Line Integral Methods for Conservative Problems

This book deals with the numerical solution of differential problems within the framework of Geometric Integration, a branch of numerical analysis which aims to devise numerical methods able to reproduce, in the discrete solution, relevant geometric properties of the continuous vector field. Among them, a paramount role is played by the so called constants of motion, which are physical quantities that are conserved along the solution trajectories of a large set of differential systems, named Conservative Problems. In particular, the major emphasis will be on Hamiltonian systems, though more general problems will be also considered.