An iterative method based on the average quadrature formula
In our research, a new third-order iterative method has been introduced. This method involves the creation of a new quadrature formula by averaging Simpson's 1/3 rd and Trapezoidal rules. The newly developed quadrature formula is then used to establish the new iterative scheme, which modifies t...
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| Format: | Article |
| Language: | English |
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REA Press
2025-03-01
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| Series: | Computational Algorithms and Numerical Dimensions |
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| Online Access: | https://www.journal-cand.com/article_209205_bfcb61453a336707bc245d0e7471ee6f.pdf |
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| _version_ | 1832580009429041152 |
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| author | Tusar Singh Dwiti Behera Shno Othman Ahmed Rostam Saeed |
| author_facet | Tusar Singh Dwiti Behera Shno Othman Ahmed Rostam Saeed |
| author_sort | Tusar Singh |
| collection | DOAJ |
| description | In our research, a new third-order iterative method has been introduced. This method involves the creation of a new quadrature formula by averaging Simpson's 1/3 rd and Trapezoidal rules. The newly developed quadrature formula is then used to establish the new iterative scheme, which modifies the Newton-Raphson method. It has been demonstrated that the new iterative technique exhibits a convergence order of 3. Finally, examples have been provided to illustrate the effectiveness of the new process. The results indicate that the new approach finds the root of the nonlinear equation in fewer iterations compared to other methods, suggesting the potential superiority of our newly developed scheme. |
| format | Article |
| id | doaj-art-1b19bc40027043d18691d42ed8937599 |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-1b19bc40027043d18691d42ed89375992025-01-30T11:24:22ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202025-03-0141576410.22105/cand.2024.485552.1155209205An iterative method based on the average quadrature formulaTusar Singh0Dwiti Behera1Shno Othman Ahmed2Rostam Saeed3Department of Mathematics, Siksha O Anusandhan University, Bhubaneswar, Odisha, India.Department of Mathematics, Ravenshaw University, Cuttack, Odisha, India.Department of Computer, College of Science, Salahaddin University-Erbil, Erbil, Iraq.Department of Mathematics, College of Science, Salahaddin University-Erbil, Kurdistan Region, Erbil, Iraq.In our research, a new third-order iterative method has been introduced. This method involves the creation of a new quadrature formula by averaging Simpson's 1/3 rd and Trapezoidal rules. The newly developed quadrature formula is then used to establish the new iterative scheme, which modifies the Newton-Raphson method. It has been demonstrated that the new iterative technique exhibits a convergence order of 3. Finally, examples have been provided to illustrate the effectiveness of the new process. The results indicate that the new approach finds the root of the nonlinear equation in fewer iterations compared to other methods, suggesting the potential superiority of our newly developed scheme.https://www.journal-cand.com/article_209205_bfcb61453a336707bc245d0e7471ee6f.pdftrapezoidal rulesimpson' s 1/3 rdnewton’s methodorder of convergenceiterative method |
| spellingShingle | Tusar Singh Dwiti Behera Shno Othman Ahmed Rostam Saeed An iterative method based on the average quadrature formula Computational Algorithms and Numerical Dimensions trapezoidal rule simpson' s 1/3 rd newton’s method order of convergence iterative method |
| title | An iterative method based on the average quadrature formula |
| title_full | An iterative method based on the average quadrature formula |
| title_fullStr | An iterative method based on the average quadrature formula |
| title_full_unstemmed | An iterative method based on the average quadrature formula |
| title_short | An iterative method based on the average quadrature formula |
| title_sort | iterative method based on the average quadrature formula |
| topic | trapezoidal rule simpson' s 1/3 rd newton’s method order of convergence iterative method |
| url | https://www.journal-cand.com/article_209205_bfcb61453a336707bc245d0e7471ee6f.pdf |
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