ISSN 23473487 25 | Page Sept 15, 2013 On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains Ahmed A. Khidir Faculty of Technology of Mathematical Sciences and Statistics Alneelain University, Algamhoria Street, P.O. Box 12702, Khartoum - Sudan E-mail: ahmed.khidir@yahoo.com Abstract In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. Keywords: Chebyshev spectral method; Homotopy perturbation method; nonlinear boundary value problems. Council for Innovative Research Peer Review Research Publishing System Journal: Journal of Advances in Physics Vol. 1, No. 1 editor@cirworld.com www.cirworld.com , member.cirworld.com