Advances in Numerical Analysis: Applications of Finite Element Methods, Fractional Differential Equations, and Emerging Computational Techniques

Dear Colleagues,

This Special Issue aims to present the significant advancements in numerical analysis, focusing on finite element methods, fractional differential equations, wavelet methods, epidemic models, and emerging computational techniques. We invite original research articles, comprehensive review papers, and case studies that address the development, application, and interdisciplinary integration of these computational approaches into complex systems.

The objective of this Special Issue is to provide a collaborative platform for researchers and practitioners to exchange ideas, explore new methodologies, and address challenges in the numerical simulations of real-world problems. All submissions will undergo a rigorous peer-review process to ensure academic quality and integrity.

Topics of interest include, but are not limited to, the following:

• Advanced numerical methods for solving ordinary, partial, and fractional differential equations;
• Theoretical and practical applications of finite element methods in modeling complex systems;
• The role of fractional calculus in science, engineering, and applied mathematics;
• Wavelet-based methods and their applications in solving differential equations, signal processing, and image analysis;
• Numerical approaches for epidemic models, including the integration of fractional differential equations to model disease dynamics;
• Emerging computational techniques, such as machine learning, high-performance computing, and optimization methods, applied to numerical simulations;
• Stability analysis, error estimation, and convergence studies of novel algorithms;
• Fractional optimal control problems and their numerical solutions;
• Applications of these methods in biomedical engineering, materials science, environmental modeling, and social dynamics;
• Hybrid approaches that combine classical numerical methods, wavelets, and modern computational tools for efficient solutions.

This Special Issue aims to advance the development of innovative computational frameworks that improve the understanding of complex systems, with a particular focus on epidemic modeling and applied mathematics. It seeks to expand the scope of numerical analysis by incorporating wavelet methods and fractional approaches, offering more accurate and efficient solutions to real-world challenges.

Dr. Ahmed Al-Taweel
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 250 words) can be sent to the Editorial Office for assessment.

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.

• numerical analysis
• numerical simulations
• numerical solutions
• finite element methods
• fractional differential equations
• fractional calculus
• wavelet methods
• epidemic models
• machine learning
• high-performance computing
• stability analysis
• fractional optimal control
• computational techniques
• optimization methods