An algorithm of multisummation of formal power series, solutions of linear ODE equations

In the neighbourhood of irregular singularities the formal power series solutions of complex analytic ordinary differential equations are generally divergent. The resummation theory developed by J. Ecalle and J.P. Ramis enables us to sum these series by multisummation effective algorithms. In particular we illustrate the computation of solutions of linear differential equations using the principle of multiple summation by iterated Laplace integrals proposed by W. Balser.