Affine-invariant projection methods for conservative integration of differential equations

Abstract

Numerical integrators which conserve invariants of original differential equations are called conservative integrators. While most of them are computationally expensive, a cheaper class is the projection methods, where conservation is realized by simple projections. However, such methods do not necessarily preserve affine invariance originally held in differential equations. In this study, we point out several affine-invariant projections and discuss how the affine invariance affects the quality of numerical solutions.