Extension of Picard’s Iteration Method to a Class of nth-Order Initial Value Problems

Abstract

This paper extends the method of successive approximations to an nth-order initial value problem without converting it to a first-order system. We obtain a bound in a closed form for the difference between two successive iterates. Finally, an error estimate for the solutions has been calculated and it is shown to be increasingly accurate as n increases. Suitable illustrations to support the result are provided.