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Some variants of the numerical Picard iterations method are presented tosolve an IVP for an ordinary differential system. The term numerical emphasizesthat a numerical solution is computed. The method consists in replacing theright hand side of the differential system by Lagrange interpolationpolynomials followed by successive approximations. In the case when the numberof interpolation point is fixed a convergence result is given. Finally somenumerical experiments are reported.

On the numerical Picard iterations method with collocations for the IVP