Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approxi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/26/1/18 |
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| author | Riccardo Fazio |
| author_facet | Riccardo Fazio |
| author_sort | Riccardo Fazio |
| collection | DOAJ |
| description | This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context, the numerical test is illustrated by two examples where we find meaningful numerical results. |
| first_indexed | 2024-03-09T00:36:58Z |
| format | Article |
| id | doaj.art-e531d987b44d4c66a74e10cb0a62ddf5 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-09T00:36:58Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-e531d987b44d4c66a74e10cb0a62ddf52023-12-11T18:09:23ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472021-02-012611810.3390/mca26010018Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation MethodRiccardo Fazio0Department of Mathematics, Computer Science, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno D’Alcontres, 31, 98166 Messina, ItalyThis work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context, the numerical test is illustrated by two examples where we find meaningful numerical results.https://www.mdpi.com/2297-8747/26/1/18boundary value problemssemi-infinite intervalsexistence and uniquenessiterative transformation methodnumerical test |
| spellingShingle | Riccardo Fazio Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method Mathematical and Computational Applications boundary value problems semi-infinite intervals existence and uniqueness iterative transformation method numerical test |
| title | Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method |
| title_full | Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method |
| title_fullStr | Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method |
| title_full_unstemmed | Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method |
| title_short | Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method |
| title_sort | existence and uniqueness of bvps defined on semi infinite intervals insight from the iterative transformation method |
| topic | boundary value problems semi-infinite intervals existence and uniqueness iterative transformation method numerical test |
| url | https://www.mdpi.com/2297-8747/26/1/18 |
| work_keys_str_mv | AT riccardofazio existenceanduniquenessofbvpsdefinedonsemiinfiniteintervalsinsightfromtheiterativetransformationmethod |