Efficient iterative scheme for solving non-linear equations with engineering applications
A family of three-step optimal eighth-order iterative algorithm is developed in this paper in order to find single roots of nonlinear equations using the weight function technique. The newly proposed iterative methods of eight order convergence need three function evaluations and one first derivativ...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2022-12-01
|
| Series: | Applied Mathematics in Science and Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/27690911.2022.2130914 |
| _version_ | 1797640988611575808 |
|---|---|
| author | Mudassir Shams Nasreen Kausar Praveen Agarwal Georgia Irina Oros |
| author_facet | Mudassir Shams Nasreen Kausar Praveen Agarwal Georgia Irina Oros |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | A family of three-step optimal eighth-order iterative algorithm is developed in this paper in order to find single roots of nonlinear equations using the weight function technique. The newly proposed iterative methods of eight order convergence need three function evaluations and one first derivative evaluation that satisfies the Kung–Traub optimality conjecture in terms of computational cost per iteration (i.e. $ {2^{n - 1}} $ ). Furthermore, using the primary theorem that establishes the convergence order, the theoretical convergence properties of our schemes are thoroughly investigated. On several engineering applications, the performance and efficiency of our optimal iteration algorithms are examined to those of existing competitors. The new iterative schemes are more efficient than the existing methods in the literature, as illustrated by the basins of attraction, dynamical planes, efficiency, log of residual, and numerical test examples. |
| first_indexed | 2024-03-11T13:39:06Z |
| format | Article |
| id | doaj.art-1f3a989eceb14d3491ee2e4f43300c5c |
| institution | Directory Open Access Journal |
| issn | 2769-0911 |
| language | English |
| last_indexed | 2024-03-11T13:39:06Z |
| publishDate | 2022-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj.art-1f3a989eceb14d3491ee2e4f43300c5c2023-11-02T13:48:31ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112022-12-0130170873510.1080/27690911.2022.21309142130914Efficient iterative scheme for solving non-linear equations with engineering applicationsMudassir Shams0Nasreen Kausar1Praveen Agarwal2Georgia Irina Oros3Riphah International UniversityYildiz Technical University, Faculty of Arts and ScienceAnand International College of EngineeringUniversity of OradeaA family of three-step optimal eighth-order iterative algorithm is developed in this paper in order to find single roots of nonlinear equations using the weight function technique. The newly proposed iterative methods of eight order convergence need three function evaluations and one first derivative evaluation that satisfies the Kung–Traub optimality conjecture in terms of computational cost per iteration (i.e. $ {2^{n - 1}} $ ). Furthermore, using the primary theorem that establishes the convergence order, the theoretical convergence properties of our schemes are thoroughly investigated. On several engineering applications, the performance and efficiency of our optimal iteration algorithms are examined to those of existing competitors. The new iterative schemes are more efficient than the existing methods in the literature, as illustrated by the basins of attraction, dynamical planes, efficiency, log of residual, and numerical test examples.http://dx.doi.org/10.1080/27690911.2022.2130914numerical techniqueiterative methodscomputational timeoptimal ordercomputational efficiency |
| spellingShingle | Mudassir Shams Nasreen Kausar Praveen Agarwal Georgia Irina Oros Efficient iterative scheme for solving non-linear equations with engineering applications Applied Mathematics in Science and Engineering numerical technique iterative methods computational time optimal order computational efficiency |
| title | Efficient iterative scheme for solving non-linear equations with engineering applications |
| title_full | Efficient iterative scheme for solving non-linear equations with engineering applications |
| title_fullStr | Efficient iterative scheme for solving non-linear equations with engineering applications |
| title_full_unstemmed | Efficient iterative scheme for solving non-linear equations with engineering applications |
| title_short | Efficient iterative scheme for solving non-linear equations with engineering applications |
| title_sort | efficient iterative scheme for solving non linear equations with engineering applications |
| topic | numerical technique iterative methods computational time optimal order computational efficiency |
| url | http://dx.doi.org/10.1080/27690911.2022.2130914 |
| work_keys_str_mv | AT mudassirshams efficientiterativeschemeforsolvingnonlinearequationswithengineeringapplications AT nasreenkausar efficientiterativeschemeforsolvingnonlinearequationswithengineeringapplications AT praveenagarwal efficientiterativeschemeforsolvingnonlinearequationswithengineeringapplications AT georgiairinaoros efficientiterativeschemeforsolvingnonlinearequationswithengineeringapplications |