Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering Models
Nonlinear equations are essential in research and engineering because they simulate complicated processes such as fluid dynamics, chemical reactions, and population growth. The development of advanced methods to address them becomes essential for scientific and applied research enhancements, as thei...
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MDPI AG
2024-12-01
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| author | Mudassir Shams Bruno Carpentieri |
| author_facet | Mudassir Shams Bruno Carpentieri |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | Nonlinear equations are essential in research and engineering because they simulate complicated processes such as fluid dynamics, chemical reactions, and population growth. The development of advanced methods to address them becomes essential for scientific and applied research enhancements, as their resolution influences innovations by aiding in the proper prediction or optimization of the system. In this research, we develop a novel biparametric family of inverse parallel techniques designed to improve stability and accelerate convergence in parallel iterative algorithm. Bifurcation and chaos theory were used to find the best parameter regions that increase the parallel method’s effectiveness and stability. Our newly developed biparametric family of parallel techniques is more computationally efficient than current approaches, as evidenced by significant reductions in the number of iterations and basic operations each iterations step for solving nonlinear equations. Engineering applications examined with rough beginning data demonstrate high accuracy and superior convergence compared to existing classical parallel schemes. Analysis of global convergence further shows that the proposed methods outperform current methods in terms of error control, computational time, percentage convergence, number of basic operations per iteration, and computational order. These findings indicate broad usage potential in engineering and scientific computation. |
| format | Article |
| id | doaj-art-19f2831e0f40401e8ac53819813b8ce4 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-19f2831e0f40401e8ac53819813b8ce42025-01-10T13:18:09ZengMDPI AGMathematics2227-73902024-12-011316710.3390/math13010067Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering ModelsMudassir Shams0Bruno Carpentieri1Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, ItalyFaculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, ItalyNonlinear equations are essential in research and engineering because they simulate complicated processes such as fluid dynamics, chemical reactions, and population growth. The development of advanced methods to address them becomes essential for scientific and applied research enhancements, as their resolution influences innovations by aiding in the proper prediction or optimization of the system. In this research, we develop a novel biparametric family of inverse parallel techniques designed to improve stability and accelerate convergence in parallel iterative algorithm. Bifurcation and chaos theory were used to find the best parameter regions that increase the parallel method’s effectiveness and stability. Our newly developed biparametric family of parallel techniques is more computationally efficient than current approaches, as evidenced by significant reductions in the number of iterations and basic operations each iterations step for solving nonlinear equations. Engineering applications examined with rough beginning data demonstrate high accuracy and superior convergence compared to existing classical parallel schemes. Analysis of global convergence further shows that the proposed methods outperform current methods in terms of error control, computational time, percentage convergence, number of basic operations per iteration, and computational order. These findings indicate broad usage potential in engineering and scientific computation.https://www.mdpi.com/2227-7390/13/1/67parallel schemesbifurcationchaosglobal convergence |
| spellingShingle | Mudassir Shams Bruno Carpentieri Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering Models Mathematics parallel schemes bifurcation chaos global convergence |
| title | Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering Models |
| title_full | Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering Models |
| title_fullStr | Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering Models |
| title_full_unstemmed | Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering Models |
| title_short | Chaos in Inverse Parallel Schemes for Solving Nonlinear Engineering Models |
| title_sort | chaos in inverse parallel schemes for solving nonlinear engineering models |
| topic | parallel schemes bifurcation chaos global convergence |
| url | https://www.mdpi.com/2227-7390/13/1/67 |
| work_keys_str_mv | AT mudassirshams chaosininverseparallelschemesforsolvingnonlinearengineeringmodels AT brunocarpentieri chaosininverseparallelschemesforsolvingnonlinearengineeringmodels |