Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations

Abstract

In this study, we aim to solve Lane-Emden equations numerically by the Gegenbauer wavelet method. This method is mainly based on orthonormal Gegenbauer polynomials and takes advantage of orthonormality which reduces the computational cost. As a further advantage, Gegenbauer polynomials are associated with a real parameter allowing them to be defined as Legendre polynomials or Chebyshev polynomials for some values. Although this provides an opportunity to be able to analyze the problem under consideration from a wide point of view, the effect of the Gegenbauer parameter on the solution of Lane-Emden equations has not been studied so far. This study demonstrates the robustness of the Gegenbauer wavelet method on three problems of Lane-Emden equations considering different values of this parameter.