On the process of successive approximation in initial value problems

Summary The convergence of the process of the successive approximations for the initial value problem dw/dz=f(z, w), w(0)=0, is studied in the complex field. The resulting z-domains of convergence are more favorable than those supplied by the classical approach. The improvement is made possible by the use of a ? principle of subordination ?, which allows a ? comparison test ? relative to the real field.