On the numerical Picard iterations with collocations for the initial value problem

Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term "numerical" emphasizes that a numerical solution is computed. The method consists in replacing the right hand side of the differential system by Lagrange interpolation polynomials followed by successive approximations. In the case when the number of interpolation point is fixed a convergence result is given. Finally some numerical experiments are reported.