NEW ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS BASED ON MODIFIED OPEN MIDPOINT INTEGRATION FORMULA

In this paper, we propose and analyze three new iterative methods with third- and sixth-order convergence for solving nonlinear equations based on the modified open midpoint integration formula and fundamental theorem of calculus. The convergence analysis of our methods is discussed. Some numerical examples are given to demonstrate the performance of the proposed methods. Comparisons with the classical Newton's method, Halley's method and some other similar methods are included.