Projection of Second Derivative Methods for Ordinary Differential Equations with Invariants

For the numerical solution of ordinary differential equations with some invariants, several efficient integrators have been introduced. For such problems with known invariants, we use explicit second derivative general linear methods with standard projection technique that, while preserving invariants of the problems as well, their low computational cost makes them more efficient than the existing conservative integrators. To show the capability and advantages of the proposed schemes, some numerical experiments are presented.