# Time integration schemes

We develop and analyze methods to improve accuracy and efficiency in the numerical simulation of a variety of time dependent phenomena. In particular, we have been focussing on **semi-implicit and semi-Lagrangian techniques** for fluid dynamics problems and on **exponential methods.**

**Semi-implicit and semi-Lagrangian techniques** are classical approaches to time discretization for a number of problems, including low Mach number fluid dynamics and plasma physics. Researchers at MOX have investigated their extension to DG an adaptive space discretizations.

**Exponential methods **are based on classical representation formulae for the solution of linear ODE systems, along with advanced numerical linear algebra methods for the computation of matrix exponentials. Their applications to nonlinear problems allow to increase accuracy remarkably. Their application to large scale scientific computing is quite recent and MOX researchers are investigating how to reduce the computational cost of these techniques.

People interested in our activities can have a look at our journal publications