Doha, E. H.Bhrawy, A. H.Hafez, R. M.2019-11-112019-11-112012Cited References in Web of Science Core Collection: 311007-5704https://www.sciencedirect.com/science/article/pii/S1007570412000846Accession Number: WOS:000304578000006This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved. (C) 2012 Elsevier B.V. All rights reserved.enUniversity for Multi-point boundary value problemHigh-order differential equationNonlinear boundary value problemsTau methodCollocation methodShifted Jacobi polynomialsGauss quadratureArticle