On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations
Fractional-order nonlinear equation-solving methods are crucial in engineering, where complex system modeling requires great precision and accuracy. Engineers may design more reliable mechanisms, enhance performance, and develop more accurate predictions regarding outcomes across a range of applicat...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/22/3501 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850267157702639616 |
|---|---|
| author | Mudassir Shams |
| author_facet | Mudassir Shams |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | Fractional-order nonlinear equation-solving methods are crucial in engineering, where complex system modeling requires great precision and accuracy. Engineers may design more reliable mechanisms, enhance performance, and develop more accurate predictions regarding outcomes across a range of applications where these problems are effectively addressed. This research introduces a novel hybrid multiplicative calculus-based parallel method for solving complex nonlinear models in engineering. To speed up the method’s rate of convergence, we utilize a second-order multiplicative root-finding approach as a corrector in the parallel framework. Using rigorous theoretical analysis, we illustrate how the hybrid parallel technique based on multiplicative calculus achieves a remarkable convergence order of 12, indicating its effectiveness and efficiency in solving complex nonlinear equations. The intrinsic stability and consistency of the approach—when applied to nonlinear situations—are clearly indicated by the symmetry seen in the dynamical planes for various parameter values. The method’s symmetrical behavior indicates that it produces accurate findings under a range of scenarios. Using a dynamical system procedure, the ideal parameter values are systematically analyzed in order to further improve the method’s performance. Implementing the aforementioned parameter values using the parallel approach yields very reliable and consistent outcomes. The method’s effectiveness, reliability, and consistency are evaluated through the analysis of numerous nonlinear engineering problems. The analysis provides a detailed comparison with current techniques, emphasizing the benefits and potential improvements of the novel approach. |
| format | Article |
| id | doaj-art-90c0ee662af045159074bc4bc087c12e |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-90c0ee662af045159074bc4bc087c12e2025-08-20T01:53:54ZengMDPI AGMathematics2227-73902024-11-011222350110.3390/math12223501On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear EquationsMudassir Shams0Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bolzano, ItalyFractional-order nonlinear equation-solving methods are crucial in engineering, where complex system modeling requires great precision and accuracy. Engineers may design more reliable mechanisms, enhance performance, and develop more accurate predictions regarding outcomes across a range of applications where these problems are effectively addressed. This research introduces a novel hybrid multiplicative calculus-based parallel method for solving complex nonlinear models in engineering. To speed up the method’s rate of convergence, we utilize a second-order multiplicative root-finding approach as a corrector in the parallel framework. Using rigorous theoretical analysis, we illustrate how the hybrid parallel technique based on multiplicative calculus achieves a remarkable convergence order of 12, indicating its effectiveness and efficiency in solving complex nonlinear equations. The intrinsic stability and consistency of the approach—when applied to nonlinear situations—are clearly indicated by the symmetry seen in the dynamical planes for various parameter values. The method’s symmetrical behavior indicates that it produces accurate findings under a range of scenarios. Using a dynamical system procedure, the ideal parameter values are systematically analyzed in order to further improve the method’s performance. Implementing the aforementioned parameter values using the parallel approach yields very reliable and consistent outcomes. The method’s effectiveness, reliability, and consistency are evaluated through the analysis of numerous nonlinear engineering problems. The analysis provides a detailed comparison with current techniques, emphasizing the benefits and potential improvements of the novel approach.https://www.mdpi.com/2227-7390/12/22/3501nonlinear equationsmultiplicative calculusmultiplicative schemeconvergence planescomputational time |
| spellingShingle | Mudassir Shams On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations Mathematics nonlinear equations multiplicative calculus multiplicative scheme convergence planes computational time |
| title | On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations |
| title_full | On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations |
| title_fullStr | On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations |
| title_full_unstemmed | On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations |
| title_short | On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations |
| title_sort | on a stable multiplicative calculus based hybrid parallel scheme for nonlinear equations |
| topic | nonlinear equations multiplicative calculus multiplicative scheme convergence planes computational time |
| url | https://www.mdpi.com/2227-7390/12/22/3501 |
| work_keys_str_mv | AT mudassirshams onastablemultiplicativecalculusbasedhybridparallelschemefornonlinearequations |