title: Two Legendre-dual-Petrov-Galerkin algorithms for solving the integrated forms of high odd-order boundary value problems.
abstract: Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made.
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia ; Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
authors.forename: Waleed M
authors.initials: WM
authors.lastname: Abd-Elhameed
authors.affiliation: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
authors.forename: Eid H
authors.initials: EH
authors.lastname: Doha
authors.affiliation: Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt.
authors.forename: Mahmoud A
authors.initials: MA
authors.lastname: Bassuony
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical