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 solutions are obtained. The solutions have been compared with those obtained by exact solutions. We use modified Adomian decomposition method to solving singular boundary value problems and singular initial value problem of higher-order ordinary differential equations. The numerical results obtained by this way have been compared with the exact solution to show that the Adomian method is a powerful method for the solution of linear and nonlinear differential equations.

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Adomian Decomposition Method Taylor Series Initial Boundary Value Problem Singular Boundary Value Problems Higher-order Ordinary Differential Equation