Predicting the evolution of most physical systems requires numerical methods to approximate numerically their laws of motion, represented by systems of ordinary differential equations. The errors introduced by the numerical approximation must be kept under control to achieve a reliable prediction, which can entail very large computational cost for high resolution simulations.

My contribution to this field has focused on several topics:

• semi-Lagrangian and semi-implicit methods, mostly in the framework of numerical weather prediction applications

• application of diagonally implicit Runge Kutta methods to partial differential equations

• analysis of implicit multi-rate methods

• application of exponential methods to partial differential equations

• analysis of traditional and less traditional methods for structural mechanics

• methods for numerical tracking in particle accelerators