Numerical comparisons among some methods for Hamiltonian problems

TL;DR

This paper compares various numerical methods, including energy-preserving integrators and symplectic methods, for solving Hamiltonian problems using both constant and variable step sizes.

Contribution

It provides a comparative analysis of newly defined energy-preserving integrators against symplectic methods for Hamiltonian problems.

Findings

Energy-preserving integrators perform well with variable steps.

Symplectic methods are effective for Hamiltonian problems.

Numerical tests highlight differences in accuracy and stability.

Abstract

We report a few sumerical tests comparing some newly defined energy-preserving integrators and symplectic methods, using either constant and variable stepsize.