Abstract
In this paper, we present, analyze, and test a family of high order iterative methods for finding simple and multiple roots of nonlinear algebraic equations of the form f(x) = 0. The proposed method can achieve convergence of order p, where p≥ 2 is a positive integer. The standard Newton–Raphson method (p= 2 ) and the Chebyshev’s method (p= 3 ) are both special cases of this family of methods. The pth order method requires evaluation of the function and its derivative up to order p- 1 at each step. Several numerical experiments are provided to validate the theoretical order of convergence for nonlinear functions with simple and multiple roots.
Original language | English (US) |
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Pages (from-to) | 1119-1133 |
Number of pages | 15 |
Journal | International Journal of Applied and Computational Mathematics |
Volume | 3 |
DOIs | |
State | Published - Dec 1 2017 |
Keywords
- High order iterative methods
- Newton’s method
- Nonlinear equations
- Order of convergence
- Root-finding problem
- Simple and multiple roots
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics