Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications
It is essential to solve nonlinear equations in engineering, where accuracy and precision are critical. In this paper, a novel family of iterative methods for finding the simple roots of nonlinear equations based on multiplicative calculus is introduced. Based on theoretical research, a novel family...
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MDPI AG
2024-11-01
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| Series: | Mathematics |
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| author | Mudassir Shams Nasreen Kausar Ioana Alexandra Șomîtcă |
| author_facet | Mudassir Shams Nasreen Kausar Ioana Alexandra Șomîtcă |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | It is essential to solve nonlinear equations in engineering, where accuracy and precision are critical. In this paper, a novel family of iterative methods for finding the simple roots of nonlinear equations based on multiplicative calculus is introduced. Based on theoretical research, a novel family of simple root-finding schemes based on multiplicative calculus has been devised, with a convergence order of seven. The symmetry in the pie graph of the convergence–divergence areas demonstrates that the method is stable and consistent when dealing with nonlinear engineering problems. An extensive examination of the numerical results of the engineering applications is presented in order to assess the effectiveness, stability, and consistency of the recently established method in comparison to current methods. The analysis includes the total number of functions and derivative evaluations per iteration, elapsed time, residual errors, local computational order of convergence, and error graphs, which demonstrate our method’s better convergence behavior when compared to other approaches. |
| format | Article |
| id | doaj-art-7d63b024c2eb4bd688b8d3e0dbd3c381 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-7d63b024c2eb4bd688b8d3e0dbd3c3812025-08-20T02:47:59ZengMDPI AGMathematics2227-73902024-11-011222351710.3390/math12223517Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering ApplicationsMudassir Shams0Nasreen Kausar1Ioana Alexandra Șomîtcă2Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, ItalyDepartment of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul 34220, TürkiyeDepartment of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Baritiu Street, no 26–28, 40027 Cluj-Napoca, RomaniaIt is essential to solve nonlinear equations in engineering, where accuracy and precision are critical. In this paper, a novel family of iterative methods for finding the simple roots of nonlinear equations based on multiplicative calculus is introduced. Based on theoretical research, a novel family of simple root-finding schemes based on multiplicative calculus has been devised, with a convergence order of seven. The symmetry in the pie graph of the convergence–divergence areas demonstrates that the method is stable and consistent when dealing with nonlinear engineering problems. An extensive examination of the numerical results of the engineering applications is presented in order to assess the effectiveness, stability, and consistency of the recently established method in comparison to current methods. The analysis includes the total number of functions and derivative evaluations per iteration, elapsed time, residual errors, local computational order of convergence, and error graphs, which demonstrate our method’s better convergence behavior when compared to other approaches.https://www.mdpi.com/2227-7390/12/22/3517nonlinear equationsmultiplicative calculusiterative-schemepie chartpercentage convergence |
| spellingShingle | Mudassir Shams Nasreen Kausar Ioana Alexandra Șomîtcă Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications Mathematics nonlinear equations multiplicative calculus iterative-scheme pie chart percentage convergence |
| title | Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications |
| title_full | Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications |
| title_fullStr | Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications |
| title_full_unstemmed | Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications |
| title_short | Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications |
| title_sort | efficient multiplicative calculus based iterative scheme for nonlinear engineering applications |
| topic | nonlinear equations multiplicative calculus iterative-scheme pie chart percentage convergence |
| url | https://www.mdpi.com/2227-7390/12/22/3517 |
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