Abstract:
This article discusses a new one-step iterative methods based on Thiele's Continued
Fraction by applying the third trucanted Thiele's Continued Fraction for solving
equations. Analytically it is shown that the iterative method has a fourth order
of convergences. Furthermore, the computational test shows that the discussed this
method is superior to other mentioned methods, in terms of the number of iterations
required to obtain the estimated root.
