Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness
A Master of Science thesis in Mathematics by Amer Mahmoud Malbanji entitled, "Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness," submitted in May 2017. Thesis advisor is Dr. Suheil A. Khoury. Soft and hard copy available.
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | doctoralThesis |
| منشور في: |
2017
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/8860 |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513443293298688 |
|---|---|
| author | Malbanji, Amer Mahmoud |
| author_facet | Malbanji, Amer Mahmoud |
| author_role | author |
| dc.contributor.none.fl_str_mv | Khoury, Suheil A. |
| dc.creator.none.fl_str_mv | Malbanji, Amer Mahmoud |
| dc.date.none.fl_str_mv | 2017-06-04T09:37:21Z 2017-06-04T09:37:21Z 2017-05 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2017.08 http://hdl.handle.net/11073/8860 |
| dc.language.none.fl_str_mv | en_US |
| dc.subject.none.fl_str_mv | Fourth Order BVPs Green's Function Fixed Point Iteration Picard Iteration Mann Iteration Beam Theory Dynamics Existence Uniqueness Iterations Convergence Numerical solutions Boundary value problems Differential equations, Nonlinear Green's functions |
| dc.title.none.fl_str_mv | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/doctoralThesis |
| description | A Master of Science thesis in Mathematics by Amer Mahmoud Malbanji entitled, "Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness," submitted in May 2017. Thesis advisor is Dr. Suheil A. Khoury. Soft and hard copy available. |
| format | doctoralThesis |
| id | aus_efb33bae5ca49942eed78d43e96b0fe4 |
| identifier_str_mv | 29.232-2017.08 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/8860 |
| publishDate | 2017 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Solving Fourth Order Differential Non-Linear Equations, Existence and UniquenessMalbanji, Amer MahmoudFourth Order BVPsGreen's FunctionFixed Point IterationPicard IterationMann IterationBeam TheoryDynamicsExistenceUniquenessIterations ConvergenceNumerical solutionsBoundary value problemsDifferential equations, NonlinearGreen's functionsA Master of Science thesis in Mathematics by Amer Mahmoud Malbanji entitled, "Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness," submitted in May 2017. Thesis advisor is Dr. Suheil A. Khoury. Soft and hard copy available.The aim of this thesis is to present a novel numerical approach for the solution of a class of non-linear fourth-order boundary value problems. The method is based on embedding Green's function into some fixed point iteration schemes, an idea previously used in other works to investigate nonlinear boundary value problems of lower order. To this end, the thesis is divided in 6 chapters. The first chapter is a short description of the main ideas of this thesis. The second chapter represents a review on Green's functions for differential equations. In Chapter 3 some existence and uniqueness results for the fourth order boundary value problems are presented. The proposed numerical method is then explained and applied on numerical examples in Chapter 4, where a comparison with the Spline method is also given, demonstrating thus that our method yields accurate results up to 10 e-20, compared to the Spline method, where the results are accurate up to 10 e-13. The results obtained by our method were achieved within a reasonable time limit compared with other methods. Chapter 5 is concerned with the convergence analysis of our method. More precisely, some conditions which guarantees the convergence of the solution under specific conditions is given. For the proof we used the Banach-Picard theorem along with the Green's function. Finally, in Chapter 6 we present a short conclusions and a summary of the whole thesis.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Khoury, Suheil A.2017-06-04T09:37:21Z2017-06-04T09:37:21Z2017-05info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2017.08http://hdl.handle.net/11073/8860en_USoai:repository.aus.edu:11073/88602025-06-26T12:31:02Z |
| spellingShingle | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness Malbanji, Amer Mahmoud Fourth Order BVPs Green's Function Fixed Point Iteration Picard Iteration Mann Iteration Beam Theory Dynamics Existence Uniqueness Iterations Convergence Numerical solutions Boundary value problems Differential equations, Nonlinear Green's functions |
| status_str | publishedVersion |
| title | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness |
| title_full | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness |
| title_fullStr | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness |
| title_full_unstemmed | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness |
| title_short | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness |
| title_sort | Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness |
| topic | Fourth Order BVPs Green's Function Fixed Point Iteration Picard Iteration Mann Iteration Beam Theory Dynamics Existence Uniqueness Iterations Convergence Numerical solutions Boundary value problems Differential equations, Nonlinear Green's functions |
| url | http://hdl.handle.net/11073/8860 |