1. UKM Learning and Research Repository
2. PHD Thesis / Tesis PHD
3. Faculty of Science and Technology / Fakulti Sains dan Teknologi

Title:	Approximate solutions for different types of differential equations based on operational matrices of Bernstein polynomials
Authors:	Sana'a Nazmi Yousef Khataybeh (P82707)
Supervisor:	Ishak Hashim, Prof. Dr.
Keywords:	Bernstein polynomials Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	8-Jan-2019
Description:	In this thesis, different types of differential equations were solved approximately based on operational matrices of Bernstein polynomials. Bernstein polynomials and their operational matrices have many important properties, such as continuity and unity partition, which makes them suitable for solving differential equations. First, an operational matrix of derivative was extended and applied with Chebyshev collocation points to solve directly a class of third-order ordinary differential equations (ODEs) including the famous Blasius' equation describing a boundary layer flow over a flat plate and a thirdorder ODE for thin film flow. The equations were first converted to a system of algebraic equations, which were then solved using a computer algebra system. Next, a new operational matrix of derivative based on general Bernstein polynomials defined on [a, b],which have the same properties as the classical Bernstein polynomials on [0,1], was employed to solve systems of second-order ODEs on an arbitrary interval by dividing it into subintervals. This method was applied iteratively on each subinterval using general Bernstein polynomials and Chebyshev collocation points for the arbitrary interval [a, b]. The approximate solutions obtained in series form were tested on several examples to determine the validity and applicability of the introduced method. Furthermore, an operational matrices method based on modified Bernstein polynomials with a suitable collocation point was introduced to find an approximate solution for nonlinear Bratu's equation. Finally, a novel approach for obtaining operational matrices method for integration and differentiation based on Bernstein polynomials was presented to solve higher-order boundary-value problems of integro-differential equations and systems of Volterra integral equations. The equations were converted into algebraic systems which can be easily solved directly. Comparisons were made in terms of the absolute errors for all examples. Also, numerical results presented in this thesis for three important types of differential equations, given by ODEs, fractional differential equations, and integrodifferential equations, demonstrated that the method based on operational matrices of Bernstein polynomials are promising tools for nonlinear equations.,'Certification of Masters/Doctoral Thesis' is not available,Ph.D.
Pages:	141
Call Number:	QA295.K483 2019 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.