Comparative Study of Padé Approximation Methods in Solving Lane-Emden Type Differential Equations

  • Hayder Ali Abdulsada Alkinani University of Mohaghegh Ardabili Faculty of Mathematical Sciences Department of Mathematics and Applications
Keywords: Lane-Emden Equation, Padé Approximation, Nonlinear Differential Equations, Polytropic Models, Numerical Analysis

Abstract

This study examines how effective Padé approximation methods are for solving Lane-Emden type differential equations. These are special types of equations that are often used in astronomy, like when understanding the structure of some stars and how gases act in round shapes. These equations are hard because there’s an issue at the beginning point and they get more complicated due to the polytropic index. Traditional power series methods usually don't work well beyond a small range because they are only effective within specific limits. Padé approximants are a kind of math tool that can give more accurate estimates. They are effective because they can be used in many different situations and show what happens accurately at places where functions act strangely. In this study, we apply different Padé approximations of different levels to the Lane-Emden equation. They are evaluated based on how correct they are, how fast they find a solution, and how well they use computer resources. Computer simulations are performed, and the results are compared with older techniques, such as the Runge-Kutta method and standard series solutions. The comparison shows that Padé approximants are better because they give accurate results faster over larger areas, especially when the polytropic index goes up. But there are still issues with picking the best orders for the estimates and handling more complicated nonlinear problems. The results show that Padé approximation is a helpful way to understand things while being efficient with computers. This makes it a helpful tool in both ideas and real life, especially when regular methods don’t work well due to unusual situations or high computer expenses.

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Published
2025-05-19
How to Cite
Alkinani, H. A. A. (2025). Comparative Study of Padé Approximation Methods in Solving Lane-Emden Type Differential Equations. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 6(3), 494-505. Retrieved from https://cajmtcs.centralasianstudies.org/index.php/CAJMTCS/article/view/770
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Articles