Application of error control differential equations software to information flow models

Abstract

In this thesis, we consider three scientific computing projects. The first project investigates a mathematical model [16] associated with the study of misinformation from the Twitter feed associated with the death of George Floyd. This investigation includes using an error control initial value ODE solver from Python to attempt to verify the results from [16]. The second project investigates mathematical models [19] associated with information diffusion during epidemics. This investigation involves a careful study of how well several of the initial value ODE solvers from Python are able to solve one of the models given the presence of a discontinuity in the definition of the model. Finally, we describe some new work involving the development of a GUI, called G-ODE-PDE, that allows a user to access the suite of error control initial value ODE solvers available in scipy.integrate.solve_ivp and the FORTRAN error control PDE solver, BACOLI, available through the Bacoli_py Python interface.