Quadratically convergent algorithm for computing real root of non-linear transcendental equations
Abstract Objectives The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton–Raphson method does not give guaranteed result but faster than Regula-Falsi...
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| Format: | Article |
| Language: | English |
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BMC
2018-12-01
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| Series: | BMC Research Notes |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13104-018-4008-z |
| _version_ | 1818864161877131264 |
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| author | Srinivasarao Thota Vivek Kumar Srivastav |
| author_facet | Srinivasarao Thota Vivek Kumar Srivastav |
| author_sort | Srinivasarao Thota |
| collection | DOAJ |
| description | Abstract Objectives The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton–Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the present paper used these two ideas and developed a new algorithm which has better convergence than Regula-Falsi and guaranteed result. One of the major issue in Newton–Raphson method is, it fails when first derivative is zero or approximately zero. Results The proposed method implemented the failure condition of Newton–Raphson method with better convergence. Error calculation has been discussed for certain real life examples using Bisection, Regula-Falsi, Newton–Raphson method and new proposed method. The computed results show that the new proposed quadratically convergent method provides better convergence than other methods. |
| first_indexed | 2024-12-19T10:27:16Z |
| format | Article |
| id | doaj.art-6a8f5d40d6cf46e3848c1fc0492b365c |
| institution | Directory Open Access Journal |
| issn | 1756-0500 |
| language | English |
| last_indexed | 2024-12-19T10:27:16Z |
| publishDate | 2018-12-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Research Notes |
| spelling | doaj.art-6a8f5d40d6cf46e3848c1fc0492b365c2022-12-21T20:25:52ZengBMCBMC Research Notes1756-05002018-12-011111610.1186/s13104-018-4008-zQuadratically convergent algorithm for computing real root of non-linear transcendental equationsSrinivasarao Thota0Vivek Kumar Srivastav1Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology UniversityDepartment of Mathematics, Motihari College of Engineering MotihariAbstract Objectives The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton–Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the present paper used these two ideas and developed a new algorithm which has better convergence than Regula-Falsi and guaranteed result. One of the major issue in Newton–Raphson method is, it fails when first derivative is zero or approximately zero. Results The proposed method implemented the failure condition of Newton–Raphson method with better convergence. Error calculation has been discussed for certain real life examples using Bisection, Regula-Falsi, Newton–Raphson method and new proposed method. The computed results show that the new proposed quadratically convergent method provides better convergence than other methods.http://link.springer.com/article/10.1186/s13104-018-4008-zRoot of transcendental equationsRegula-Falsi methodNewton–Raphson methodQuadratic convergence |
| spellingShingle | Srinivasarao Thota Vivek Kumar Srivastav Quadratically convergent algorithm for computing real root of non-linear transcendental equations BMC Research Notes Root of transcendental equations Regula-Falsi method Newton–Raphson method Quadratic convergence |
| title | Quadratically convergent algorithm for computing real root of non-linear transcendental equations |
| title_full | Quadratically convergent algorithm for computing real root of non-linear transcendental equations |
| title_fullStr | Quadratically convergent algorithm for computing real root of non-linear transcendental equations |
| title_full_unstemmed | Quadratically convergent algorithm for computing real root of non-linear transcendental equations |
| title_short | Quadratically convergent algorithm for computing real root of non-linear transcendental equations |
| title_sort | quadratically convergent algorithm for computing real root of non linear transcendental equations |
| topic | Root of transcendental equations Regula-Falsi method Newton–Raphson method Quadratic convergence |
| url | http://link.springer.com/article/10.1186/s13104-018-4008-z |
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