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 newmodied krasnoselskii iteration method in order to solve dierent types of ordinary lineardierential equations having initial conditions. by applying the new modied krasnoselskiiiteration method, not only do we obtain the approximate solutions for the problem, butalso establish the corresponding iterative schemes. finally, it is shown that the accuracyof the new iteration method (called the new modied krasnoselskii iteration method) issubstantially improved by employing variable steps which adjust themselves to the solutionof the dierential equation.