The derivation of numerical schemes for the solution of Lane-Emden equations requires meticulous consideration
because they are highly nonlinear in nature; have singularity behaviors at the origin and in some cases, their
exact solutions are known for only a few parameter ranges. This explains the reason for the failure of some
existing methods in approximating such problems. Thus, in this research, a convergence-preserving Non-Stan-
dard Finite Difference Scheme (NSFDS) shall be derived for the solution of Lane-Emden equations. The main idea
in this work is the approximation of both the linear and nonlinear terms non-locally and the renormalization/
reformulation of the numerator and denominator functions of the Lane-Emden equations. The need for this
approach came up due to some setbacks of existing methods where the exact solutions’ qualitative properties are
not routinely transferred to the approximate solutions. The analysis of some properties of the NSFDS like
convergence, dynamical consistency, monotone dependence on the initial value, and monotonicity of solutions as
well as perturbation solution analysis shall be carried out. The NSFDS was then employed in solving some classes
of singular initial value problems of the Lane-Emden type and the results obtained show that the proposed
method is efficient and computationally cheap.