A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method
We have considered linear partial differential algebraic equations (LPDAEs) of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot b...
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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/10.1155/2013/705313 |
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| _version_ | 1832545690422607872 |
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| author | Murat Osmanoglu Mustafa Bayram |
| author_facet | Murat Osmanoglu Mustafa Bayram |
| author_sort | Murat Osmanoglu |
| collection | DOAJ |
| description | We have considered linear partial differential algebraic equations (LPDAEs) of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution. |
| format | Article |
| id | doaj-art-089e1acabfbc4a60853acef753f07030 |
| 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-089e1acabfbc4a60853acef753f070302025-02-03T07:24:52ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/705313705313A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform MethodMurat Osmanoglu0Mustafa Bayram1Department of Mathematical Engineering, Chemical and Metallurgical Faculty, Yildiz Technical University, Esenler 34210, Istanbul, TurkeyDepartment of Mathematical Engineering, Chemical and Metallurgical Faculty, Yildiz Technical University, Esenler 34210, Istanbul, TurkeyWe have considered linear partial differential algebraic equations (LPDAEs) of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.http://dx.doi.org/10.1155/2013/705313 |
| spellingShingle | Murat Osmanoglu Mustafa Bayram A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method Abstract and Applied Analysis |
| title | A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method |
| title_full | A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method |
| title_fullStr | A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method |
| title_full_unstemmed | A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method |
| title_short | A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method |
| title_sort | numerical method for partial differential algebraic equations based on differential transform method |
| url | http://dx.doi.org/10.1155/2013/705313 |
| work_keys_str_mv | AT muratosmanoglu anumericalmethodforpartialdifferentialalgebraicequationsbasedondifferentialtransformmethod AT mustafabayram anumericalmethodforpartialdifferentialalgebraicequationsbasedondifferentialtransformmethod AT muratosmanoglu numericalmethodforpartialdifferentialalgebraicequationsbasedondifferentialtransformmethod AT mustafabayram numericalmethodforpartialdifferentialalgebraicequationsbasedondifferentialtransformmethod |