Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form
A numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Engineering |
| Online Access: | http://dx.doi.org/10.1155/2020/3972573 |
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| _version_ | 1832566011304345600 |
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| author | Abdelrady Okasha Elnady M. Fayek Abd Rabbo Hani M. Negm |
| author_facet | Abdelrady Okasha Elnady M. Fayek Abd Rabbo Hani M. Negm |
| author_sort | Abdelrady Okasha Elnady |
| collection | DOAJ |
| description | A numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the Chebyshev series. Using matrix representation of a function and their derivatives, the problem is reduced to a system of algebraic equations in a simple way. From the computational point of view, the results are in excellent agreement with those presented in published works. |
| format | Article |
| id | doaj-art-9b4dab8860ba4bdb89d0f3a6f7ec2741 |
| institution | Kabale University |
| issn | 2314-4904 2314-4912 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Engineering |
| spelling | doaj-art-9b4dab8860ba4bdb89d0f3a6f7ec27412025-02-03T01:05:25ZengWileyJournal of Engineering2314-49042314-49122020-01-01202010.1155/2020/39725733972573Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix FormAbdelrady Okasha Elnady0M. Fayek Abd Rabbo1Hani M. Negm2Mechatronics Department, Faculty of Engineering, O6University, Cairo, EgyptMechanical Engineering Department, Shoubra Faculty of Engineering, Benha University, Banha, EgyptAerospace Engineering Department, Cairo University, Giza, EgyptA numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the Chebyshev series. Using matrix representation of a function and their derivatives, the problem is reduced to a system of algebraic equations in a simple way. From the computational point of view, the results are in excellent agreement with those presented in published works.http://dx.doi.org/10.1155/2020/3972573 |
| spellingShingle | Abdelrady Okasha Elnady M. Fayek Abd Rabbo Hani M. Negm Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form Journal of Engineering |
| title | Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form |
| title_full | Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form |
| title_fullStr | Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form |
| title_full_unstemmed | Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form |
| title_short | Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form |
| title_sort | solution of the falkner skan equation using the chebyshev series in matrix form |
| url | http://dx.doi.org/10.1155/2020/3972573 |
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