Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 24, Issue.: 3

Original Research Article

ANALYSIS OF LANE-EMDEN EQUATION BY USING NONSTANDARD FINITE DIFFERENCE METHODS

 

R. RANGARAJAN1 AND CHANDRALI BAISHYA2*
1Department of Studies in Mathematics, University of Mysore, Mysuru, India.
2Department of Studies and Research in Mathematics, Tumkur University, Tumkur -572103, Karnataka, India.

Abstracts

In this paper,we construct two nonstandard finite difference schemes viz. nonstandard adomian decomposition method and nonstandard Runge-Kutta fourth order method based on the eigenvalues at the fixed points. Stability of the nonstandard Runge-Kutta fourth order method is analysed with the assistance of Pade approximant. Positivity of the solution is taken into consideration to construct an appropriate nonstandard adomian decomposition method for Lane-Emden equation. A comparative graphical analysis is made among these methods and standard Runge-Kutta fourth order method.

Keywords :

Lane-emden equation; padé approximant; stability; nonstandard finite difference method.