Many differential equations of practical interest evolve on Lie groups or on manifolds acted
upon by Lie groups. The retention of Lie-group structure under discretization is often vital in …

Recently, there has been a great deal of interest in the construction of exponential
integrators. These integrators, as their name suggests, use the exponential function (and …

We present a family of Runge-Kutta type integration schemes of arbitrarily high order for
differential equations evolving on manifolds. We prove that any classical Runge-Kutta …

Abstract We construct generalized Runge-Kutta methods for integration of differential
equations evolving on a Lie group. The methods are using intrinsic operations on the group …

The subject matter of this paper is the solution of the linear differential equation y′= a (t) y, y
(0)= y 0, where y 0∈ G, a (.): R+→ g and g is a Lie algebra of the Lie group G. By building …

The integrating factor (IF) method for numerical integration of stiff nonlinear PDEs has the
disadvantage of producing large error coefficients when the linear term has large norm. We …

The first step in investigating the dynamics of a continuous time system described by a set of
ordinary differential equations is to integrate to obtain trajectories. In this paper, we convert …

In the last few decades the concepts of structure-preserving discretization, geometric
integration and compatible discretizations have emerged as subfields in the numerical …

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di
erential equations (ODEs) is undertaken. The goal of this review is to summarize the …

Numerical integration methods based on the Lie group theoretic geometrical approach are
applied to articulated multibody systems with rigid body displacements, belonging to the …