In this paper a numerical procedure to generate approximations to periodic traveling wave profiles of some nonlinear dispersive wave systems is introduced. The method is based on a suitable modification of a fixed point algorithm of Petviashvili type and solves several drawbacks of some previous algorithms presented in the literature. By way of illustration, the method is applied to generate numerically periodic traveling waves of two problems of interest: the fractional KdV type equations and the extended Boussinesq system.
