Deadline Date: 31 March 2026
Differential equations are essential for modeling and analyzing phenomena across the various engineering domains. While traditional analytical methods exist, recent decades have seen significant advancements in semi-analytical and computational methods, making it possible to solve complex, nonlinear, and multi-physics systems that were previously unsolvable. The emergence of hybrid approaches and high-performance computing is transforming how we approach these equations.
This Special Issue aims to be a hub for cutting-edge research on these advanced methods for solving ordinary and partial differential equations. We seek contributions that highlight both foundational developments and real-world, interdisciplinary applications.
By bringing together diverse contributions, the issue will provide a comprehensive overview of modern solution strategies, encouraging the integration of classical theory with modern computational tools. It will also foster collaborations among mathematicians, computational scientists, and applied researchers, offering valuable benchmarks and insights for both theoretical and practical applications across various fields. This collection is unique in its unified focus, exploring the synergy between different solution techniques to advance the field.
Approximate and Semi-Analytical Approaches: These methods provide solutions that are not exact but are highly accurate. They're especially useful for problems where finding an exact solution is impossible.
• Applications: Quantum mechanics (solving the Schrödinger equation for complex systems), fluid dynamics (modeling boundary layers), and engineering (analyzing vibrations in structures).
Numerical and Computational Methods: These involve using algorithms and computers to find approximate solutions to differential equations. They are critical for high-dimensional or non-linear problems.
• Applications: There are various scientific field that require the numerical methods for the analysis of the under phenomenon. For example: climate modeling (predicting weather patterns), pattern formation, and computational biology (simulating protein folding and drug interactions).
Differential equations are essential for modeling and analyzing phenomena across the various engineering domains. While traditional analytical methods exist, recent decades have seen significant advancements in semi-analytical and computational methods, making it possible to solve ... show more
Editorial board
