بعض التطبيقات المتقدمة للمعادلات التفاضلية الجزئية في الفيزياء الحديثة: من الأنظمة الكلاسيكية الى الحديثة. (Comprehensive Journal of Science, 2026)
This research paper presents a study of some advanced application of partial differential equations (PDEs) in modeling physics. The conclusion of this research is that PDES are the cornerstone of physical systems across multiple scales, and at explores some advanced applications of PDES in classical field theory, quantum mechanics, and relativistic physics. We analyze the heat equation as a prototype for diffusion processes, the wave equation for electromagnetic radiation, and the Schrodinger equation for quantum dynamics. Novel contributions include a comparative analysis of numerical methods for solving nonlinear PDEs and a discussion of their implications for emerging technologies. The results highlight the predictive power of PDE-based modeling and its critical role in theoretical and applied physics.
Keywords: Partial Differential Equations, Heat Equation, Wave Equations and Electromagnetism, Numerical Methods, Schrodinger equation