The new modified Jarratt method for the approximate solution of different type of differential equations

Abstract

The purpose of this project is to introduce the new modified Jarratt method to find the approximate solution of an ordinary differential equation with an initial condition. Also, some numerical examples with initial conditions are given to show the properties of the iteration method. The results of absolute errors are compared with Newton, Euler, Runge-Kutta and Picard iteration methods. Finally, the presented method, namely the new modified Jarratt method, is highlighted as one of the effective and efficient ways in solving different type of the problem.