Explicit variable step-size and time-reversible integration

Abstract

In Huang and Leimkuhler [SIAM J. Sci. Comput. 18 (1997) 239–256], a variable step-size, semi-explicit variant of the explicit Störmer–Verlet method has been suggested for the time-reversible integration of Newton's equations of motion. Here we propose a fully explicit version of this approach applicable to explicit and symmetric integration methods for general time-reversible differential equations. This approach greatly simplifies the implementation of the method while providing a straightforward approach to higher-order reversible variable time-step integration. As applications, we discuss the variable step-size, time-reversible, and fully explicit integration of rigid body motion and the Kepler problem.