Original Articles

Efficient spectral-Petrov-Galerkin methods for third- and fifth-order differential equations using general parameters generalized Jacobi polynomials

Published in: Quaestiones Mathematicae
Volume 36, issue 1, 2013 , pages: 15–38
DOI: 10.2989/16073606.2013.779945
Author(s): W.M. Abd-ElhameedDepartment of Mathematics, Faculty of Science, Saudi Arabia, E.H. DohaDepartment of Mathematics, Faculty of Science, Giza-Egypt, Y.H. YoussriDepartment of Mathematics, Faculty of Science, Giza-Egypt

Abstract

Two new families of general parameters generalized Jacobi polynomials are introduced. Some efficient and accurate algorithms based on these families are developed and implemented for solving third- and fifth-order differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a dual Petrov-Galerkin method. The use of general parameters generalized Jacobi polynomials leads to simplified analysis, more precise error estimates and well conditioned algorithms. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results indicating the high accuracy and effectiveness of the proposed algorithms are presented.

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