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https://ptsldigital.ukm.my/jspui/handle/123456789/500347Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Ishak Hashim, Prof. Dr. | |
| dc.contributor.author | Khaled Yousef Ahmad Moaddy (P47400) | |
| dc.date.accessioned | 2023-10-13T09:41:55Z | - |
| dc.date.available | 2023-10-13T09:41:55Z | - |
| dc.date.issued | 2012-04-19 | |
| dc.identifier.other | ukmvital:117473 | |
| dc.identifier.uri | https://ptsldigital.ukm.my/jspui/handle/123456789/500347 | - |
| dc.description | A great deal of effort has been paid recently in an attempt to find robust and stable numerical and analytical methods for solving fractional or non-fractional differential equations. In this thesis, the non-standard finite difference method (in short NSFD) is implemented to give numerical solutions for various types of differential equations of integer and non-integer orders. NSFD has developed as an alternative method for solving a wide range of problems whose mathematical models involve algebraic, differential, biological, and chaotic systems. The technique has many advantages over the classical techniques, and provides an efficient numerical solution. The NSFD was introduced and demonstrated for the first time with different applications to investigate the natural convection in a 2-D porous enclosure with an inclined magnetic and non-uniform internal heating, linear inhomogeneous time-fractional equation, linear space-fractional telegraph equation, linear inhomogeneous fractional Burgers equation, and the fractional wave equation. Further, the general framework of the NSFD solution for fractional-order chaotic and hyperchaotic systems was proposed. The fractional-order Rössler system and Chua's circuit were used to test the applicability of the framework. Moreover, NSFD was also adopted to obtain the attractor for chaotic system in Memristor-based fractional-order Chua's circuit and it's stability in both the W-plane and s-plane for general different orders. The general framework for the NSFD solution of the chaotic synchronization with a gap junction of multi-coupled-neurons of fractional-orders was presented. Furthermore, the synchronization of multi-coupled-neurons was studied with different fractional-orders and with different values of the synchronization parameter. In addition, the NSFD has been successfully applied to find the numeric simulations of the synchronization of different fractional-order chaotic systems using active control. Four different synchronization cases, six different examples with different orders, and static and dynamic synchronization are introduced in this thesis. These examples are based on a new block diagram controlled by two switching parameters. Finally, a hybrid non-standard finite difference and Adomian decomposition method (NSFD-ADM) was introduced. The new scheme does not need to linearize or non-locally linearize the nonlinear term of the differential equation. Two examples are given to demonstrate the efficiency of this scheme. Comparisons of the results obtained by the NSFD and the fourth-order Runge-Kutta method (RK4) reveal that the NSFD-ADM is a powerful method for solving nonlinear systems for longer time span.,Tesis ini tiada perakuan deklarasi pelajar,Doktor Falsafah | |
| dc.language.iso | eng | |
| dc.publisher | UKM, Bangi | |
| dc.relation | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
| dc.rights | UKM | |
| dc.subject | Finite differences | |
| dc.subject | Differential equations | |
| dc.subject | numerical solutions | |
| dc.title | Non-standard finite difference solutions for integer and non-integer order differential equations | |
| dc.type | Theses | |
| dc.format.pages | 135 | |
| dc.identifier.callno | QA431.M633 2012 tesis | |
| dc.identifier.barcode | 002588 (2012) | |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_117473+SOURCE1+SOURCE1.0.PDF Restricted Access | 774.91 kB | Adobe PDF |  View/Open |
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