New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0
Construction of higher-order optimal and globally convergent methods for computing simple roots of nonlinear equations is an earliest and challenging problem in numerical analysis. Therefore, the aim of this paper is to present optimal and globally convergent families of King's method and Ostro...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/264529 |
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| author | Ramandeep Behl V. Kanwar |
| author_facet | Ramandeep Behl V. Kanwar |
| author_sort | Ramandeep Behl |
| collection | DOAJ |
| description | Construction of higher-order optimal and globally convergent methods for computing simple roots of nonlinear equations is an earliest and challenging problem in numerical analysis. Therefore, the aim of this paper is to present optimal and globally convergent families of King's method and Ostrowski's method having biquadratic and eight-order convergence, respectively, permitting f′(x)=0
in the vicinity of the required root. Fourth-order King's family and Ostrowski's method can be seen as special cases of our proposed scheme. All the methods considered here are found to be more effective to the similar robust methods available in the literature. In their dynamical study, it has been observed that the proposed methods have equal or better stability and robustness as compared to the other methods. |
| format | Article |
| id | doaj-art-18eadca9b1704f3a902940464aa673c0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-18eadca9b1704f3a902940464aa673c02025-02-03T07:24:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/264529264529New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0Ramandeep Behl0V. Kanwar1School of Mathematics & Computer Applications, Thapar University, Patiala 147 004, IndiaUniversity Institute of Engineering and Technology, Panjab University, Chandigarh 160 014, IndiaConstruction of higher-order optimal and globally convergent methods for computing simple roots of nonlinear equations is an earliest and challenging problem in numerical analysis. Therefore, the aim of this paper is to present optimal and globally convergent families of King's method and Ostrowski's method having biquadratic and eight-order convergence, respectively, permitting f′(x)=0 in the vicinity of the required root. Fourth-order King's family and Ostrowski's method can be seen as special cases of our proposed scheme. All the methods considered here are found to be more effective to the similar robust methods available in the literature. In their dynamical study, it has been observed that the proposed methods have equal or better stability and robustness as compared to the other methods.http://dx.doi.org/10.1155/2014/264529 |
| spellingShingle | Ramandeep Behl V. Kanwar New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0 International Journal of Mathematics and Mathematical Sciences |
| title | New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0 |
| title_full | New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0 |
| title_fullStr | New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0 |
| title_full_unstemmed | New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0 |
| title_short | New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0 |
| title_sort | new highly efficient families of higher order methods for simple roots permitting f xn 0 |
| url | http://dx.doi.org/10.1155/2014/264529 |
| work_keys_str_mv | AT ramandeepbehl newhighlyefficientfamiliesofhigherordermethodsforsimplerootspermittingfxn0 AT vkanwar newhighlyefficientfamiliesofhigherordermethodsforsimplerootspermittingfxn0 |