Recently an implicit method has been presented for solving first order singular initial value problem. The method is extended to solve second or higher order problems having a singular point. The method presents more correct result than those obtained by the implicit Euler and second order implicit Runge-Kutta (RK2) methods. The method is illustrated by suitable examples.

Singular initial-value problems in second-order ordinary differential equations of Lane–Emden type are investigated. In this study, we shall introduce a further development in the Adomian decomposition method to overcome the difficulty at the singular point of non-homogeneous, linear and non-linear Lane–Emden-like equations; especially when the singularity appears on the right-hand side of this...