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The aim of the present analysis is to apply a relatively recent method, the residual-power series method (RPSM), in order to obtain efficient analytical numerical solutions for a class of nonlinear systems of initial value problems with finitely many singularities. The solution methodology provided the analytical solutions in terms of a rapidly convergent series with easily computable components. This novel approach possesses main advantage as compared to other exiting methods; it reproduces exact form when the solution is polynomial without linearization or perturbation; it can be applied without any limitation on the nature of the problem, type of classification, and the number of mesh points. Numerical experiments are discussed quantitatively to illustrate the theoretical statements and to show potentiality, superiority, and applicability of the proposed technique for solving such nonlinear singular system of differential equations. The results demonstrate reliability and efficiency of the technique developed.

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