# A study on the local convergence and dynamics of the two-step and derivative-free Kung–Traub’s method

## Abstract

We present a local convergence analysis of a two-step and derivative-free Kung–Traub’s method, which is based on a parameter and has fourth order of convergence. Using basins of attraction of the method, dynamical behavior of the scheme is studied and the best choice of the parameter is found in the sense of reliability and stability. Some illustrative examples show that as the parameter gets close to zero, radius of convergence of the method becomes larger.

- Authors:

- Islamic Azad University, Department of Applied Mathematics, Hamedan Branch (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22769306

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; RELIABILITY; STABILITY

### Citation Formats

```
Veiseh, Hana, Lotfi, Taher, and Allahviranloo, Tofigh.
```*A study on the local convergence and dynamics of the two-step and derivative-free Kung–Traub’s method*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0458-5.

```
Veiseh, Hana, Lotfi, Taher, & Allahviranloo, Tofigh.
```*A study on the local convergence and dynamics of the two-step and derivative-free Kung–Traub’s method*. United States. doi:10.1007/S40314-017-0458-5.

```
Veiseh, Hana, Lotfi, Taher, and Allahviranloo, Tofigh. Sun .
"A study on the local convergence and dynamics of the two-step and derivative-free Kung–Traub’s method". United States. doi:10.1007/S40314-017-0458-5.
```

```
@article{osti_22769306,
```

title = {A study on the local convergence and dynamics of the two-step and derivative-free Kung–Traub’s method},

author = {Veiseh, Hana and Lotfi, Taher and Allahviranloo, Tofigh},

abstractNote = {We present a local convergence analysis of a two-step and derivative-free Kung–Traub’s method, which is based on a parameter and has fourth order of convergence. Using basins of attraction of the method, dynamical behavior of the scheme is studied and the best choice of the parameter is found in the sense of reliability and stability. Some illustrative examples show that as the parameter gets close to zero, radius of convergence of the method becomes larger.},

doi = {10.1007/S40314-017-0458-5},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}

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