Stiffness, order reduction and fake news: multivalue numerical modeling and applications

Our lives have significantly been influenced by the birth of social networks, which provide a large reservoir of news. The veracity of this information and the spread of fake news certainly requires a special attention [5] and mathematical modeling for the diffusion of fake news has attracted the attention of many authors (see, for instance, [1, 2, 4] and references therein). We emphasize in this talk the role of the stiffness ratio that characterize differential problems modeling the diffusion of fake news. In particular, we show that the stiffness ratio allows to understand how fast is the transit of fake news in a given country, providing a numerical evidence based on real data [2]. Moreover, for an efficient numerical modeling of stiff problems, we also introduce a theory of multivalue collocation methods free from order reduction [3], which is typical of Runge-Kutta (RK) methods. The theoretical analysis, examples of methods as well as numerical experiments on a selection of stiff problems are presented in this talk.