This research group brings together researchers from different institutions in Spain (Universitat Jaume I, Universitat Politècnica de València, Universidad del País Vasco, Universidad de Valladolid, Universidad Carlos III de Madrid and BCAM) working on the field of geometric numerical integration of differential equations. By this we understand the design and analysis of numerical integrators that preserve by construction relevant qualitative properties of the continuous system. Our work covers a variety of goals and applications, ranging from the theoretical analysis of numerical integrators by algebraic and combinatorial techniques to numerical tests and actual simulations in relevant applications in Quantum Mechanics, Monte Carlo simulations, Celestial Mechanics, dynamical astronomy, optimization, etc.
We collect some of the topics we are currently addressing. All of them, in a way or another, deal with Geometric Numerical Integration (a terminology introduced by J.M. Sanz-Serna in 1997 and now internationally accepted) and splitting and composition methods.
We actively engage in the promotion of mathematics in general and of our research projects in particular. This is achieved, for example, by organizing regular series of general audience talks devoted to applications of mathematics (e.g. Ciclo Matemáticas y Sociedad en Castellón), by members of the team giving public lectures in different institutions, and by getting in touch with schools and university students at the early years of their grade (for instance, through the "Estudia i Investiga" program of the Universitat Jaume I).
Some activities in which members of the group are involved.