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| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Ishak Hashim, Prof. Dr. | |
| dc.contributor.author | Anakira Nidal Ratib Sulaiman (P62999) | |
| dc.date.accessioned | 2023-10-13T09:34:43Z | - |
| dc.date.available | 2023-10-13T09:34:43Z | - |
| dc.date.issued | 2015-03-25 | |
| dc.identifier.other | ukmvital:83033 | |
| dc.identifier.uri | https://ptsldigital.ukm.my/jspui/handle/123456789/499787 | - |
| dc.description | Real life phenomena are interrelated with subjects like chemistry, physics, biology and engineering which are modelled using different kinds of differential equations. It is difficult to solve these equations numerically or analytically due to the fact that the majority of these phenomena are nonlinear. Recently, much attention has been dedicated by researchers to come up with improved and more effective solution techniques that help decide solutions to nonlinear models, whether approximate or exact, analytical or numerical. Along these lines, it is vital to find exact or approximate solutions for these models. The optimal homotopy asymptotic method (OHAM) is the method adopted in this thesis. The OHAM is focused around the homotopy map between the initial approximations to the exact solution and having an auxiliary function including a number of optimally determined convergent control parameters that adjust the convergence region and the rate of the series solution. The map breaks down a challenging problem into a set of problems which can be solved more easier. OHAM is examined and modified in this thesis to obtain exact or approximate results for ordinary, boundary value problems (BVPs), initial value problems (IVPs), and delay differential equations (DDEs) without any discretization or transformations. The objectives of this study are to investigate the general framework of OHAM to obtain approximate solutions for singular two-point BVPs and nonlinear system of two-point BVPs. To present a new algorithm based on the classical OHAM known as the predictor OHAM (POHAM) to predict the multiplicity of the solutions of nonlinear differential equations with boundary conditions. The validity and accuracy of this algorithm have been investigated for a mixed convection flow model in a vertical channel and a nonlinear model arising in heat transfer. OHAM is applied for the first time to linear, nonlinear and system of initial value problems of DDEs. Lastly, for the first time, the multistage technique based on OHAM (MOHAM) was presented and shown with a number of applications to get approximate analytical solutions for linear, nonlinear, system of initial value problems and for second-order nonlinear BVP with Robin and Neumann boundary conditions. MOHAM is more efficient and stable for a long time span than the standard OHAM in view of the cases examined. The results of the solutions of the equations studied using OHAM, POHAM, OHAM for DDEs and MOHAM were significant and reliable compared to the results from other techniques. It is concluded that OHAM, POHAM, OHAM for DDEs and MOHAM are very capable and efficient algorithms in finding analytical as well as numerical solutions for a wide class equations. These algorithms offer more realistic series solutions that converge very quickly to the exact solution and have remarkable low error.,Ph.D. | |
| dc.language.iso | eng | |
| dc.publisher | UKM, Bangi | |
| dc.relation | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
| dc.rights | UKM | |
| dc.subject | Homotopy theory | |
| dc.subject | Differential equations -- Asymptotic theory | |
| dc.subject | Differential equations | |
| dc.subject | Universiti Kebangsaan Malaysia -- Dissertations | |
| dc.subject | Dissertations, Academic -- Malaysia | |
| dc.title | Application and modifications of optimal homotopy asymptotic method for solutions of linear and nonlinear ordinary differential equations | |
| dc.type | Theses | |
| dc.format.pages | 172 | |
| dc.identifier.callno | QA612.7.A533 2015 tesis | |
| dc.identifier.barcode | 001810 | |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_83033+SOURCE1+SOURCE1.0.PDF Restricted Access | 1.15 MB | Adobe PDF |  View/Open |
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