The zhou’s method for solving the nonlinear lane-emden type equations: a special case (2013)
In this work we apply the differential transformation method (the Zhou’s method) for solving some classes of Lane- Emden type equations as a model for the dimensionless density distribution in an isothermal gas sphere, which are nonlinear ordinary differential equations on the semi-infinite domain, as a special case y′′ + 2 y′ +ey = 0 and y′′ + 2 y′ + e−y = 0. Differential transformation method may be considered as alternative and efficient for finding the approximate solutions of the initial values problems. Superiority of these methods by applying them on the some type Lane-Emden type equations was demonstrated. The power series solution of the reduced equation transforms into an approximate implicit solution of the original equation.