  The aim of this study is to present a good modernistic strategy for solving
some well-known classes of Lane-Emden type singular differential equations. The
proposed approach is based on the reproducing kernel Hilbert space (RKHS) and
introducing the reproducing kernel properties in which the initial conditions
of the problem are satisfied. The analytical solution that obtained involves in
the form of a convergent series with easily computable terms in its reproducing
kernel space. The approximation solution is expressed by n-term summation of
reproducing kernel functions and it is converge to the analytical solution. Our
investigations indicate that there is excellent agreement between the numerical
results and the RKHS method, which is applied to some examples to illustrate
the accuracy, efficiency, and applicability of the method. The present work
shows the potential of the RKHS technique in solving such nonlinear singular
initial value problems.
