RUNGE-KUTTA METHODS FOR ORTHOGONAL AND ISOSPECTRAL FLOWS

Orthogonal and isospectral flows occur in many applications and they p ossess important invariants. However, a naive application of Runge-Kut ta methods is bound to render these invariants incorrectly. In this pa per we describe how to retain relevant invariants with Runge-Kutta met hods or, alternatively, incur an error in the rendition of the invaria nts which is significantly smaller than the overall numerical error.