Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering
In this paper, we propose two novel iteration schemes for computing zeros of nonlinear equations in one dimension. We develop these iteration schemes with the help of Taylor’s series expansion, generalized Newton-Raphson’s method, and interpolation technique. The convergence analysis of the proposed...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/5566379 |
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| author | M. A. Rehman Amir Naseem Thabet Abdeljawad |
| author_facet | M. A. Rehman Amir Naseem Thabet Abdeljawad |
| author_sort | M. A. Rehman |
| collection | DOAJ |
| description | In this paper, we propose two novel iteration schemes for computing zeros of nonlinear equations in one dimension. We develop these iteration schemes with the help of Taylor’s series expansion, generalized Newton-Raphson’s method, and interpolation technique. The convergence analysis of the proposed iteration schemes is discussed. It is established that the newly developed iteration schemes have sixth order of convergence. Several numerical examples have been solved to illustrate the applicability and validity of the suggested schemes. These problems also include some real-life applications associated with the chemical and civil engineering such as adiabatic flame temperature equation, conversion of nitrogen-hydrogen feed to ammonia, the van der Wall’s equation, and the open channel flow problem whose numerical results prove the better efficiency of these methods as compared to other well-known existing iterative methods of the same kind. |
| format | Article |
| id | doaj-art-10efd059488541ff95e81b2b3aa239e1 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-10efd059488541ff95e81b2b3aa239e12025-02-03T06:05:45ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/55663795566379Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in EngineeringM. A. Rehman0Amir Naseem1Thabet Abdeljawad2Department of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, 11586 Riyadh, Saudi ArabiaIn this paper, we propose two novel iteration schemes for computing zeros of nonlinear equations in one dimension. We develop these iteration schemes with the help of Taylor’s series expansion, generalized Newton-Raphson’s method, and interpolation technique. The convergence analysis of the proposed iteration schemes is discussed. It is established that the newly developed iteration schemes have sixth order of convergence. Several numerical examples have been solved to illustrate the applicability and validity of the suggested schemes. These problems also include some real-life applications associated with the chemical and civil engineering such as adiabatic flame temperature equation, conversion of nitrogen-hydrogen feed to ammonia, the van der Wall’s equation, and the open channel flow problem whose numerical results prove the better efficiency of these methods as compared to other well-known existing iterative methods of the same kind.http://dx.doi.org/10.1155/2021/5566379 |
| spellingShingle | M. A. Rehman Amir Naseem Thabet Abdeljawad Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering Journal of Function Spaces |
| title | Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering |
| title_full | Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering |
| title_fullStr | Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering |
| title_full_unstemmed | Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering |
| title_short | Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering |
| title_sort | some novel sixth order iteration schemes for computing zeros of nonlinear scalar equations and their applications in engineering |
| url | http://dx.doi.org/10.1155/2021/5566379 |
| work_keys_str_mv | AT marehman somenovelsixthorderiterationschemesforcomputingzerosofnonlinearscalarequationsandtheirapplicationsinengineering AT amirnaseem somenovelsixthorderiterationschemesforcomputingzerosofnonlinearscalarequationsandtheirapplicationsinengineering AT thabetabdeljawad somenovelsixthorderiterationschemesforcomputingzerosofnonlinearscalarequationsandtheirapplicationsinengineering |