One of the fundamental problems of information theory, since its foundation by Shannon in 1948, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can travel through the channel. In the literature, several algorithms were proposed to estimate the channel capacity, as an analytical solution is unavailable for the general channel. We propose a novel approach based on a continuous-time dynamical system to compute the capacity. We then derive an algorithm for computing the capacity, obtained by discretizing the flow that rules the evolution of this dynamical system. In the experimental analysis, we test the performance of our algorithm when different numerical ordinary differential equation solvers are utilized for its implementation. Remarkably, the results show that the algorithm is effective in computing the capacity.