Solving initial and boundary value problems by homotopy perturbation method /
The viability of homotopy perturbation method (HPM) in treating the initial (IVPs) and boundary value problems (BVPs) is examined. The HPM is a merging between perturbation method and homotopy method. The crucial aspect of HPM is the ability to deform a difficult problem into set of easier equations...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
Kuala Lumpur :
Kulliyyah of Engineering, International Islamic University Malaysia,
2015
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| Subjects: | |
| Online Access: | Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. |
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| 041 | |a eng | ||
| 043 | |a a-my--- | ||
| 050 | 0 | 0 | |a QA612.7 |
| 100 | 0 | |a Nur Isnida binti Razali | |
| 245 | 1 | |a Solving initial and boundary value problems by homotopy perturbation method / |c by Nur Isnida binti Razali | |
| 260 | |a Kuala Lumpur : |b Kulliyyah of Engineering, International Islamic University Malaysia, |c 2015 | ||
| 300 | |a xiv, 125 leaves : |b ill. ; |c 30cm. | ||
| 502 | |a Thesis (MSCM)--International Islamic University Malaysia, 2015. | ||
| 504 | |a Includes bibliographical references (leaves 111-118). | ||
| 520 | |a The viability of homotopy perturbation method (HPM) in treating the initial (IVPs) and boundary value problems (BVPs) is examined. The HPM is a merging between perturbation method and homotopy method. The crucial aspect of HPM is the ability to deform a difficult problem into set of easier equations. The solution of HPM shows rapid convergence towards exact or approximate numerical solution. Chaos is a very exciting phenomenon in nonlinear science and has been studied over the last three decades. Due to high unpredictability and extreme sensitivity towards initial conditions, it has been applied widely various field. However, there is also lack of literature available in finding the approximate solution of chaotic system. Thus several chaotic and hyper chaotic system including chaotic Rossler, Lu and hyper chaotic Lu, Chen and Lorenz are selected in this study. The solutions of HPM valid for only a small time span as comparing to the solution of RK4 and its multistage HPM (MHPM) is used to extend the validity domains by recursively applying the HPM over successive time intervals. The time step of is used for RK4 and MHPM for entire calculations. The results show that the solutions by MHPM agree very well to those by RK4. The solution of HPM for linear BVPs of heat problems indicate a great result that quickly converges to the exact solution with 6 terms used. Besides that, the HPM which is also tested to the wave equation gives a remarkable with 6 terms added together. Another example is nonlinear BVP with product nonlinearity. The HPM solves this problem using only 3 terms. At t=0.6s, the solution totally same with the exact solution. Comparing to Adomian decomposition method (ADM), with 2 terms involved, the HPM presents better solution. Also, the HPM is tested to the seventh-order nonlinear BVPs which give excellent solution using only 3 terms. In addition, a new alternative approach of HPM (NAAHPM) is introduced in this thesis to choose initial component that helps in minimizing computational work and pace up the convergence of HPM series solution. The NAAHPM can overcome the limitations of the alternative approach of HPM (AAHPM) which is on trial basis only. Thus it can be concluded that the HPM is a very powerful and efficient in finding analytical as well as approximate numerical solution for a wide range of initial and boundary value problems. | ||
| 596 | |a 1 | ||
| 655 | 7 | |a Theses, IIUM local | |
| 690 | |a Dissertations, Academic |x Department of Mechanical Engineering |z IIUM | ||
| 710 | 2 | |a International Islamic University Malaysia. |b Department of Mechatronics Engineering | |
| 856 | 4 | |u http://studentrepo.iium.edu.my/handle/123456789/5224 |z Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. | |
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