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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30139/ http://psasir.upm.edu.my/id/eprint/30139/1/30139.pdf |
| _version_ | 1848846593311113216 |
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| author | Toutounian, Faezeh Tohidi, Emran Kilicman, Adem |
| author_facet | Toutounian, Faezeh Tohidi, Emran Kilicman, Adem |
| author_sort | Toutounian, Faezeh |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T09:05:10Z |
| format | Article |
| id | upm-30139 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:10Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301392017-10-20T03:29:34Z http://psasir.upm.edu.my/id/eprint/30139/ Fourier operational matrices of differentiation and transmission: introduction and applications Toutounian, Faezeh Tohidi, Emran Kilicman, Adem 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. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30139/1/30139.pdf Toutounian, Faezeh and Tohidi, Emran and Kilicman, Adem (2013) Fourier operational matrices of differentiation and transmission: introduction and applications. Abstract and Applied Analysis, 2013. art. no. 198926. pp. 1-11. ISSN 1085-3375; ESSN: 1687-0409 https://www.hindawi.com/journals/aaa/2013/198926/abs/ 10.1155/2013/198926 |
| spellingShingle | Toutounian, Faezeh Tohidi, Emran Kilicman, Adem Fourier operational matrices of differentiation and transmission: introduction and applications |
| 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://psasir.upm.edu.my/id/eprint/30139/ http://psasir.upm.edu.my/id/eprint/30139/ http://psasir.upm.edu.my/id/eprint/30139/ http://psasir.upm.edu.my/id/eprint/30139/1/30139.pdf |