Abstract
We apply the reproducing kernel method and group preserving scheme for investigating the Lane–Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These approximations demonstrate the preciseness of the investigated techniques.
Highlights
The work of singular initial value problems modeled by second order nonlinear ordinary differential equations (ODEs) have captivated many mathematicians and physicists
The reproducing kernel function rς of o W23 [0, 1] is given as rς (η ) =
Internal symmetry group of a system, especially dynamical systems obtained from Equation (1), preserves using the group preserving scheme (GPS) and when we do not have the symmetry group of nonlinear Lane–Emden equation, it is possible to embed them into the augmented dynamical systems
Summary
The work of singular initial value problems modeled by second order nonlinear ordinary differential equations (ODEs) have captivated many mathematicians and physicists. In the early development stage of the reproducing kernel theory, most of the works were implemented by Bergman. This researcher obtained the corresponding kernels of the harmonic functions with one or several. Mathematics 2017, 5, 77 variables, and the corresponding kernel of the analytic function in squared metric, and implemented them in the research of the boundary value problem of the elliptic partial differential equation. This is the first stage in the development history of reproducing kernel.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
