Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions
The ordinary differential equation of second order is being used in many engineering disciplines and sciences to model many real-life problems. These problems are mostly uncertain, vague and incomplete and thus they require some more advanced tool for modelling. Neutrosophic logic becomes the soluti...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of New Mexico
2020-11-01
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| Series: | Neutrosophic Sets and Systems |
| Subjects: | |
| Online Access: | https://fs.unm.edu/NSS/SumuduTransformForSolvingSecond18.pdf |
| _version_ | 1797774503676215296 |
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| author | Meghna Parikh Manoj Sahni |
| author_facet | Meghna Parikh Manoj Sahni |
| author_sort | Meghna Parikh |
| collection | DOAJ |
| description | The ordinary differential equation of second order is being used in many engineering disciplines and sciences to model many real-life problems. These problems are mostly uncertain, vague and incomplete and thus they require some more advanced tool for modelling. Neutrosophic logic becomes the solution of all these kind of uncertain problems as it describe the conditions of uncertainty which occurs during the process of modelling on the basis of grade of membership of truth values, indeterminacy values and falsity values, that means it consider all the uncertain parameters on the basis of these degrees. In this research paper, we have considered the ordinary differential equation of second order with neutrosophic numbers as initial conditions of spring mass system is solved using Sumudu transform method which has advantage of unit preserving property over the well established Laplace Transform method. The solution obtained at various computational points by this method is shown in the form of table. Furthermore, the results obtained at different (α, β, γ)-cut and time values are also depicted graphically and are verified analytically by de-fuzzifying the data. |
| first_indexed | 2024-03-12T22:21:03Z |
| format | Article |
| id | doaj.art-b9beb868c2194ef89dcd9a2162f759f6 |
| institution | Directory Open Access Journal |
| issn | 2331-6055 2331-608X |
| language | English |
| last_indexed | 2024-03-12T22:21:03Z |
| publishDate | 2020-11-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj.art-b9beb868c2194ef89dcd9a2162f759f62023-07-23T07:33:38ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2020-11-013825827510.5281/zenodo.4300510Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial ConditionsMeghna ParikhManoj SahniThe ordinary differential equation of second order is being used in many engineering disciplines and sciences to model many real-life problems. These problems are mostly uncertain, vague and incomplete and thus they require some more advanced tool for modelling. Neutrosophic logic becomes the solution of all these kind of uncertain problems as it describe the conditions of uncertainty which occurs during the process of modelling on the basis of grade of membership of truth values, indeterminacy values and falsity values, that means it consider all the uncertain parameters on the basis of these degrees. In this research paper, we have considered the ordinary differential equation of second order with neutrosophic numbers as initial conditions of spring mass system is solved using Sumudu transform method which has advantage of unit preserving property over the well established Laplace Transform method. The solution obtained at various computational points by this method is shown in the form of table. Furthermore, the results obtained at different (α, β, γ)-cut and time values are also depicted graphically and are verified analytically by de-fuzzifying the data.https://fs.unm.edu/NSS/SumuduTransformForSolvingSecond18.pdffuzzy numbersneutrosophic numbersneutrosophic triangular numbersstrongly-generalized differentiabilitysumudu transform |
| spellingShingle | Meghna Parikh Manoj Sahni Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions Neutrosophic Sets and Systems fuzzy numbers neutrosophic numbers neutrosophic triangular numbers strongly-generalized differentiability sumudu transform |
| title | Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions |
| title_full | Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions |
| title_fullStr | Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions |
| title_full_unstemmed | Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions |
| title_short | Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions |
| title_sort | sumudu transform for solving second order ordinary differential equation under neutrosophic initial conditions |
| topic | fuzzy numbers neutrosophic numbers neutrosophic triangular numbers strongly-generalized differentiability sumudu transform |
| url | https://fs.unm.edu/NSS/SumuduTransformForSolvingSecond18.pdf |
| work_keys_str_mv | AT meghnaparikh sumudutransformforsolvingsecondorderordinarydifferentialequationunderneutrosophicinitialconditions AT manojsahni sumudutransformforsolvingsecondorderordinarydifferentialequationunderneutrosophicinitialconditions |