We consider the leap-frog scheme for the IVP ū' = F(ū) on (0,T], ū(0) = uo: given a uniform (to simplify) time step &t, the scheme consists in finding (Un)n=0,...,n such that uo is the initial condition and Ui - Uo = F(uo), & Un+1 – Un-1 F(un) 28 for all n = 1,...,N – 1. We suppose that F is Lipschitz continuous with constant L. 1. Prove that the scheme is consistent of order 1, assuming as usual that ū e C?([0, T]).
