In this paper, we introduce two numerical methods for finding the simple real roots,
multiple real roots and complex roots of the nonlinear equations f (x) 0 . The first
method is based on approximations the function f by third Taylor polynomial about the
roots of the nonlinear equations. After that, Gordano method is used which is transformed
to iterative method. The second method is based on modifies of Halley method . The two
algorithms are designed of the presented methods, and programming Mathematica Version
9 is used.
Numerical experiments are given for finding the simple real roots, multiple real roots
and complex roots of some test problems. Comparisons of the results obtained by two
methods with other methods illustrate the efficiency and highly accurate of the proposed
Key Words: Third Taylor Polynomial, Halley method, Multiple root of multiplicity m,
Iterative method , Nonlinear equations.
Tishreen University Journal for Research and Scientific Studies – Basic Sciences Series Vol. (38) No. (1) 2016