Applications of the Anuj Integral Transform in Physical Systems

الملخص

The derivation of analytical solutions to differential equations is paramount for comprehending the dynamic characteristics of intricate physical systems. This research examines the utilization of the Anuj Integral Transform as a mathematical framework for addressing a variety of interdisciplinary challenges, encompassing damped mechanical oscillations, sequential radioactive decay phenomena, and transient behaviors in RLC electrical circuits. The methodology emphasizes the transformation of linear ordinary differential equations into algebraic representations that facilitate the direct integration of initial conditions while simultaneously minimizing intermediate computational intricacies. The results attained align with traditional analytical solutions and Laplace-based methodologies, thereby substantiating the mathematical legitimacy of the proposed approach. Furthermore, the study elucidates that the Anuj transform provides enhanced algebraic simplicity and computational efficacy, particularly in the context of coupled systems and higher-order differential equations. These conclusions imply that the Anuj Integral Transform may function as a dependable analytical instrument for the modeling of stability and transient dynamics in diverse physical systems.