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dc.contributor.advisorKhoury, Suheil A.
dc.contributor.authorAbushammala, Mariam B. H.
dc.date.accessioned2014-09-21T06:04:53Z
dc.date.available2014-09-21T06:04:53Z
dc.date.issued2014-06
dc.identifier.other29.232-2014.04
dc.identifier.urihttp://hdl.handle.net/11073/7501
dc.descriptionA 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.abstractThe 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.sponsorshipCollege of Arts and Sciencesen_US
dc.description.sponsorshipDepartment of Mathematics and Statisticsen_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesMaster of Science in Mathematics (MSMTH)en_US
dc.relation.ispartofseriesAmerican University of Sharjah Student Worken_US
dc.subjectAdomian Decomposition Method (ADM)en_US
dc.subjectVariational Iteration Method (VIM)en_US
dc.subjectnumerical solutionsen_US
dc.subjectGreen's functionsen_US
dc.subjectPicard's schemeen_US
dc.subjectKrasnoselskii-Mann's schemeen_US
dc.subject.lcshBoundary value problemsen_US
dc.subject.lcshMathematicsen_US
dc.titleIterative Methods for the Numerical Solutions of Boundary Value Problemsen_US
dc.typeThesisen_US


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