Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications
This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gau...
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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/10.1155/2013/198926 |
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| author | F. Toutounian Emran Tohidi A. Kilicman |
| author_facet | F. Toutounian Emran Tohidi A. Kilicman |
| author_sort | F. Toutounian |
| collection | DOAJ |
| description | This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solution of Pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods. |
| format | Article |
| id | doaj-art-ba820f2065b04ce7a842c65884ad3461 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ba820f2065b04ce7a842c65884ad34612025-02-03T05:59:50ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/198926198926Fourier Operational Matrices of Differentiation and Transmission: Introduction and ApplicationsF. Toutounian0Emran Tohidi1A. Kilicman2Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranDepartment of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranDepartment of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaThis paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solution of Pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods.http://dx.doi.org/10.1155/2013/198926 |
| spellingShingle | F. Toutounian Emran Tohidi A. Kilicman Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications Abstract and Applied Analysis |
| title | Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications |
| title_full | Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications |
| title_fullStr | Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications |
| title_full_unstemmed | Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications |
| title_short | Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications |
| title_sort | fourier operational matrices of differentiation and transmission introduction and applications |
| url | http://dx.doi.org/10.1155/2013/198926 |
| work_keys_str_mv | AT ftoutounian fourieroperationalmatricesofdifferentiationandtransmissionintroductionandapplications AT emrantohidi fourieroperationalmatricesofdifferentiationandtransmissionintroductionandapplications AT akilicman fourieroperationalmatricesofdifferentiationandtransmissionintroductionandapplications |