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The aim of this study is to present a good modernistic strategy for solvingsome well-known classes of Lane-Emden type singular differential equations. Theproposed approach is based on the reproducing kernel Hilbert space (RKHS) andintroducing the reproducing kernel properties in which the initial conditionsof the problem are satisfied. The analytical solution that obtained involves inthe form of a convergent series with easily computable terms in its reproducingkernel space. The approximation solution is expressed by n-term summation ofreproducing kernel functions and it is converge to the analytical solution. Ourinvestigations indicate that there is excellent agreement between the numericalresults and the RKHS method, which is applied to some examples to illustratethe accuracy, efficiency, and applicability of the method. The present workshows the potential of the RKHS technique in solving such nonlinear singularinitial value problems.

A reliable numerical method for solving a certain class of singular initial value problems using reproducing kernel algorithm