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Chebyshev Operational Matrix Method for Lane-Emden Problem

2018; De Gruyter; Volume: 8; Issue: 1 Linguagem: Inglês

10.1515/nleng-2017-0157

2192-8010

Bhuvnesh Sharma, Sunil Kumar, Manikant Paswan, Dindayal Mahato,

Matrix Theory and Algorithms

Abstract In the this paper, a new modified method is proposed for solving linear and nonlinear Lane-Emden type equations using first kind Chebyshev operational matrix of differentiation. The properties of first kind Chebyshev polynomial and their shifted polynomial are first presented. These properties together with the operation matrix of differentiation of first kind Chebyshev polynomial are utilized to obtain numerical solutions of a class of linear and nonlinear LaneEmden type singular initial value problems (IVPs). The absolute error of this method is graphically presented. The proposed framework is different from other numerical methods and can be used in differential equations of the same type. Several examples are illuminated to reveal the accuracy and validity of the proposed method.