Improving the order of convergence of iteration functions
Journal of Computational and Applied Mathematics
Second-derivative-free variant of the Chebyshev method for nonlinear equations
Journal of Optimization Theory and Applications
An acceleration of Newton's method: Super-Halley method
Applied Mathematics and Computation
Some variant of Newton's method with third-order convergence
Applied Mathematics and Computation
On Newton-type methods with cubic convergence
Journal of Computational and Applied Mathematics
Construction of Newton-like iteration methods for solving nonlinear equations
Numerische Mathematik
Letter to the Editor: Third-order modification of Newton's method
Journal of Computational and Applied Mathematics
Iterative methods improving newton's method by the decomposition method
Computers & Mathematics with Applications
| Hi-index | 7.29 |
In this paper, we present a simple and easily applicable approach to construct some third-order modifications of Newton's method for solving nonlinear equations. It is shown by way of illustration that existing third-order methods can be employed to construct new third-order iterative methods. The proposed approach is applied to the classical Chebyshev-Halley methods to derive their second-derivative-free variants. Numerical examples are given to support that the methods thus obtained can compete with known third-order methods.