Revisiting Blasius Flow by Fixed Point Method
The well-known Blasius flow is governed by a third-order nonlinear ordinary differential equation with two-point boundary value. Specially, one of the boundary conditions is asymptotically assigned on the first derivative at infinity, which is the main challenge on handling this problem. Through int...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/953151 |
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| author | Ding Xu Jinglei Xu Gongnan Xie |
| author_facet | Ding Xu Jinglei Xu Gongnan Xie |
| author_sort | Ding Xu |
| collection | DOAJ |
| description | The well-known Blasius flow is governed by a third-order nonlinear ordinary differential equation with two-point boundary value. Specially, one of the boundary conditions is asymptotically assigned on the first derivative at infinity, which is the main challenge on handling this problem. Through introducing two transformations not only for independent variable bur also for function, the difficulty originated from the semi-infinite interval and asymptotic boundary condition is overcome. The deduced nonlinear differential equation is subsequently investigated with the fixed point method, so the original complex nonlinear equation is replaced by a series of integrable linear equations. Meanwhile, in order to improve the convergence and stability of iteration procedure, a sequence of relaxation factors is introduced in the framework of fixed point method and determined by the steepest descent seeking algorithm in a convenient manner. |
| format | Article |
| id | doaj-art-e6da69f3cfce4ba8b5bf7dfc37a265e9 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e6da69f3cfce4ba8b5bf7dfc37a265e92025-08-20T02:21:10ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/953151953151Revisiting Blasius Flow by Fixed Point MethodDing Xu0Jinglei Xu1Gongnan Xie2State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, No. 28, Xianning West Road, Xi'an 710049, ChinaSchool of Jet Propulsion, Beijing University of Aeronautics and Astronautics, Xueyuan Road, No. 37, Beijing 100191, ChinaSchool of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, ChinaThe well-known Blasius flow is governed by a third-order nonlinear ordinary differential equation with two-point boundary value. Specially, one of the boundary conditions is asymptotically assigned on the first derivative at infinity, which is the main challenge on handling this problem. Through introducing two transformations not only for independent variable bur also for function, the difficulty originated from the semi-infinite interval and asymptotic boundary condition is overcome. The deduced nonlinear differential equation is subsequently investigated with the fixed point method, so the original complex nonlinear equation is replaced by a series of integrable linear equations. Meanwhile, in order to improve the convergence and stability of iteration procedure, a sequence of relaxation factors is introduced in the framework of fixed point method and determined by the steepest descent seeking algorithm in a convenient manner.http://dx.doi.org/10.1155/2014/953151 |
| spellingShingle | Ding Xu Jinglei Xu Gongnan Xie Revisiting Blasius Flow by Fixed Point Method Abstract and Applied Analysis |
| title | Revisiting Blasius Flow by Fixed Point Method |
| title_full | Revisiting Blasius Flow by Fixed Point Method |
| title_fullStr | Revisiting Blasius Flow by Fixed Point Method |
| title_full_unstemmed | Revisiting Blasius Flow by Fixed Point Method |
| title_short | Revisiting Blasius Flow by Fixed Point Method |
| title_sort | revisiting blasius flow by fixed point method |
| url | http://dx.doi.org/10.1155/2014/953151 |
| work_keys_str_mv | AT dingxu revisitingblasiusflowbyfixedpointmethod AT jingleixu revisitingblasiusflowbyfixedpointmethod AT gongnanxie revisitingblasiusflowbyfixedpointmethod |