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

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.