On the numerical solution of differential equations of Lane-Emden type

Authors:
S. Karimi Vanani;A. Aminataei
Affiliations:
Department of Mathematics, Faculty of Science, K.N. Toosi University of Technology, P.O. Box: 16315-1618, Tehran, Iran;Department of Mathematics, Faculty of Science, K.N. Toosi University of Technology, P.O. Box: 16315-1618, Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 4
Cited 3

A new method for solving singular initial value problems in the second-order ordinary differential equations

Applied Mathematics and Computation
Numerical solutions of chemical differential-algebraic equations

Applied Mathematics and Computation
Numerical Methods for Evolutionary Differential Equations

Numerical Methods for Evolutionary Differential Equations
Approximate solutions of Emden-Fowler type equations

International Journal of Computer Mathematics

A numerical approach for solving the high-order linear singular differential-difference equations

Computers & Mathematics with Applications
An implicit series solution for a boundary value problem modelling a thermal explosion

Mathematical and Computer Modelling: An International Journal
A technique for the numerical solution of initial-value problems based on a class of Birkhoff-type interpolation method

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, a numerical method which produces an approximate polynomial solution is presented for solving Lane-Emden equations as singular initial value problems. Firstly, we use an integral operator (Yousefi (2006) [4]) and convert Lane-Emden equations into integral equations. Then, we convert the acquired integral equation into a power series. Finally, transforming the power series into Pade series form, we obtain an approximate polynomial of arbitrary order for solving Lane-Emden 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.