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https://ptsldigital.ukm.my/jspui/handle/123456789/499471Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Ishak Hashim, Prof. Dr. | |
| dc.contributor.author | Mohammad Maleki (P57881) | |
| dc.date.accessioned | 2023-10-13T09:32:12Z | - |
| dc.date.available | 2023-10-13T09:32:12Z | - |
| dc.date.issued | 2014-04-21 | |
| dc.identifier.other | ukmvital:74820 | |
| dc.identifier.uri | https://ptsldigital.ukm.my/jspui/handle/123456789/499471 | - |
| dc.description | As problems with time-delay and problems involving fractional derivatives describe systems with memory, innovative multiple-interval numerical methods are needed to solve them. Adaptive pseudospectral or multiple-interval orthogonal collocation methods have become quite popular in several field areas due to their high accuracy and their suitability for nonsmooth solutions. In this thesis, some error estimates for the multiple-interval Lagrange interpolation based on shifted Legendre-Gauss (ShLG) and shifted Legendre-Gauss-Radau (ShLGR) points are first analyzed. Then, an adaptive collocation method using ShLGR points is developed for solving time-varying constant delay systems. This method replaces the delay system with a sequence of initial value problems (IVPs) and interacts well with the method of steps. Next, a new adaptive pseudospectral method using ShLG points is presented for solving constrained linear optimal control problems with state and/or input delays. The linear time-delay optimal control problem is transcribed to a quadratic programming problem. This method provides accurate approximations to piecewise smooth controls. Furthermore, an iterative-adaptive ShLG pseudospectral method using the quasilinearization scheme is developed for solving nonlinear time-delay optimal control problems. The nonlinear problem is converted into a sequence of linear-quadratic sub-problems whose solutions converge to the solution of the original nonlinear problem. Further, a one-step and a multiple-step adaptive ShLG pseudospectral methods are presented for solving multi-term fractional boundary value problems (FBVPs) and fractional IVPs (FIVPs) involving Caputo derivatives. The first method converts a FBVP to a singular Volterra integro-differential equation (SVIDE) and then reduces it to a system of algebraic equations. The second method first converts a FIVP into a sequence of SVIDEs in subintervals and then, step by step, reduces them to a sequence of systems of algebraic equations. Lastly, a new direct adaptive ShLG pseudospectral method for solving a class of fractional variational problems (FVPs) that involve Caputo fractional derivatives is presented. A pseudospectral scheme is introduced for approximating the fractional derivatives of order 0 < α < 1 at the ShLG points. The FVP is then transcribed to a nonlinear programming problem. Some error estimates and convergence properties of the method are also discussed. The computational efficiency and accuracy of the adaptive pseudospectral methods developed in this thesis is demonstrated on several examples ranging from problems whose solutions are smooth to problems whose solutions are not smooth. It is shown empirically that the accuracy of the solution can be improved either by increasing the number of collocation points within each mesh interval or by decreasing the mesh spacing. Consequently, the proposed methods are both more flexible and more accurate than global collocation methods. It is also shown that the proposed methods are highly suited for large-domain calculations and also for some solutions having oscillatory behavior.,PhD | |
| dc.language.iso | eng | |
| dc.publisher | UKM, Bangi | |
| dc.relation | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
| dc.rights | UKM | |
| dc.subject | Adaptive pseudospectral | |
| dc.subject | Adaptive pseudospectral methods | |
| dc.subject | Solving time-delay | |
| dc.subject | Fractional order problems | |
| dc.subject | Universiti Kebangsaan Malaysia -- Dissertations | |
| dc.title | Adaptive pseudospectral methods for solving time-delay and fractional order problems | |
| dc.type | Theses | |
| dc.format.pages | 204 | |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_74820+Source01+Source010.PDF Restricted Access | 4.36 MB | Adobe PDF |  View/Open |
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