This self-contained book explains the numerical solution of differential equations within the
framework of geometric integration, a branch of numerical analysis that devises numerical …

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

We propose a modification of collocation methods extending the 'averaged vector field
method'to high order. These new integrators exactly preserve energy for Hamiltonian …

Energy-preserving Runge-Kutta methods Page 1 ESAIM: M2AN 43 (2009) 645–649 ESAIM:
Mathematical Modelling and Numerical Analysis DOI: 10.1051/m2an/2009020 www.esaim-m2an.org …

We rigorously study a novel type of trigonometric Fourier collocation methods for solving
multi-frequency oscillatory second-order ordinary differential equations (ODEs) q^ ′ ′ (t)+ …

A general procedure for constructing conservative numerical integrators for time-dependent
partial differential equations is presented. In particular, linearly implicit methods preserving a …

We introduce a new family of symplectic integrators for canonical Hamiltonian systems. Each
method in the family depends on a real parameter α. When α=0 we obtain the classical …

In this paper, we focus our attention on deriving and analyzing an efficient energy-
preserving formula for the system of nonlinear oscillatory or highly oscillatory second-order …

In the last few decades, numerical simulation for nonlinear oscillators has received a great
deal of attention, and manyresearchers have been concerned with the design and analysis …

Recently, the symplectic exponentially-fitted methods for Hamiltonian systems with periodic
or oscillatory solutions have been attracting a lot of interest. As an alternative to them, in this …