Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
group
Campus
Daytona Beach
Authors' Class Standing
Jasman Jasmanjot, Senior Bailey Dale Ryan Dick
Lead Presenter's Name
Jasman Jasmanjot
Lead Presenter's College
DB College of Engineering
Faculty Mentor Name
Dr. Hemanta Kunwar
Abstract
The Lane-Emden equation is a differential equation that is often used in astrophysics to describe the distribution of the density inside a star, and by extension, its pressure distribution. Analytic solutions of the Lane-Emden equation can only be found at polytropic indices n = 0,1,5, matching certain physical conditions. For all other polytropic values, a numerical solution is needed. In this work, a comparison between two numerical schemes for solving the Lane-Emden equation is presented, namely the Euler method and the classical 4th order Runge-Kutta method. The accuracy of these models is first compared to the cases with known analytical solutions before being applied to other polytropic indices. With a more accurate description of the pressure distribution inside stars, observed stellar phenomena can be more readily compared to mathematical modeling.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Numerical Analysis and Computation Commons, Stars, Interstellar Medium and the Galaxy Commons
Modeling Stellar Structure: Comparing Numerical Solutions of the Lane-Emden Equation
The Lane-Emden equation is a differential equation that is often used in astrophysics to describe the distribution of the density inside a star, and by extension, its pressure distribution. Analytic solutions of the Lane-Emden equation can only be found at polytropic indices n = 0,1,5, matching certain physical conditions. For all other polytropic values, a numerical solution is needed. In this work, a comparison between two numerical schemes for solving the Lane-Emden equation is presented, namely the Euler method and the classical 4th order Runge-Kutta method. The accuracy of these models is first compared to the cases with known analytical solutions before being applied to other polytropic indices. With a more accurate description of the pressure distribution inside stars, observed stellar phenomena can be more readily compared to mathematical modeling.