Numerical Modeling for Stiff Problems and Fake News

This talk is focused on presenting recent advances in the numerical modeling for stiff systems of ordinary differential equations, with a special emphasis on the role of stiff problems in understanding the diffusion of fake information in a given country and the subsequent re-affirmation of the truth. We are all aware that our lives have significantly been influenced by the birth of social networks, which provide a large reservoir of news, whose veracity requires a special attention. Mathematical modeling for the diffusion of fake information has attracted the attention of many authors in the recent years and, in this talk, we aim to emphasize the role of stiff problems in understanding the spread of fake news in a given country. In particular, we show that the stiffness ratio (associated to the spectrum of the Jacobian of the vector field) allows to understand how fast is the transit of fake news in a given country, providing a numerical evidence based on real data. Moreover, for an efficient numerical modeling of stiff problems, we also introduce a theory of multivalue collocation methods free from order reduction, which is typical of Runge-Kutta methods. We introduce new multivalue collocation methods both based on algebraic polynomials and mixed functional basis. The theoretical analysis, examples of methods as well as numerical experiments on a selection of stiff problems are presented in this talk.