Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behavior
The aim of this paper is to develop some novel numerical algorithms for finding roots of one-dimensional non-linear equations. We derive these algorithms by utilizing the main and basic idea of the variational iteration technique. The convergence rate of the suggested algorithms is discussed. It is...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-07-01
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| Series: | Journal of King Saud University: Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S101836472100118X |
| _version_ | 1818740723736903680 |
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| author | Amir Naseem M.A. Rehman Thabet Abdeljawad Yu-Ming Chu |
| author_facet | Amir Naseem M.A. Rehman Thabet Abdeljawad Yu-Ming Chu |
| author_sort | Amir Naseem |
| collection | DOAJ |
| description | The aim of this paper is to develop some novel numerical algorithms for finding roots of one-dimensional non-linear equations. We derive these algorithms by utilizing the main and basic idea of the variational iteration technique. The convergence rate of the suggested algorithms is discussed. It is corroborated that the proposed numerical algorithms possess sixth-order convergence. To demonstrate the validity, applicability, and the performance of the proposed algorithms, we solved different test problems. These problems also include some real-life applications associated with the chemical engineering such as van der Wall’s equation, conversion of nitrogen-hydrogen feed to ammonia and the fractional-transformation in the chemical reactor problem. The numerical results of these problems show that the proposed algorithms are more effective against the other well-known similar nature existing methods. Finally, the dynamics of the suggested algorithms in the form of the polynomiographs of different complex polynomials have been analyzed that reveals the fractal nature and the other dynamical aspects of the suggested algorithms. |
| first_indexed | 2024-12-18T01:45:16Z |
| format | Article |
| id | doaj.art-5d91a49746d347a79ccc666143353c12 |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-12-18T01:45:16Z |
| publishDate | 2021-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-5d91a49746d347a79ccc666143353c122022-12-21T21:25:12ZengElsevierJournal of King Saud University: Science1018-36472021-07-01335101457Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behaviorAmir Naseem0M.A. Rehman1Thabet Abdeljawad2Yu-Ming Chu3Department of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan; Department of Computer Science and Information Engineering, Asia University, Taichung, TaiwanDepartment of Mathematics, Huzhou University, Huzhou 313000, PR China; Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, PR China; Corresponding author at: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.The aim of this paper is to develop some novel numerical algorithms for finding roots of one-dimensional non-linear equations. We derive these algorithms by utilizing the main and basic idea of the variational iteration technique. The convergence rate of the suggested algorithms is discussed. It is corroborated that the proposed numerical algorithms possess sixth-order convergence. To demonstrate the validity, applicability, and the performance of the proposed algorithms, we solved different test problems. These problems also include some real-life applications associated with the chemical engineering such as van der Wall’s equation, conversion of nitrogen-hydrogen feed to ammonia and the fractional-transformation in the chemical reactor problem. The numerical results of these problems show that the proposed algorithms are more effective against the other well-known similar nature existing methods. Finally, the dynamics of the suggested algorithms in the form of the polynomiographs of different complex polynomials have been analyzed that reveals the fractal nature and the other dynamical aspects of the suggested algorithms.http://www.sciencedirect.com/science/article/pii/S101836472100118XNon-linear equationsNewton’s methodGolbabai and Javedi's methodPolynomiography |
| spellingShingle | Amir Naseem M.A. Rehman Thabet Abdeljawad Yu-Ming Chu Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behavior Journal of King Saud University: Science Non-linear equations Newton’s method Golbabai and Javedi's method Polynomiography |
| title | Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behavior |
| title_full | Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behavior |
| title_fullStr | Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behavior |
| title_full_unstemmed | Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behavior |
| title_short | Some engineering applications of newly constructed algorithms for one-dimensional non-linear equations and their fractal behavior |
| title_sort | some engineering applications of newly constructed algorithms for one dimensional non linear equations and their fractal behavior |
| topic | Non-linear equations Newton’s method Golbabai and Javedi's method Polynomiography |
| url | http://www.sciencedirect.com/science/article/pii/S101836472100118X |
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