  In this work, we develop a class of high-order multiderivative time
integration methods that is able to preserve certain functionals discretely.
Important ingredients are the recently developed
Hermite-Birkhoff-Predictor-Corrector methods and the technique of relaxation
for numerical methods of ODEs. We explain the algorithm in detail and show
numerical results for two- and three-derivative methods, comparing relaxed and
unrelaxed methods. The numerical results demonstrate that, at the slight cost
of the relaxation, an improved scheme is obtained.
