A New Class of Scaling Correction Methods

Abstract

When conventional integrators like Runge—Kutta-type algorithms are used, numerical errors can make an orbit deviate from a hypersurface determined by many constraints, which leads to unreliable numerical solutions. Scaling correction methods are a powerful tool to avoid this. We focus on their applications, and also develop a family of new velocity multiple scaling correction methods where scale factors only act on the related components of the integrated momenta. They can preserve exactly some first integrals of motion in discrete or continuous dynamical systems, so that rapid growth of roundoff or truncation errors is suppressed significantly.

$ \mathbb{C}P(2)$-multiplicative Hirzebruch genera and elliptic cohomology

“…Geometric integrators including manifold correction schemes [12] and symplectic integrators [13−14] that have good long-term behaviors are greatly superior to conventional integrators such as Runge-Kutta ones. In particular, the symplectic integrators can maintain the symplectic structure besides the energy integral.…”