Finding the Approximate Real and Complex Roots of Nonlinear Equations by Taylor’s Third-Degree Publication Dr. Nidal E. Hassan

 ABSTRACT 
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 methods.
Key Words: Third Taylor Polynomial, Halley method, Multiple root of multiplicity m,Iterative method , Nonlinear equations

Assistant Prof, Depart. of Mathematics, Faculty of Science, Al-Baath Universty, Homes, Syr

إيجاد-الجذور-الحقيقية-والعقدية-التقريبية-للمعادلات-غير-الخطية

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