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