SOLUTION OF LANE-EMDEN TYPE EQUATIONS ARISING IN ASTROPHYSICS BASED ON A HYBRID DISCRETIZATION SCHEME

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Published: 2015-09-14

Page: 201-214


H. R. MARZBAN *

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran

S. M. HOSEINI

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran

*Author to whom correspondence should be addressed.


Abstract

In this paper, a composite Chebyshev nite di erence method for solving nonlinear initial-value problems is successfully implemented. The Lane -Emden type equations which have many applications in mathematical physics and astrophysics are then investigated. They are categorized as singular initial-value problems. The proposed approximation method is based on a hybrid of blockpulse functions and Chebyshev polynomials. Our approach is an extension of Chebyshev nite difference scheme. The nice properties of hybrid functions together with the well-known Chebyshev Gauss-Lobatto points are then used to transform the main problem into a system of nonlinear algebraic equations whose solution is much easier than the original one. The convergence of the method is discussed. Several numerical experiments are examined to show the e ectiveness of the suggested discretization scheme.

Keywords: Hybrid functions, composite chebyshev nite di erence, chebyshev gauss-lobatto points, nonlinear initial-value problems, lane-emden equations


How to Cite

MARZBAN, H. R., & HOSEINI, S. M. (2015). SOLUTION OF LANE-EMDEN TYPE EQUATIONS ARISING IN ASTROPHYSICS BASED ON A HYBRID DISCRETIZATION SCHEME. Asian Journal of Mathematics and Computer Research, 7(3), 201–214. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/406

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