Exponential RK-methods for semilinear Ordinary Differential Equations and Abstract Differential Equations : definition, order conditions, convergence analysis. Application to delay equations and one-structured population models.

The program is the following:

1. Introduction to stiff equations and explicit/implicit methods for ordinary differential equations
2. Semilinear ordinary differential equations. Variation-of-constants formula. Exponential quadrature rules
3. Explicit exponential Runge-Kutta methods. Stiff order conditions and convergence. Explicit exponential Runge-Kutta methods in an abstract setting
4. Abstract reformulation of delay equations and explicit exponential Runge-Kutta in the abstract setting
5. Pseudospectral discretization of delay equations and explicit exponential Runge-Kutta for the discretized system

In collaboration with Alessia Andò, the course will include also laboratory sessions on the application of the methods for time integration of delay equations.