On efficient iterative schemes for finding all solutions of non-linear engineering problems
Nonlinear equations are important in engineering because they may simulate complicated real-world phenomena such as fluid dynamics, material stress, and electrical circuits, where linear assumptions fail. They allow engineers to more correctly estimate how a system will respond in certain conditions...
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| Format: | Article |
| Language: | English |
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REA Press
2024-09-01
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| Series: | Computational Algorithms and Numerical Dimensions |
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| Online Access: | https://www.journal-cand.com/article_203261_9ce68fd458eda518093afa07067df1e4.pdf |
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| _version_ | 1832580029831184384 |
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| author | Mudassir Shams Nasreen Kausar |
| author_facet | Mudassir Shams Nasreen Kausar |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | Nonlinear equations are important in engineering because they may simulate complicated real-world phenomena such as fluid dynamics, material stress, and electrical circuits, where linear assumptions fail. They allow engineers to more correctly estimate how a system will respond in certain conditions. The main aim of this effort is to develop an efficient higher-order simultaneous computer approach capable of computing all solutions concurrently. The convergence theorem analysis indicates that the scheme has a local convergence order of 10. Using a few engineering applications, we show that the order strategy surpasses the current approach in terms of residual error, stability, and consistency. |
| format | Article |
| id | doaj-art-9674cf49dcf94f25be38a769b4d2fecc |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-9674cf49dcf94f25be38a769b4d2fecc2025-01-30T11:23:23ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202024-09-013320120710.22105/cand.2024.474645.1103203261On efficient iterative schemes for finding all solutions of non-linear engineering problemsMudassir Shams0Nasreen Kausar1Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, Pakistan.Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler, 34220, Istanbul, Turkey.Nonlinear equations are important in engineering because they may simulate complicated real-world phenomena such as fluid dynamics, material stress, and electrical circuits, where linear assumptions fail. They allow engineers to more correctly estimate how a system will respond in certain conditions. The main aim of this effort is to develop an efficient higher-order simultaneous computer approach capable of computing all solutions concurrently. The convergence theorem analysis indicates that the scheme has a local convergence order of 10. Using a few engineering applications, we show that the order strategy surpasses the current approach in terms of residual error, stability, and consistency.https://www.journal-cand.com/article_203261_9ce68fd458eda518093afa07067df1e4.pdfnon-linear equationoptimal orderiterative methodssimultaneous methodscpu time |
| spellingShingle | Mudassir Shams Nasreen Kausar On efficient iterative schemes for finding all solutions of non-linear engineering problems Computational Algorithms and Numerical Dimensions non-linear equation optimal order iterative methods simultaneous methods cpu time |
| title | On efficient iterative schemes for finding all solutions of non-linear engineering problems |
| title_full | On efficient iterative schemes for finding all solutions of non-linear engineering problems |
| title_fullStr | On efficient iterative schemes for finding all solutions of non-linear engineering problems |
| title_full_unstemmed | On efficient iterative schemes for finding all solutions of non-linear engineering problems |
| title_short | On efficient iterative schemes for finding all solutions of non-linear engineering problems |
| title_sort | on efficient iterative schemes for finding all solutions of non linear engineering problems |
| topic | non-linear equation optimal order iterative methods simultaneous methods cpu time |
| url | https://www.journal-cand.com/article_203261_9ce68fd458eda518093afa07067df1e4.pdf |
| work_keys_str_mv | AT mudassirshams onefficientiterativeschemesforfindingallsolutionsofnonlinearengineeringproblems AT nasreenkausar onefficientiterativeschemesforfindingallsolutionsofnonlinearengineeringproblems |