LAUSR

Various iterative methods have been introduced by involving Taylor’s series on the auxiliary function g(x) to solve the nonlinear equation f(x) � 0. In this paper, we introduce the expansion of g(x) with the inclusion of weights wi such that ???? p i�1wi � 1 and knots τi ∈ [0, 1] in order to develop a new family of iterative methods. ,e methods proposed in the present paper are applicable for different choices of auxiliary function g(x), and some already known methods can be viewed as the special cases of these methods. We consider the diverse scientific/engineering models to demonstrate the efficiency of the proposed methods.