My research focuses on dynamically-consistent high-order methods for differential (ODEs and PDEs) and non-local evolutionary equations (IEs and IDEs). Specifically, I am interested in integrators that unconditionally preserve the positivity, the monotonicity and the asymptotic behavior of the solution, as well as some system invariants. I develop numerical schemes using non-standard finite differences, Gregory quadrature rules, modified Patankar discretizations and predictor-corrector approaches and provide theoretical and experimental proof of the aformentioned properties.
