An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions
The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equat...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/36403/1/An%20efficient%20spectral%20approximation%20for%20solving%20several%20types%20of%20parabolic%20PDEs%20with%20nonlocal%20boundary%20conditions.pdf |
| _version_ | 1796972905216606208 |
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| author | Tohidi, Emran Kilicman, Adem |
| author_facet | Tohidi, Emran Kilicman, Adem |
| author_sort | Tohidi, Emran |
| collection | UPM |
| description | The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy. |
| first_indexed | 2024-03-06T08:35:13Z |
| format | Article |
| id | upm.eprints-36403 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:35:13Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-364032015-12-08T01:24:56Z http://psasir.upm.edu.my/id/eprint/36403/ An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions Tohidi, Emran Kilicman, Adem The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36403/1/An%20efficient%20spectral%20approximation%20for%20solving%20several%20types%20of%20parabolic%20PDEs%20with%20nonlocal%20boundary%20conditions.pdf Tohidi, Emran and Kilicman, Adem (2014) An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions. Mathematical Problems in Engineering, 2014. art. no. 369029. pp. 1-6. ISSN 1024-123X; ESSN: 1563-5147 http://www.hindawi.com/journals/mpe/2014/369029/abs/ 10.1155/2014/369029 |
| spellingShingle | Tohidi, Emran Kilicman, Adem An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions |
| title | An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions |
| title_full | An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions |
| title_fullStr | An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions |
| title_full_unstemmed | An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions |
| title_short | An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions |
| title_sort | efficient spectral approximation for solving several types of parabolic pdes with nonlocal boundary conditions |
| url | http://psasir.upm.edu.my/id/eprint/36403/1/An%20efficient%20spectral%20approximation%20for%20solving%20several%20types%20of%20parabolic%20PDEs%20with%20nonlocal%20boundary%20conditions.pdf |
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