Comparison and successive iteration of approximate solution of ordinary dierential equations with initial conditions by the new modified krasnoselskii iteration method

In this paper, we used the Picard successive iteration method and the new modied Krasnoselskii iteration method in order to solve dierent types of ordinary linear dierential equations having initial conditions. By applying the new modied Krasnoselskii iteration method, not only do 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 (called the new modied Krasnoselskii iteration method) is substantially improved by employing variable steps which adjust themselves to the solution of the dierential equation.