ANALYSIS OF LANE-EMDEN EQUATION BY USING NONSTANDARD FINITE DIFFERENCE METHODS
Department of Studies in Mathematics, University of Mysore, Mysuru, India.
CHANDRALI BAISHYA *
Department of Studies and Research in Mathematics, Tumkur University, Tumkur -572103, Karnataka, India.
*Author to whom correspondence should be addressed.
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, pade approximant, stability, nonstandard finite difference method