On the numerical solution of differential equations of LaneEmden type
In this paper, a numerical method which produces an approximate polynomial solution is presented for solving LaneEmden equations as singular initial value problems. Firstly, we use an integral operator (Yousefi (2006) [4]) and convert LaneEmden equations into integral equations. Then, we convert the acquired integral equation into a power series. Finally, transforming the power series into Pad series form, we obtain an approximate polynomial of arbitrary order for solving LaneEmden equations. The advantages of using the proposed method are presented. Then, an efficient error estimation for the proposed method is also introduced and finally some experiments and their numerical solutions are given; and comparing between the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method.
laneemden equations power series pad series arbitrary order