A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method
The main feature of the boundary layer flow problems is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such problems. To the best of the authors’ knowledge, two procedures were used extensively in...
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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/10.1155/2013/753049 |
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| author | Abdelhalim Ebaid Nwaf Al-Armani |
| author_facet | Abdelhalim Ebaid Nwaf Al-Armani |
| author_sort | Abdelhalim Ebaid |
| collection | DOAJ |
| description | The main feature of the boundary layer flow problems is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such problems. To the best of the authors’ knowledge, two procedures were used extensively in the past two decades to deal with the boundary conditions at infinity, either the Padé approximation or the direct numerical codes. However, an intensive work is needed to perform the calculations using the Padé technique. Regarding this point, a new idea is proposed in this paper. The idea is based on transforming the unbounded domain into a bounded one by the help of a transformation. Accordingly, the original differential equation is transformed into a singular differential equation with classical boundary conditions. The current approach is applied to solve a class of the Blasius problem and a special class of the Falkner-Skan problem via an improved version of Adomian’s method (Ebaid, 2011). In addition, the numerical results obtained by using the proposed technique are compared with the other published solutions, where good agreement has been achieved. The main characteristic of the present approach is the avoidance of the Padé approximation to deal with the infinity boundary conditions. |
| format | Article |
| id | doaj-art-5be24396b24642fbbc515bc5e6a129af |
| 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-5be24396b24642fbbc515bc5e6a129af2025-02-03T01:11:46ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/753049753049A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s MethodAbdelhalim Ebaid0Nwaf Al-Armani1Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaThe main feature of the boundary layer flow problems is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such problems. To the best of the authors’ knowledge, two procedures were used extensively in the past two decades to deal with the boundary conditions at infinity, either the Padé approximation or the direct numerical codes. However, an intensive work is needed to perform the calculations using the Padé technique. Regarding this point, a new idea is proposed in this paper. The idea is based on transforming the unbounded domain into a bounded one by the help of a transformation. Accordingly, the original differential equation is transformed into a singular differential equation with classical boundary conditions. The current approach is applied to solve a class of the Blasius problem and a special class of the Falkner-Skan problem via an improved version of Adomian’s method (Ebaid, 2011). In addition, the numerical results obtained by using the proposed technique are compared with the other published solutions, where good agreement has been achieved. The main characteristic of the present approach is the avoidance of the Padé approximation to deal with the infinity boundary conditions.http://dx.doi.org/10.1155/2013/753049 |
| spellingShingle | Abdelhalim Ebaid Nwaf Al-Armani A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method Abstract and Applied Analysis |
| title | A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method |
| title_full | A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method |
| title_fullStr | A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method |
| title_full_unstemmed | A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method |
| title_short | A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method |
| title_sort | new approach for a class of the blasius problem via a transformation and adomian s method |
| url | http://dx.doi.org/10.1155/2013/753049 |
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