Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models
In this paper, we present and demonstrate an innovative numerical method, which makes use of fuzzy numbers and fuzzy parameters that is effective in the solution of fuzzy type Volterra integro-differential equations, which was previously thought to be impossible using conventional methods. The first...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3991262 |
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| _version_ | 1832551813267587072 |
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| author | Jingwen Zhang |
| author_facet | Jingwen Zhang |
| author_sort | Jingwen Zhang |
| collection | DOAJ |
| description | In this paper, we present and demonstrate an innovative numerical method, which makes use of fuzzy numbers and fuzzy parameters that is effective in the solution of fuzzy type Volterra integro-differential equations, which was previously thought to be impossible using conventional methods. The first application of a technique for solving Volterra integro-differential equations of the fuzzy type, which was devised and tested in this paper, is shown here. This is the first time that this approach has been used. This system’s overall quality may be improved as a consequence of the use of the Hilbert space replicating kernel idea, which is a possibility. Separate evaluations are made of the algorithms’ correctness and sloppiness, as well as their foundations in the computationally effective kernel Hilbert space, which has been extensively researched in the past. Numerical examples are provided of the article to demonstrate how the technique outlined before may achieve convergence and accuracy. Here are a few illustrations to help understand that it is possible to deal with physical issues that require complicated geometric calculations with the assistance of the method explained in this article. |
| format | Article |
| id | doaj-art-6e277c07562542a28507b6fe05a2b7b6 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6e277c07562542a28507b6fe05a2b7b62025-02-03T06:00:27ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3991262Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential ModelsJingwen Zhang0Basic Teaching DepartmentIn this paper, we present and demonstrate an innovative numerical method, which makes use of fuzzy numbers and fuzzy parameters that is effective in the solution of fuzzy type Volterra integro-differential equations, which was previously thought to be impossible using conventional methods. The first application of a technique for solving Volterra integro-differential equations of the fuzzy type, which was devised and tested in this paper, is shown here. This is the first time that this approach has been used. This system’s overall quality may be improved as a consequence of the use of the Hilbert space replicating kernel idea, which is a possibility. Separate evaluations are made of the algorithms’ correctness and sloppiness, as well as their foundations in the computationally effective kernel Hilbert space, which has been extensively researched in the past. Numerical examples are provided of the article to demonstrate how the technique outlined before may achieve convergence and accuracy. Here are a few illustrations to help understand that it is possible to deal with physical issues that require complicated geometric calculations with the assistance of the method explained in this article.http://dx.doi.org/10.1155/2022/3991262 |
| spellingShingle | Jingwen Zhang Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models Journal of Mathematics |
| title | Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models |
| title_full | Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models |
| title_fullStr | Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models |
| title_full_unstemmed | Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models |
| title_short | Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models |
| title_sort | convergence analysis hilbert space approach for fuzzy integro differential models |
| url | http://dx.doi.org/10.1155/2022/3991262 |
| work_keys_str_mv | AT jingwenzhang convergenceanalysishilbertspaceapproachforfuzzyintegrodifferentialmodels |