Some Third Order Methods for Solving Systems of Nonlinear Equations

Abstract—Based on Traub’s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations. Keywords—Nonlinear equations and systems, Newton’s method, fixed point iteration, order of convergence. I