eng
Science and Education Publishing
American Journal of Numerical Analysis
2328-7292
2014-05-09
2
4
98
101
10.12691/ajna-2-4-1
AJNA2014241
article
A Modification of Newton Method with Third-Order Convergence
Gentian Zavalani
zavalanigentian@hotmail.com
1
Faculty of Mathematics and Physics Engineering Polytechnic University of Tirana, Albania
In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself. Finally, we give some numerical examples to demonstrate our method is more efficient than other classical iterative methods.
http://pubs.sciepub.com/ajna/2/4/1/ajna-2-4-1.pdf
Newton method
third-order convergence
non-linear equations
iterative method
quadrature formulas