Exploring Numerical Methods: Solving Lane-Emden Type Equations with Padé Approximations

This research explores the effectiveness of using Padé approximations to enhance the
accuracy of numerical solutions for Lane-Emden type differential equations. By applying the
Adomian decomposition method to series solutions derived from previous studies, Padé techniques
are integrated to obtain more precise approximate solutions. The supplied examples demonstrate
that Padé approximations extensively outperform conventional strategies, yielding numerical
results with smaller mistakes and nearer proximity to genuine solutions. Additionally, those
approximations make a contribution to a higher information of the behavior of the studied
structures by providing more stable and comprehensive answers. When in comparison to
conventional answers, Padé approximations show off advanced performance throughout a number
of situations, highlighting the importance of choosing the right numerical approach based on the
nature of the hassle. This approach plays a crucial role in scientific and engineering fields that
require high precision in modeling and analysis. Overall, the research emphasizes that Padé
approximations represent an advanced and reliable option for addressing complex differential
equations, opening new avenues for understanding mathematical and physical phenomena more
effectively.