An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques
We consider a novel approach to providing highly accurate analytic solutions to non-classical, non-linear problems. This approach is then implemented to the highly sensitive Troesch-problem, which possesses a boundary layer at the right-end: we determine an upper and lower envelope solution, and com...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-12-01
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| Series: | Chaos, Solitons & Fractals: X |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590054423000064 |
| _version_ | 1797400866880225280 |
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| author | Mihai Halic Roshan Tajarod Helmi Temimi |
| author_facet | Mihai Halic Roshan Tajarod Helmi Temimi |
| author_sort | Mihai Halic |
| collection | DOAJ |
| description | We consider a novel approach to providing highly accurate analytic solutions to non-classical, non-linear problems. This approach is then implemented to the highly sensitive Troesch-problem, which possesses a boundary layer at the right-end: we determine an upper and lower envelope solution, and compare the average to existing numerical results. Computer simulations show that the proposed analytic solution is highly accurate when compared to the existing benchmark. This confirms that the proposed approach to deal with such non-linear problems can be used to treat similar non-classical boundary-value problems. |
| first_indexed | 2024-03-09T02:01:46Z |
| format | Article |
| id | doaj.art-702aac3518eb44ca87b13bc63c16d20a |
| institution | Directory Open Access Journal |
| issn | 2590-0544 |
| language | English |
| last_indexed | 2024-03-09T02:01:46Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Chaos, Solitons & Fractals: X |
| spelling | doaj.art-702aac3518eb44ca87b13bc63c16d20a2023-12-08T04:45:55ZengElsevierChaos, Solitons & Fractals: X2590-05442023-12-0111100096An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope TechniquesMihai Halic0Roshan Tajarod1Helmi Temimi2Corresponding author.; Dept. Mathematics and Natural Sciences, Gulf University for Science and Technology, Masjid Al Aqsa St., Mubarak Al-Abdullah, West Mishref, KuwaitDept. Mathematics and Natural Sciences, Gulf University for Science and Technology, Masjid Al Aqsa St., Mubarak Al-Abdullah, West Mishref, KuwaitDept. Mathematics and Natural Sciences, Gulf University for Science and Technology, Masjid Al Aqsa St., Mubarak Al-Abdullah, West Mishref, KuwaitWe consider a novel approach to providing highly accurate analytic solutions to non-classical, non-linear problems. This approach is then implemented to the highly sensitive Troesch-problem, which possesses a boundary layer at the right-end: we determine an upper and lower envelope solution, and compare the average to existing numerical results. Computer simulations show that the proposed analytic solution is highly accurate when compared to the existing benchmark. This confirms that the proposed approach to deal with such non-linear problems can be used to treat similar non-classical boundary-value problems.http://www.sciencedirect.com/science/article/pii/S2590054423000064Primary 34B15Secondary 34L3034B60 |
| spellingShingle | Mihai Halic Roshan Tajarod Helmi Temimi An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques Chaos, Solitons & Fractals: X Primary 34B15 Secondary 34L30 34B60 |
| title | An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques |
| title_full | An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques |
| title_fullStr | An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques |
| title_full_unstemmed | An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques |
| title_short | An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques |
| title_sort | accurate analytical solution to troesch s problem through lower and upper envelope techniques |
| topic | Primary 34B15 Secondary 34L30 34B60 |
| url | http://www.sciencedirect.com/science/article/pii/S2590054423000064 |
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