Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic Method
A new algorithm based on the standard optimal homotopy asymptotic method, namely, the predictor optimal homotopy asymptotic method (POHAM), is proposed to predict the multiplicity of the solutions of nonlinear differential equations with boundary conditions. This approach is successfully implemented...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2014-11-01
|
| Series: | Advances in Mechanical Engineering |
| Online Access: | https://doi.org/10.1155/2014/372537 |
| _version_ | 1818453035803738112 |
|---|---|
| author | A. K. Alomari N. Ratib Anakira I. Hashim |
| author_facet | A. K. Alomari N. Ratib Anakira I. Hashim |
| author_sort | A. K. Alomari |
| collection | DOAJ |
| description | A new algorithm based on the standard optimal homotopy asymptotic method, namely, the predictor optimal homotopy asymptotic method (POHAM), is proposed to predict the multiplicity of the solutions of nonlinear differential equations with boundary conditions. This approach is successfully implemented to obtain multiple solutions of a mixed convection flow model in a vertical channel and a nonlinear model arising in heat transfer. A new technique for obtaining the initial guess to accelerate the convergence of the series solution is presented. |
| first_indexed | 2024-12-14T21:32:35Z |
| format | Article |
| id | doaj.art-a4dbf623dc0743be8a6e61c4a05a6805 |
| institution | Directory Open Access Journal |
| issn | 1687-8132 |
| language | English |
| last_indexed | 2024-12-14T21:32:35Z |
| publishDate | 2014-11-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Advances in Mechanical Engineering |
| spelling | doaj.art-a4dbf623dc0743be8a6e61c4a05a68052022-12-21T22:46:40ZengSAGE PublishingAdvances in Mechanical Engineering1687-81322014-11-01610.1155/2014/37253710.1155_2014/372537Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic MethodA. K. Alomari0N. Ratib Anakira1I. Hashim2 Department of Mathematics, Faculty of Science, Yarmouk University, Irbid 211-63, Jordan Centre for Modelling and Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi ArabiaA new algorithm based on the standard optimal homotopy asymptotic method, namely, the predictor optimal homotopy asymptotic method (POHAM), is proposed to predict the multiplicity of the solutions of nonlinear differential equations with boundary conditions. This approach is successfully implemented to obtain multiple solutions of a mixed convection flow model in a vertical channel and a nonlinear model arising in heat transfer. A new technique for obtaining the initial guess to accelerate the convergence of the series solution is presented.https://doi.org/10.1155/2014/372537 |
| spellingShingle | A. K. Alomari N. Ratib Anakira I. Hashim Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic Method Advances in Mechanical Engineering |
| title | Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic Method |
| title_full | Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic Method |
| title_fullStr | Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic Method |
| title_full_unstemmed | Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic Method |
| title_short | Multiple Solutions of Problems in Fluid Mechanics by Predictor Optimal Homotopy Asymptotic Method |
| title_sort | multiple solutions of problems in fluid mechanics by predictor optimal homotopy asymptotic method |
| url | https://doi.org/10.1155/2014/372537 |
| work_keys_str_mv | AT akalomari multiplesolutionsofproblemsinfluidmechanicsbypredictoroptimalhomotopyasymptoticmethod AT nratibanakira multiplesolutionsofproblemsinfluidmechanicsbypredictoroptimalhomotopyasymptoticmethod AT ihashim multiplesolutionsofproblemsinfluidmechanicsbypredictoroptimalhomotopyasymptoticmethod |