Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations
A multi-step derivative-free iterative technique is developed by extending the well-known Traub-Steffensen iteration for solving the systems of nonlinear equations. Keeping in mind the computational aspects, the general idea to construct the scheme is to utilize the single inverse operator per iter...
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| Format: | Article |
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Vilnius Gediminas Technical University
2025-04-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://bme.vgtu.lt/index.php/MMA/article/view/21097 |
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| author | Janak Raj Sharma Harmandeep Singh Sunil Kumar |
| author_facet | Janak Raj Sharma Harmandeep Singh Sunil Kumar |
| author_sort | Janak Raj Sharma |
| collection | DOAJ |
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A multi-step derivative-free iterative technique is developed by extending the well-known Traub-Steffensen iteration for solving the systems of nonlinear equations. Keeping in mind the computational aspects, the general idea to construct the scheme is to utilize the single inverse operator per iteration. In fact, these type of techniques are hardly found in literature. Under the standard assumption, the proposed technique is found to possess the fifth order of convergence. In order to demonstrate the computational complexity, the efficiency index is computed and further compared with the efficiency of existing methods of similar nature. The complexity analysis suggests that the developed method is computationally more efficient than their existing counterparts. Furthermore, the performance of method is examined numerically through locating the solutions to a variety of systems of nonlinear equations. Numerical results regarding accuracy, convergence behavior and elapsed CPU time confirm the efficient behavior of the proposed technique.
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| format | Article |
| id | doaj-art-039bfccb61884710ae8dd82b3ec4a5d0 |
| institution | DOAJ |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-039bfccb61884710ae8dd82b3ec4a5d02025-08-20T03:14:12ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-04-0130210.3846/mma.2025.21097Development and analysis of an efficient Jacobian-free method for systems of nonlinear equationsJanak Raj Sharma0Harmandeep Singh1Sunil Kumar2Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148106, IndiaDepartment of Mathematics, Statistics and Physics, Punjab Agricultural University, Ludhiana-141004, IndiaDepartment of Mathematics, University Centre for Research and Development, Chandigarh University, Mohali-140413, India A multi-step derivative-free iterative technique is developed by extending the well-known Traub-Steffensen iteration for solving the systems of nonlinear equations. Keeping in mind the computational aspects, the general idea to construct the scheme is to utilize the single inverse operator per iteration. In fact, these type of techniques are hardly found in literature. Under the standard assumption, the proposed technique is found to possess the fifth order of convergence. In order to demonstrate the computational complexity, the efficiency index is computed and further compared with the efficiency of existing methods of similar nature. The complexity analysis suggests that the developed method is computationally more efficient than their existing counterparts. Furthermore, the performance of method is examined numerically through locating the solutions to a variety of systems of nonlinear equations. Numerical results regarding accuracy, convergence behavior and elapsed CPU time confirm the efficient behavior of the proposed technique. https://bme.vgtu.lt/index.php/MMA/article/view/21097systems of nonlinear equationsTraub-Steffensen methodcomputational efficiencyconvergence analysis |
| spellingShingle | Janak Raj Sharma Harmandeep Singh Sunil Kumar Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations Mathematical Modelling and Analysis systems of nonlinear equations Traub-Steffensen method computational efficiency convergence analysis |
| title | Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations |
| title_full | Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations |
| title_fullStr | Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations |
| title_full_unstemmed | Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations |
| title_short | Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations |
| title_sort | development and analysis of an efficient jacobian free method for systems of nonlinear equations |
| topic | systems of nonlinear equations Traub-Steffensen method computational efficiency convergence analysis |
| url | https://bme.vgtu.lt/index.php/MMA/article/view/21097 |
| work_keys_str_mv | AT janakrajsharma developmentandanalysisofanefficientjacobianfreemethodforsystemsofnonlinearequations AT harmandeepsingh developmentandanalysisofanefficientjacobianfreemethodforsystemsofnonlinearequations AT sunilkumar developmentandanalysisofanefficientjacobianfreemethodforsystemsofnonlinearequations |