An efficient numerical algorithm for solving the Lane-Emden type functional boundary value problems

Abstract

In this article, we analyze collocation points and shifted Chebyshev polynomials based strategy to approximate the solution of the Lane-Emden type functional differential equations subjected to three-point boundary conditions. Shifted Chebyshev polynomials are used to reduce the problem into a matrix form, and then, collocation points are used to transform the matrix form into a system of nonlinear algebraic equations. The simplicity of the mathematical formulation and ease of code computation, demonstrate the accessibility and flexibility of the proposed numerical technique. The outcomes clearly show that the proposed approach achieves rapid convergence, exhibits a high level of computational efficiency, and delivers precise approximations. Finally, numerous examples are included to illustrate and confirm the applicability, validity and superiority of the proposed approach over the existing methods.