Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method
Joint Authors
Abd-Elhameed, W. M.
Doha, E. H.
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-22
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
This paper presents some efficient spectral algorithms for solving linear sixth-order two-point boundary value problems in one dimension based on the application of the Galerkin method.
The proposed algorithms are extended to solve the two-dimensional sixth-order differential equations.
A family of symmetric generalized Jacobi polynomials is introduced and used as basic functions.
The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted.
The various matrix systems resulting from the proposed algorithms are carefully investigated, especially their condition numbers and their complexities.
These algorithms are extensions to some of the algorithms proposed by Doha and Abd-Elhameed (2002) and Doha and Bhrawy (2008) for second- and fourth-order elliptic equations, respectively.
Three numerical results are presented to demonstrate the efficiency and the applicability of the proposed algorithms.
American Psychological Association (APA)
Doha, E. H.& Abd-Elhameed, W. M.. 2012. Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-495669
Modern Language Association (MLA)
Doha, E. H.& Abd-Elhameed, W. M.. Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method. Abstract and Applied Analysis No. 2012 (2012), pp.1-19.
https://search.emarefa.net/detail/BIM-495669
American Medical Association (AMA)
Doha, E. H.& Abd-Elhameed, W. M.. Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-495669
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-495669