N-dimensional quintic B-spline functions for solving n-dimensional partial differential equations
In continuation to what we started from developing the B-spline functions and putting them in n-dimensional to solve mathematical models in n-dimensions, we present in this article a new structure for the quintic B-spline collocation algorithm in n-dimensional. The quintic B-spline collocation algor...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-04-01
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| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2022-0016 |
| _version_ | 1811235782321504256 |
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| author | Raslan K. R. Ali Khalid K. Al-Jeaid Hind K. |
| author_facet | Raslan K. R. Ali Khalid K. Al-Jeaid Hind K. |
| author_sort | Raslan K. R. |
| collection | DOAJ |
| description | In continuation to what we started from developing the B-spline functions and putting them in n-dimensional to solve mathematical models in n-dimensions, we present in this article a new structure for the quintic B-spline collocation algorithm in n-dimensional. The quintic B-spline collocation algorithm is shown in three different formats: one, two, and three dimensional. These constructs are critical for solving mathematical models in different fields. The proposed method’s efficiency and accuracy are illustrated by their application to a few two- and three-dimensional test problems. We use other numerical methods available in the literature to make comparisons. |
| first_indexed | 2024-04-12T11:57:56Z |
| format | Article |
| id | doaj.art-4626fd41aa9f4bfd9aacea58e012d0d1 |
| institution | Directory Open Access Journal |
| issn | 2192-8029 |
| language | English |
| last_indexed | 2024-04-12T11:57:56Z |
| publishDate | 2022-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-4626fd41aa9f4bfd9aacea58e012d0d12022-12-22T03:33:57ZengDe GruyterNonlinear Engineering2192-80292022-04-0111112313410.1515/nleng-2022-0016N-dimensional quintic B-spline functions for solving n-dimensional partial differential equationsRaslan K. R.0Ali Khalid K.1Al-Jeaid Hind K.2Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptDepartment of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptDepartment of Mathematical Sciences, Umm Al-Qura University, Makkah, KSAIn continuation to what we started from developing the B-spline functions and putting them in n-dimensional to solve mathematical models in n-dimensions, we present in this article a new structure for the quintic B-spline collocation algorithm in n-dimensional. The quintic B-spline collocation algorithm is shown in three different formats: one, two, and three dimensional. These constructs are critical for solving mathematical models in different fields. The proposed method’s efficiency and accuracy are illustrated by their application to a few two- and three-dimensional test problems. We use other numerical methods available in the literature to make comparisons.https://doi.org/10.1515/nleng-2022-0016collocation methodn-dimensional b-spline functionsmathematical models |
| spellingShingle | Raslan K. R. Ali Khalid K. Al-Jeaid Hind K. N-dimensional quintic B-spline functions for solving n-dimensional partial differential equations Nonlinear Engineering collocation method n-dimensional b-spline functions mathematical models |
| title | N-dimensional quintic B-spline functions for solving n-dimensional partial differential equations |
| title_full | N-dimensional quintic B-spline functions for solving n-dimensional partial differential equations |
| title_fullStr | N-dimensional quintic B-spline functions for solving n-dimensional partial differential equations |
| title_full_unstemmed | N-dimensional quintic B-spline functions for solving n-dimensional partial differential equations |
| title_short | N-dimensional quintic B-spline functions for solving n-dimensional partial differential equations |
| title_sort | n dimensional quintic b spline functions for solving n dimensional partial differential equations |
| topic | collocation method n-dimensional b-spline functions mathematical models |
| url | https://doi.org/10.1515/nleng-2022-0016 |
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