Numerical Solution to Singular Ordinary Differential Equations of Lane-Emden type by Legendre collocation method
- DOI
- 10.2991/icmea-16.2016.83How to use a DOI?
- Keywords
- Lane-Emden Equation; Legendre Collocation Method; Approximation Solution.
- Abstract
The purpose of this paper is to propose an efficient numerical method for solving singular ordinary differential equations of Lane-Emden type. The singularity at initial point of the problem leads to failure of many methods such as Euler method, Runge-Kutta method, etc. The proposed method is based on shifted Legendre-Gauss-Radau collocation points and the corresponding interpolation. The first step is to convert second-order ordinary differential equation to an equivalent first order ordinary differential system, and the shifted Legendre-Gauss-Radau points are utilized to collocate the first order ordinary differential system except the initial point. Then computation of the nonlinear initial value problem is reduced to a nonlinear algebraic system. Since evaluation includes no singular point, the difficulty of singularity is overcome. Due to the stability of Gauss-type interpolation, the proposed method possesses high accuracy which is observed by several numerical tests. Also, the method can be done by proceeding in time step by step. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique, and the results have been compared with the exact solution.
- Copyright
- © 2016, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - T. G. Zhao AU - Y. Wu PY - 2016/12 DA - 2016/12 TI - Numerical Solution to Singular Ordinary Differential Equations of Lane-Emden type by Legendre collocation method BT - Proceedings of the 3rd International Conference on Material Engineering and Application (ICMEA 2016) PB - Atlantis Press SP - 496 EP - 501 SN - 2352-5401 UR - https://doi.org/10.2991/icmea-16.2016.83 DO - 10.2991/icmea-16.2016.83 ID - Zhao2016/12 ER -