https://cutt.ly/hePtIOEDoha, E. H.Bhrawy, A. H.Hafez, R. M.2019-11-122019-11-122011Cited References in Web of Science Core Collection: 320895-7177https://doi.org/10.1016/j.mcm.2011.01.002https://www.sciencedirect.com/science/article/pii/S0895717711000057Accession Number: WOS:000287729700024his paper analyzes a method for solving the third-and fifth-order differential equations with constant coefficients using a Jacobi dual-Petrov-Galerkin method, which is more reasonable than the standard Galerkin one. The spatial approximation is based on Jacobi polynomials P-n((alpha,beta)) with alpha,beta is an element of (-1,infinity) and n is the polynomial degree. By choosing appropriate base functions, the resulting system is sparse and the method can be implemented efficiently. A Jacobi-Jacobi dual-Petrov-Galerkin method for the differential equations with variable coefficients is developed. This method is based on the Petrov-Galerkin variational form of one Jacobi polynomial class, but the variable coefficients and the right-hand terms are treated by using the Gauss-Lobatto quadrature form of another Jacobi class. Numerical results illustrate the theory and constitute a convincing argument for the feasibility of the proposed numerical methods. (C) 2011 Elsevier Ltd. All rights reserved.enOctober University for University for Petrov-Galerkin methodJacobi collocation methodJacobi polynomialsJacobi-Gauss-Lobatto quadratureFast Fourier transformJacobi-Jacobi Galerkin methodArticlehttps://doi.org/10.1016/j.mcm.2011.01.002