Bildik N.Bakir Y.Mutlu A.2024-07-222024-07-22201316871820http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/17454In this article, the new Ishikawa iteration method is presented to find the approximate solution of an ordinary differential equation with an initial condition. Additionally, some numerical examples with initial conditions are given to show the properties of the iteration method. Furthermore, the results of absolute errors are compared with Euler, Runge-Kutta and Picard iteration methods. Finally, the present method, namely the new modified Ishikawa iteration method, is seen to be very effective and efficient in solving different type of the problem. © 2013 Bildik et al.; licensee Springer.EnglishAll Open Access; Gold Open AccessArticle10.1186/1687-1812-2013-52