I thought that instead of the great number of precepts of which logic is composed, I would
have enough with the four following ones, provided that I made a firm and unalterable …

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …

We present new symmetric fourth and sixth-order symplectic partitioned Runge–Kutta and
Runge–Kutta–Nyström methods. We studied compositions using several extra stages …

This overview is devoted to splitting methods, a class of numerical integrators intended for
differential equations that can be subdivided into different problems easier to solve than the …

Geometric integration is the numerical integration of a differential equation, while preserving
one or more of its' geometric'properties exactly, ie to within round-off error. Many of these …

We provide a comprehensive survey of splitting and composition methods for the numerical
integration of ordinary differential equations (ODEs). Splitting methods constitute an …

B-series are a fundamental tool in practical and theoretical aspects of numerical integrators
for ordinary differential equations. A composition law for B-series permits an elegant …

In this paper we analyse numerical integration methods applied to differential equations
which are separable in solvable parts. These methods are compositions of flows associated …

A class of higher order numerical methods for advancing the charged particles in a general
electromagnetic field is developed based on processing technique. By taking the volume …

We introduce a class of fourth order symplectic algorithms that are ideal for doing long time
integration of gravitational few-body problems. These algorithms have only positive time …