Rapid convergence of the iterative technique for first order initial value problems

摘要

In this paper we study the convergence of the approximate solutions of the first order problem u′(t)=f(t,w(t)); u(o)=uo.We prove that if there exists ∂kf/∂uk, k >- 1, and it is a continuous function, then it is possible to construct two sequences of approximate solutions converging to a solution with rate of convergence of order k.