NEW ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS BASED ON MODIFIED OPEN MIDPOINT INTEGRATION FORMULA
NOORI YASIR ABDUL-HASSAN *
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.
*Author to whom correspondence should be addressed.
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.
Keywords: Nonlinear equations, iterative methods, predictor-corrector technique, open mid-point integration formula, order of convergence, numerical examples