]

Scientific Contributions

The contribution described by the title is the integration of the Sardar Sub-Equation Method with a hybrid artificial neural network framework for the Gardner equation. This approach connects established analytical solution techniques with computational learning. The work provides context for comparing symbolic formulations and model-based approximations in nonlinear mathematical analysis. [1]

Conclusion

The recognized research focuses on a hybrid treatment of the Gardner equation that combines an analytical sub-equation method with artificial neural network modeling. Its publication in 2026 places the work within current mathematical research. Further assessment of solution accuracy, generalization, and comparative performance requires consultation of the complete published study. [1]

External Links

References

1. MDPI. (2026). Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model. Symmetry.
  https://doi.org/10.3390/sym18091479
2. Elsevier. (n.d.). Scopus author details: Güldem Yıldız, Author ID 55735455100. Scopus.
  https://www.scopus.com/authid/detail.uri?authorId=55735455100
3. ORCID. (n.d.). Güldem Yıldız, ORCID iD 0000-0002-8120-3525. ORCID.
  https://orcid.org/0000-0002-8120-3525

Dr. Guanyu Xue | Mathematics | Best Researcher Award

Dr. Guanyu Xue, Yantai University, China.

Dr. Guanyu Xue is a distinguished researcher in ⚡ computational mathematics and numerical analysis. With a strong academic background and postdoctoral experience, he specializes in domain decomposition methods, explicit iterative schemes, and finite volume element methods. He has published extensively in high-impact journals, contributing groundbreaking research to the field. As a principal investigator, he has secured 🔬 major research grants, advancing innovative mathematical models. His work continues to shape the future of applied mathematics and computational algorithms. 🚀

Professional Profile

Scopus Profile

🎓 Early Academic Pursuits

Dr. Guanyu Xue embarked on his academic journey with a solid foundation in mathematics and computational sciences. He pursued his undergraduate studies from HHT AS (ASI REE, FL) between 2007 and 2011, where he developed a strong interest in numerical analysis and computational methods. He then advanced his studies at FRALA, TRO, FIL, earning his master’s degree between 2011 and 2013, further honing his expertise in applied mathematics and algorithmic research. Dr. Xue completed his doctoral studies at TMA, TRB, FE between 2015 and 2018, where he focused on advanced computational techniques, laying the groundwork for his future research in numerical simulations and domain decomposition methods.

💼 Professional Endeavors

Dr. Xue’s professional career is marked by significant research contributions and academic engagements. His postdoctoral tenure at JER RAHI Ye Sit aS att from 2020 to 2022 provided him with the opportunity to work on innovative computational methods for solving complex differential equations. Following this, he took on a research position at WARS, REWER E SB, UR from 2018 to 2022, where he collaborated with experts in computational sciences. Currently, Dr. Xue is affiliated with MGA, BSR ESS, BBS, continuing his impactful research and mentoring the next generation of scholars.

🔬 Contributions and Research Focus On Mathematics

Dr. Xue’s research primarily revolves around numerical methods for solving differential equations, parallel computing algorithms, and domain decomposition techniques. His work has significantly contributed to computational mathematics, particularly in the development of explicit and implicit schemes for solving convection-dominated diffusion equations and regularized long-wave equations. His studies have advanced numerical simulations by enhancing efficiency and accuracy, benefiting various scientific and engineering applications.

🌍 Impact and Influence

Dr. Xue’s research has had a profound impact on the field of computational mathematics. His innovative methodologies have been widely adopted by researchers and practitioners dealing with large-scale simulations in physics, engineering, and applied sciences. By optimizing computational techniques, he has contributed to improving the accuracy and efficiency of simulations in areas such as fluid dynamics, heat transfer, and wave propagation. His work has also influenced the design of parallel computing algorithms, making them more accessible and effective for real-world applications.

🏅 Awards and Honors

Dr. Xue’s outstanding contributions to computational mathematics have been recognized through several academic honors and awards. His innovative research has earned him funding from prestigious organizations, including the National Natural Science Foundation of China (NSFC), where he has successfully led multiple research projects. His work on high-performance computing and numerical algorithms has also been acknowledged with invitations to present at international conferences and contribute to collaborative research initiatives.

🔍 Legacy and Future Contributions

As a leading researcher in computational mathematics, Dr. Xue continues to push the boundaries of numerical simulations. His future work aims to enhance parallel computing strategies and develop more efficient numerical schemes for multi-dimensional problems. By integrating machine learning with numerical analysis, he envisions a new era of computational techniques that can revolutionize real-world applications in engineering, physics, and climate modeling. His ongoing research is set to inspire future generations of scholars and contribute to the advancement of computational sciences.

Publications Top Notes

“A Samarskii Domain Decomposition Method for Two-Dimensional Convection–Diffusion Equations”

Authors: Guanyu Xue, Yulong Gao

Journal: Computational and Applied Mathematics

Year: 2022

“The Alternating Group Explicit Iterative Method for the Regularized Long-Wave Equation”

Authors: Anqi Xie, Xiaojia Ye, Guanyu Xue

Journal: Journal of Applied Mathematics and Physics

Year: 2024

“An Alternating Segment Explicit-Implicit Scheme with Intrinsic Parallelism for Burgers’ Equation”

Authors: Guanyu Xue, Hui Feng

Journal: Journal of Computational and Theoretical Transport

Year: 2020

“New Parallel Algorithm for Convection-Dominated Diffusion Equation”