On the numerical Picard iterations method with collocations for the IVP
This is an incremental contribution to numerical methods for solving IVPs, providing a specific variant of an existing technique.
The paper presents variants of the numerical Picard iterations method for solving initial value problems (IVPs) for ordinary differential systems, using Lagrange interpolation and successive approximations. Convergence results are given for a fixed number of interpolation points, and numerical experiments are reported.
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.