Njoseh, Ignatius N.Mamadu, Ebimene J.2016-07-212016-07-212016-07http://dx.doi.org/10.4236/am.2016.711107http://hdl.handle.net/123456789/875In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.enPower SeriesLinear and Nonlinear ProblemsBoundary Value Problem (BVP)Numerical SimulationArticle