An extension of the Tau numerical algorithm for the solution of linear and nonlinear Lane-Emden equations

作者：Vanani S Karimi^*; Soleymani F

来源：Mathematical Methods in the Applied Sciences, 2013, 36(6): 674-682.

DOI：10.1002/mma.2616

• LaneEmden equations
• spectral methods
• Tau method
• system of differential algebraic equations
• computer algorithm of the method

The purpose of this paper is to present a numerical algorithm for solving the LaneEmden equations as singular initial value problems. The proposed algorithm is based on an operational Tau method (OTM). The main idea behind the OTM is to convert the desired problem to some operational matrices. Firstly, we use a special integral operator and convert the LaneEmden equations to integral equations. Then, we use OTM to linearize the integral equations to some operational matrices and convert the problem to an algebraic system. The concepts, properties, and advantages of OTM and its application for solving LaneEmden equations are presented. Some orthogonal polynomials are also used to reduce the volume of computations. Finally, several experiments of LaneEmden equations including linear and nonlinear terms are given to illustrate the validity and efficiency of the proposed algorithm.

• 出版日期2013-4