The Comparison and Successive Iteration of Approximate Solution of Ordinary Differential Equation with Initial Condition by New Modified Krasnoselskii Iteration Method

In this paper, we used the Picard successive iteration method and behind the new Modified Krasnoselskii iteration method in order to solve the different type of the ordinary linear differential equation having initial condition.By applying the new Modified Krasnoselskii iteration method not only we obtain the approximate solutions for the problem, but also establish the corresponding iterative schemes. Finally, it is shown that the accuracy of the new iteration method (which is called new Modified Krasnoselskii iteration method) is substantially improved by employing variable steps which adjust themselves to the solution of the differential equation.