norges teknisk-naturvitenskapelige universitet Preserving multiple first integrals by discrete gradients

preprint numerics no. 11/2010 norwegian university of science and technology trondheim, norway We consider systems of ordinary differential equations with known first in-tegrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary set of discrete gradients. Integrators which exactly conserve all the first integrals simultaneously are then defined. Two approaches are presented, one based on projection and one based on local coordinates, both allowing for integrators of arbitrary order of convergence. The methods are tested on the Kepler problem.