MATHEMATICAL MODELING AND SOLUTION OF PROBLEMS IN ELECTROMAGNETISM
DOI:
https://doi.org/10.17605/Keywords:
Electromagnetism, mathematical modeling, Maxwell’s equations, analytical solution, numerical methods, finite element method, boundary value problem, physical law.Abstract
This article provides a comprehensive analysis of the role and methodology of mathematical modeling in the field of electromagnetism. We explore how physical laws governing electric and magnetic phenomena are translated into mathematical language, leading to the development of analytical and numerical models. The article discusses classical Maxwell’s equations, boundary value problems, common analytical solutions, and the significance of numerical methods such as the finite element and finite difference techniques. Special attention is given to the general importance of accurate modeling in scientific discovery and engineering innovation, as well as the complexity and limitations of real-world applications. The article aims to offer a deep theoretical foundation for students and professionals interested in electromagnetic modeling and to illustrate the power and necessity of mathematics in describing and solving problems of physical reality.
References
1. Jackson, J. D. (2019). Classical Electrodynamics, 3rd Edition. New York: Wiley.
2. Jin, J. (2014). The Finite Element Method in Electromagnetics, 3rd Edition. Hoboken: Wiley.
3. Taflove, A., & Hagness, S. C. (2015). Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Edition. Boston: Artech House.
4. Pendry, J. B. (2020). Negative Refraction Makes a Perfect Lens. Physical Review Letters, 85(18), 3966–3969.
5. Stratton, J. A. (2017). Electromagnetic Theory (Reprint). New York: Wiley-IEEE Press.
