Collocation Technique Based on Chebyshev Polynomial to Solve Lane-Emden-Fowler Boundary Value Problem

Abstract

We present an innovative technique to find numerical solutions of the Lane-Emden-Fowler singular-type BVPs which plays a crucial role in comprehending a wide range of physical phenomena. The core concept of this technique is based on transforming the differential equation into the Fredholm integral equation, then it is converted into system of linear or nonlinear algebraic equations by utilizing the collocation technique based on Chebyshev polynomials. Subsequently, we employ an iterative numerical method, such as the Newton’s method, for solving the system to get the approximate solution. Error analysis is included which helps to assess the accuracy of the obtained solutions and provides insights into the reliability of the numerical results. Furthermore, we have also considered various examples to demonstrate the applicability of the collocation technique based on Chebyshev polynomials and compared with the existing results.