We present a computer-assisted method to verify the existence of chaotic behaviour in discrete dynamical systems. Our approach is closely related to the procedure introduced by Stoffer and Palmer [Nonlinearity 12 (1999) 1683]. Yet the scheme of Stoffer an

We introduce a symmetric version of the Fer expansion for the solution of the ODE y′=γ(t,y)y. We show that the schemes are time-symmetric for linear problems. Furthermore, symmetry implies order 2p+2 whereby the classical Fer expansion would display order 2p+1 only. This reduces significantly the computational cost of the classical Fer expansion. We prove the convergence of the proposed symmetric schemes and obtain an estimate of the radius of convergence. Numerical experiments for two methods in this class confirm that time-symmetry is preserved to machine accuracy for linear problem, while, for nonlinear problems is not preserved exactly but to a higher order of accuracy.