A new adaptive nonlinear numerical method for singular and stiff differential problems
In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life. Starting with a fixed step size, the new method’s performance can be significantly enhanced by introducing an adaptive step-size approach. The q...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-07-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016823004167 |
| _version_ | 1797795257369231360 |
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| author | Sania Qureshi Moses Adebowale Akanbi Asif Ali Shaikh Ashiribo Senapon Wusu Oladotun Matthew Ogunlaran W. Mahmoud M.S. Osman |
| author_facet | Sania Qureshi Moses Adebowale Akanbi Asif Ali Shaikh Ashiribo Senapon Wusu Oladotun Matthew Ogunlaran W. Mahmoud M.S. Osman |
| author_sort | Sania Qureshi |
| collection | DOAJ |
| description | In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life. Starting with a fixed step size, the new method’s performance can be significantly enhanced by introducing an adaptive step-size approach. The qualitative properties of the proposed method have been investigated to determine the efficiency and reliability of the method. The proposed method is of fifth-order accuracy, zero stable, L-stable, and consistent. In addition, the proposed method is convergent, and its stability properties are also shown through its Order Stars. Finally, numerical experiments are conducted to illustrate the performance of the method. The results obtained show that the proposed method compares favourably with existing methods. |
| first_indexed | 2024-03-13T03:15:12Z |
| format | Article |
| id | doaj.art-a0396ed890a04d83a8aa10df081c4342 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-03-13T03:15:12Z |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-a0396ed890a04d83a8aa10df081c43422023-06-26T04:13:34ZengElsevierAlexandria Engineering Journal1110-01682023-07-0174585597A new adaptive nonlinear numerical method for singular and stiff differential problemsSania Qureshi0Moses Adebowale Akanbi1Asif Ali Shaikh2Ashiribo Senapon Wusu3Oladotun Matthew Ogunlaran4W. Mahmoud5M.S. Osman6Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan; Department of Mathematics, Near East University, 99138 Mersin, Turkey; Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, LebanonMathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, Osun State, Nigeria; Department of Mathematics; and Africa Centre of Excellence for Innovative and Transformative STEM Education (ACEITSE), Lagos State University, Lagos, NigeriaDepartment of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan; Department of Mathematics, Near East University, 99138 Mersin, TurkeyDepartment of Mathematics; and Africa Centre of Excellence for Innovative and Transformative STEM Education (ACEITSE), Lagos State University, Lagos, NigeriaMathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, Osun State, NigeriaDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt; Corresponding authors.Department of Mathematics, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia; Corresponding authors.In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life. Starting with a fixed step size, the new method’s performance can be significantly enhanced by introducing an adaptive step-size approach. The qualitative properties of the proposed method have been investigated to determine the efficiency and reliability of the method. The proposed method is of fifth-order accuracy, zero stable, L-stable, and consistent. In addition, the proposed method is convergent, and its stability properties are also shown through its Order Stars. Finally, numerical experiments are conducted to illustrate the performance of the method. The results obtained show that the proposed method compares favourably with existing methods.http://www.sciencedirect.com/science/article/pii/S111001682300416765L0565L0665L0765L20 |
| spellingShingle | Sania Qureshi Moses Adebowale Akanbi Asif Ali Shaikh Ashiribo Senapon Wusu Oladotun Matthew Ogunlaran W. Mahmoud M.S. Osman A new adaptive nonlinear numerical method for singular and stiff differential problems Alexandria Engineering Journal 65L05 65L06 65L07 65L20 |
| title | A new adaptive nonlinear numerical method for singular and stiff differential problems |
| title_full | A new adaptive nonlinear numerical method for singular and stiff differential problems |
| title_fullStr | A new adaptive nonlinear numerical method for singular and stiff differential problems |
| title_full_unstemmed | A new adaptive nonlinear numerical method for singular and stiff differential problems |
| title_short | A new adaptive nonlinear numerical method for singular and stiff differential problems |
| title_sort | new adaptive nonlinear numerical method for singular and stiff differential problems |
| topic | 65L05 65L06 65L07 65L20 |
| url | http://www.sciencedirect.com/science/article/pii/S1110016823004167 |
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