Minimal ℓ² norm discrete multiplier method

Abstract

We introduce the Minimal ℓ² Norm Discrete Multiplier Method (MN-DMM), an extension to the Discrete Multiplier Method where conservative finite difference schemes for dynamical systems with multiple conserved quantities are constructed procedurally. MN-DMM utilizes the right Moore-Penrose pseudoinverse of the discrete multiplier matrix to solve an underdetermined least-squares problem associated with the discrete multiplier conditions. We prove consistency and conservative properties of MN-DMM schemes and demonstrate their applicability on various problems including the planar restricted three-body problem, Lorenz system, and geodesic curves on Schwarzschild spacetime.