Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations

摘要

In this article, a new method is generated to solve nonlinear Lane–Emden type equations using Legendre, Hermite and Laguerre wavelets. We are interested to note that these wavelets will give same solutions with good accuracy. Theorems on convergence analysis are stated and proved on the spaces, which are created by Legendre, Hermite and Laguerre wavelets bases and justified these spaces are equivalent to polynomial linear space generated by general polynomial basis. The main idea for obtaining numerical solutions depends on converting the differential equation with initial and boundary conditions into a system of linear or nonlinear algebraic equations with unknown coefficients. A very high level of accuracy reflects the reliability of this scheme for such problems.