Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/749370 |
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| _version_ | 1832545813938569216 |
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| author | E. H. Doha W. M. Abd-Elhameed |
| author_facet | E. H. Doha W. M. Abd-Elhameed |
| author_sort | E. H. Doha |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cbddf53bdbfb408996a94c73f4d346ab |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cbddf53bdbfb408996a94c73f4d346ab2025-02-03T07:24:48ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/749370749370Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin MethodE. H. Doha0W. M. Abd-Elhameed1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptThis 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.http://dx.doi.org/10.1155/2012/749370 |
| spellingShingle | E. H. Doha W. M. Abd-Elhameed Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method Abstract and Applied Analysis |
| title | Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method |
| title_full | Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method |
| title_fullStr | Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method |
| title_full_unstemmed | Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method |
| title_short | Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method |
| title_sort | efficient solutions of multidimensional sixth order boundary value problems using symmetric generalized jacobi galerkin method |
| url | http://dx.doi.org/10.1155/2012/749370 |
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