dc.contributor.advisor Khoury, Suheil A. dc.contributor.author Abushammala, Mariam B. H. dc.date.accessioned 2014-09-21T06:04:53Z dc.date.available 2014-09-21T06:04:53Z dc.date.issued 2014-06 dc.identifier.other 29.232-2014.04 dc.identifier.uri http://hdl.handle.net/11073/7501 dc.description A Master of Science thesis in Mathematics by Mariam B. H. Abushammala entitled, "Iterative Methods for the Numerical Solutions of Boundary Value Problems," submitted in June 2014. Thesis advisor is Dr. Suheil A. Khoury. Available are both hard and soft copies of the thesis. en_US dc.description.abstract The aim of this thesis is twofold. First of all, in Chapters 1 and 2, we review the well-known Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM) for obtaining exact and numerical solutions for ordinary differential equations, partial differential equations, integral equations, integro-differential equations, delay differential equations, and algebraic equations in addition to calculus of variations problems. These schemes yield highly accurate solutions. However, local convergence is a main setback of such approaches. It means that the accuracy deteriorates as the specified domain becomes larger, that is as we move away from the initial conditions. Secondly, we present an alternative uniformly convergent iterative scheme that applies to an extended class of linear and nonlinear third order boundary value problems that arise in physical applications. The method is based on embedding Green's functions into well-established fixed point iterations, including Picard's and Krasnoselskii-Mann's schemes. The effectiveness of the proposed scheme is established by implementing it on several numerical examples, including linear and nonlinear third order boundary value problems. The resulting numerical solutions are compared with both the analytical and the numerical solutions that exist in the literature. From the results, it is observed that the present method approximates the exact solution very well and yields more accurate results than the ADM and the VIM. Finally, the numerical results confirm the applicability and superiority of the introduced method for tackling various nonlinear equations. en_US dc.description.sponsorship College of Arts and Sciences en_US dc.description.sponsorship Department of Mathematics and Statistics en_US dc.language.iso en_US en_US dc.relation.ispartofseries Master of Science in Mathematics (MSMTH) en_US dc.relation.ispartofseries American University of Sharjah Student Work en_US dc.subject Adomian Decomposition Method (ADM) en_US dc.subject Variational Iteration Method (VIM) en_US dc.subject numerical solutions en_US dc.subject Green's functions en_US dc.subject Picard's scheme en_US dc.subject Krasnoselskii-Mann's scheme en_US dc.subject.lcsh Boundary value problems en_US dc.subject.lcsh Mathematics en_US dc.title Iterative Methods for the Numerical Solutions of Boundary Value Problems en_US dc.type Thesis en_US
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