Modified Sumudu Transform Analytical Approximate Methods For Solving Boundary Value Problems
In this study, emphasis is placed on analytical approximate methods. These methods include the combination of the Sumudu transform (ST) with the homotopy perturbation method (HPM), namely the Sumudu transform homotopy perturbation method (STHPM), the combination of the ST with the variational iterat...
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| Format: | Thesis |
| Language: | English |
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2019
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| Online Access: | http://eprints.usm.my/46592/1/Asem%20thesis24.pdf |
| _version_ | 1825905589269561344 |
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| author | Al-Nemrat, Asem Mustafa Moh’ad |
| author_facet | Al-Nemrat, Asem Mustafa Moh’ad |
| author_sort | Al-Nemrat, Asem Mustafa Moh’ad |
| collection | USM |
| description | In this study, emphasis is placed on analytical approximate methods. These methods include the combination of the Sumudu transform (ST) with the homotopy perturbation method (HPM), namely the Sumudu transform homotopy perturbation method (STHPM), the combination of the ST with the variational iteration method (VIM), namely the Sumudu transform variational iteration method (STVIM) and finally, the combination of the ST with the homotopy analysis method (HAM), namely the Sumudu transform homotopy analysis method (STHAM). Although these standard methods have been successfully used in solving various types of differential equations, they still suffer from the weakness in choosing the initial guess. In addition, they require an infinite number of iterations which negatively affect the accuracy and convergence of the solutions. The main objective of this thesis is to modify, apply and analyze these methods to handle the difficulties and drawbacks and find the analytical approximate solutions for some cases of linear and nonlinear ordinary differential equations (ODEs). These cases include second-order two-point boundary value problems (BVPs), singular and systems of second-order two-point BVPs. For the proposed methods, the trial function was employed as an initial approximation to provide more accurate approximate solutions for the considered problems. In addition, for the STVIM method, a new algorithm has been proposed to solve various kinds of linear and nonlinear second-order two-point BVPs. In this algorithm, the convolution theorem has been used to find an optimal Lagrange multiplier. |
| first_indexed | 2024-03-06T15:36:43Z |
| format | Thesis |
| id | usm.eprints-46592 |
| institution | Universiti Sains Malaysia |
| language | English |
| last_indexed | 2024-03-06T15:36:43Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | usm.eprints-465922020-06-22T03:19:15Z http://eprints.usm.my/46592/ Modified Sumudu Transform Analytical Approximate Methods For Solving Boundary Value Problems Al-Nemrat, Asem Mustafa Moh’ad QA1 Mathematics (General) In this study, emphasis is placed on analytical approximate methods. These methods include the combination of the Sumudu transform (ST) with the homotopy perturbation method (HPM), namely the Sumudu transform homotopy perturbation method (STHPM), the combination of the ST with the variational iteration method (VIM), namely the Sumudu transform variational iteration method (STVIM) and finally, the combination of the ST with the homotopy analysis method (HAM), namely the Sumudu transform homotopy analysis method (STHAM). Although these standard methods have been successfully used in solving various types of differential equations, they still suffer from the weakness in choosing the initial guess. In addition, they require an infinite number of iterations which negatively affect the accuracy and convergence of the solutions. The main objective of this thesis is to modify, apply and analyze these methods to handle the difficulties and drawbacks and find the analytical approximate solutions for some cases of linear and nonlinear ordinary differential equations (ODEs). These cases include second-order two-point boundary value problems (BVPs), singular and systems of second-order two-point BVPs. For the proposed methods, the trial function was employed as an initial approximation to provide more accurate approximate solutions for the considered problems. In addition, for the STVIM method, a new algorithm has been proposed to solve various kinds of linear and nonlinear second-order two-point BVPs. In this algorithm, the convolution theorem has been used to find an optimal Lagrange multiplier. 2019-08 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/46592/1/Asem%20thesis24.pdf Al-Nemrat, Asem Mustafa Moh’ad (2019) Modified Sumudu Transform Analytical Approximate Methods For Solving Boundary Value Problems. PhD thesis, Universiti Sains Malaysia. |
| spellingShingle | QA1 Mathematics (General) Al-Nemrat, Asem Mustafa Moh’ad Modified Sumudu Transform Analytical Approximate Methods For Solving Boundary Value Problems |
| title | Modified Sumudu Transform
Analytical Approximate Methods For
Solving Boundary Value Problems |
| title_full | Modified Sumudu Transform
Analytical Approximate Methods For
Solving Boundary Value Problems |
| title_fullStr | Modified Sumudu Transform
Analytical Approximate Methods For
Solving Boundary Value Problems |
| title_full_unstemmed | Modified Sumudu Transform
Analytical Approximate Methods For
Solving Boundary Value Problems |
| title_short | Modified Sumudu Transform
Analytical Approximate Methods For
Solving Boundary Value Problems |
| title_sort | modified sumudu transform analytical approximate methods for solving boundary value problems |
| topic | QA1 Mathematics (General) |
| url | http://eprints.usm.my/46592/1/Asem%20thesis24.pdf |
| work_keys_str_mv | AT alnemratasemmustafamohad modifiedsumudutransformanalyticalapproximatemethodsforsolvingboundaryvalueproblems |