A numerical approach for solving singular nonlinear Lane–Emden type equations arising in astrophysics

• Published in: New astronomy Vol. 34; pp. 178 - 186
• Main Authors: Kazemi Nasab, A., Kılıçman, A., Pashazadeh Atabakan, Z., Leong, W.J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2015
• Subjects: Chebyshev finite difference method; Isothermal gas spheres; Lane–Emden type equations; Singular IVPs; Wavelet analysis method; Chebyshev finite difference method; Singular IVPs; Lane–Emden type equations; Isothermal gas spheres; Wavelet analysis method
• ISSN: 1384-1076; 1384-1092
• DOI: 10.1016/j.newast.2014.06.008

•To present an efficient method to solve Lane–Emden type equations.•To represent smooth and especially piecewise smooth functions properly.•To improve the accuracy by properly increasing either the number of subintervals or the number of collocation points.•To compare present solutions for more accuracy and efficiency. In this paper, we suggest a numerical method based upon hybrid of Chebyshev wavelets and finite difference methods for solving well-known nonlinear initial-value problems of Lane–Emden type. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of nonlinear algebraic equations. Making a comparison among the obtained results using the present method with those ones reported in literature by some other well-known methods confirms the accuracy and computational efficiency of the present technique.