Abstract:
This study delved into the practical application and simulation of oscillatory differential equations in the context of objects in motion. The methodology employed power series polynomials, ensuring that the fundamental properties of these functions were met. The new approach was applied to a range of oscillatory differential equations, including those related to harmonic motion, spring motion, dynamic mass motion, Betiss and Stiefel equations, and nonlinear differential equations. It has been shown to be computationally reliable, delivering improved accuracy and quicker convergence compared to the existing methods under consideration.
Description:
Many physical problems remain unexplored and not yet fully addressed by researchers. While some problems in the fields of science, social science, and technology have been approached, many others remain uncharted territory. Oscillatory phenomena often play a key role in these areas, and one of the primary tools for modeling such oscillations is through the use of differential equations.
