Modified Adomian decomposition method has been used intensively to solve linear and nonlinear singular boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. The method is illustrated by some examples of higher order ordinary equations systems and series ...

A new implicit method has been presented for solving singular initial value problems. The formula has derived in such a way that it excludes the singular point. The method is illustrated by suitable examples (first and second order). To check the results the approximate solutions have been compared to exact solutions KeywordsSingular initial value problems; Lane-Emden equations; Emden-Fowler eq...

The second-order delay differential equations often appear in the dynamical system, celestial mechanics, kinematics, and so forth. Some numerical methods for solving secondorder delay differential equations have been discussed, which include θ-method [1], trapezoidal method [2], and RungeKutta-Nyströmmethod [3].The variational iteration method (VIM) was first proposed by He [4, 5] and has been ...