Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials
The main aim of this research article is to develop two new algorithms for handling linear and nonlinear third-order boundary value problems. For this purpose, a novel operational matrix of derivatives of certain nonsymmetric generalized Jacobi polynomials is established. The suggested algorithms ar...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/672703 |
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| _version_ | 1832555330734653440 |
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| author | W. M. Abd-Elhameed |
| author_facet | W. M. Abd-Elhameed |
| author_sort | W. M. Abd-Elhameed |
| collection | DOAJ |
| description | The main aim of this research article is to develop two new algorithms for handling linear and nonlinear third-order boundary value problems. For this purpose, a novel operational matrix of derivatives of certain nonsymmetric generalized Jacobi polynomials is established. The suggested algorithms are built on utilizing the Galerkin and collocation spectral methods. Moreover, the principle idea behind these algorithms is based on converting the boundary value problems governed by their boundary conditions into systems of linear or nonlinear algebraic equations which can be efficiently solved by suitable solvers. We support our algorithms by a careful investigation of the convergence analysis of the suggested nonsymmetric generalized Jacobi expansion. Some illustrative examples are given for the sake of indicating the high accuracy and efficiency of the two proposed algorithms. |
| format | Article |
| id | doaj-art-1ddfd7e4d80e4069a59a6a6a955a46c7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1ddfd7e4d80e4069a59a6a6a955a46c72025-02-03T05:48:29ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/672703672703Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi PolynomialsW. M. Abd-Elhameed0Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaThe main aim of this research article is to develop two new algorithms for handling linear and nonlinear third-order boundary value problems. For this purpose, a novel operational matrix of derivatives of certain nonsymmetric generalized Jacobi polynomials is established. The suggested algorithms are built on utilizing the Galerkin and collocation spectral methods. Moreover, the principle idea behind these algorithms is based on converting the boundary value problems governed by their boundary conditions into systems of linear or nonlinear algebraic equations which can be efficiently solved by suitable solvers. We support our algorithms by a careful investigation of the convergence analysis of the suggested nonsymmetric generalized Jacobi expansion. Some illustrative examples are given for the sake of indicating the high accuracy and efficiency of the two proposed algorithms.http://dx.doi.org/10.1155/2015/672703 |
| spellingShingle | W. M. Abd-Elhameed Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials Abstract and Applied Analysis |
| title | Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials |
| title_full | Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials |
| title_fullStr | Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials |
| title_full_unstemmed | Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials |
| title_short | Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials |
| title_sort | some algorithms for solving third order boundary value problems using novel operational matrices of generalized jacobi polynomials |
| url | http://dx.doi.org/10.1155/2015/672703 |
| work_keys_str_mv | AT wmabdelhameed somealgorithmsforsolvingthirdorderboundaryvalueproblemsusingnoveloperationalmatricesofgeneralizedjacobipolynomials |