Line Integral Methods for Conservative Problems

Brugnano and Iavernaro deal with the numerical solution of differential problems within the framework of geometric integration, a branch of numerical analysis that aims to devise numerical methods able to reproduce, in the discrete solution, relevant geometric properties of the continuous vector field. Paramount among them are the so called constants of motion, they say, which are physical quantities that are conserved along the solution trajectories of a large set of differential systems named conservation problems. Their major emphasis is on Hamiltonian systems, but they also consider more general problems. Annotation c2016 Ringgold, Inc., Portland, OR (protoview.com)

Luigi Brugnano is a full professor of numerical analysis and chairman of the mathematics courses in the Department of Mathematics and Informatics at the University of Firenze. He is a member of several journal editorial boards. His research interests include matrix conditioning/preconditioning, parallel computing, computational fluid dynamics, numerical methods, iterative methods, geometric integration, and mathematical modeling and software.

Felice Iavernaro is an associate professor of numerical analysis in the Department of Mathematics at the University of Bari. His primary interests include the design and implementation of efficient methods for the numerical solution of differential equations, particularly for the simulation of dynamical systems with geometric properties.