Chebyshev Operational Matrix Method for Lane-Emden Problem

Nonlinear engineering: Modeling and application

article

Bhuvnesh Sharma¹  Sunil Kumar²  M.K. Paswan¹  Dindayal Mahato³ 

[1] Department of Mechanical Engg., National Institute of Technology;Department of Mathematics, National Institute of Technology;Department of Computer Science and Engg., National Institute of Technology

关键词: Lane-Emden equations;    chebyshev first kind operational matrix of differentiation;    Isothermal gas spheres equation;    Nonlinear ODE;   

DOI  :  10.1515/nleng-2017-0157

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

Unknown