Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method
The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Ga...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/513808 |
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| author | A. H. Bhrawy M. A. Alghamdi D. Baleanu |
| author_facet | A. H. Bhrawy M. A. Alghamdi D. Baleanu |
| author_sort | A. H. Bhrawy |
| collection | DOAJ |
| description | The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit and explicit forms of NFDEs to demonstrate the computation accuracy of the proposed method. We also compare the performance of the method with variational iteration method, one-leg θ-method, continuous Runge-Kutta method, and reproducing kernel Hilbert space method. |
| format | Article |
| id | doaj-art-9de4fe8149f246b2a49dadae47fe2ada |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9de4fe8149f246b2a49dadae47fe2ada2025-08-20T02:20:29ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/513808513808Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral MethodA. H. Bhrawy0M. A. Alghamdi1D. Baleanu2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit and explicit forms of NFDEs to demonstrate the computation accuracy of the proposed method. We also compare the performance of the method with variational iteration method, one-leg θ-method, continuous Runge-Kutta method, and reproducing kernel Hilbert space method.http://dx.doi.org/10.1155/2013/513808 |
| spellingShingle | A. H. Bhrawy M. A. Alghamdi D. Baleanu Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method Abstract and Applied Analysis |
| title | Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method |
| title_full | Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method |
| title_fullStr | Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method |
| title_full_unstemmed | Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method |
| title_short | Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method |
| title_sort | numerical solution of a class of functional differential equations using jacobi pseudospectral method |
| url | http://dx.doi.org/10.1155/2013/513808 |
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