Invariants preserving schemes based on explicit Runge–Kutta methods

Abstract

Numerical integration of ordinary differential equations with some invariants is considered. For such a purpose, certain projection methods have proved its high accuracy and efficiency. Unfortunately, however, sometimes they can exhibit instability. In this paper, a new, highly efficient projection method is proposed based on explicit Runge–Kutta methods. The key there is to employ the idea of the perturbed collocation method, which gives a unified way to incorporate scheme parameters for projection. Numerical experiments confirm the stability of the proposed method.