Application of Successive Linearisation Method to Squeezing Flow with Bifurcation
This paper employs the computational approach known as successive linearization method (SLM) to tackle a fourth order nonlinear differential equation modelling the transient flow of an incompressible viscous fluid between two parallel plates produced by a simple wall motion. Numerical and graphical...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/410620 |
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| author | S. S. Motsa O. D. Makinde S. Shateyi |
| author_facet | S. S. Motsa O. D. Makinde S. Shateyi |
| author_sort | S. S. Motsa |
| collection | DOAJ |
| description | This paper employs the computational approach known as successive linearization method (SLM) to tackle a fourth order nonlinear differential equation modelling the transient flow of an incompressible viscous fluid between two parallel plates produced by a simple wall motion. Numerical and graphical results obtained show excellent agreement with the earlier results reported in the literature. We obtain solution branches as
well as a turning point in the flow field accurately. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver, bvp4c, demonstrates that the SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper. |
| format | Article |
| id | doaj-art-9cd23e18942d42b18c7a8f76a63c4b11 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9cd23e18942d42b18c7a8f76a63c4b112025-08-20T03:38:15ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/410620410620Application of Successive Linearisation Method to Squeezing Flow with BifurcationS. S. Motsa0O. D. Makinde1S. Shateyi2School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South AfricaFaculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South AfricaDepartment of Mathematics & Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South AfricaThis paper employs the computational approach known as successive linearization method (SLM) to tackle a fourth order nonlinear differential equation modelling the transient flow of an incompressible viscous fluid between two parallel plates produced by a simple wall motion. Numerical and graphical results obtained show excellent agreement with the earlier results reported in the literature. We obtain solution branches as well as a turning point in the flow field accurately. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver, bvp4c, demonstrates that the SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.http://dx.doi.org/10.1155/2014/410620 |
| spellingShingle | S. S. Motsa O. D. Makinde S. Shateyi Application of Successive Linearisation Method to Squeezing Flow with Bifurcation Advances in Mathematical Physics |
| title | Application of Successive Linearisation Method to Squeezing Flow with Bifurcation |
| title_full | Application of Successive Linearisation Method to Squeezing Flow with Bifurcation |
| title_fullStr | Application of Successive Linearisation Method to Squeezing Flow with Bifurcation |
| title_full_unstemmed | Application of Successive Linearisation Method to Squeezing Flow with Bifurcation |
| title_short | Application of Successive Linearisation Method to Squeezing Flow with Bifurcation |
| title_sort | application of successive linearisation method to squeezing flow with bifurcation |
| url | http://dx.doi.org/10.1155/2014/410620 |
| work_keys_str_mv | AT ssmotsa applicationofsuccessivelinearisationmethodtosqueezingflowwithbifurcation AT odmakinde applicationofsuccessivelinearisationmethodtosqueezingflowwithbifurcation AT sshateyi applicationofsuccessivelinearisationmethodtosqueezingflowwithbifurcation |